rescued from ultra 10
This commit is contained in:
robin
commit
9cee7bf9a8
28719
21255511to266511.txt
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28719
21255511to266511.txt
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47
CVS/Entries
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47
CVS/Entries
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|
||||
/21255511to266511.txt/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/back.gif/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/back.png/1.1.1.1/Sun Sep 18 11:11:38 2005//
|
||||
/bc.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
|
||||
/bc_man_page.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
|
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/blu_bullet_half.gif/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/calc_big_expon.bc/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/calc_big_expon.sh/1.1.1.1/Sun Sep 18 11:11:38 2005//
|
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/calc_big_num.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/calc_pi.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/cbe.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/cbe.sh/1.1.1.1/Sun Sep 18 11:11:38 2005//
|
||||
/checkd/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/create_rsa_key_set.png/1.1.1.1/Sun Sep 18 11:11:38 2005//
|
||||
/decode.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/dns.ppt/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/dns5.ppt/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/encode.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/encode_pub.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/files.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/find_d.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/find_d.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/find_phi.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/findd/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/gcd.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/generate_key.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/gt100k/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/hints_to_choosing_e.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/home.png/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/index.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/index.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/ln/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/ln2/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/maths.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/multiply.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/nlhtml.sed/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/pi.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/pow_digits/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/primes.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/primes.php/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/red_bullet_half.gif/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/review.gif/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/rsa_explanations_list.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/s/1.1.1.1/Sun Sep 18 11:11:38 2005//
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/searchd/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
/security.html/1.1.1.1/Sun Sep 18 11:11:38 2005//
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||||
D
|
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1
CVS/Repository
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1
CVS/Repository
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@ -0,0 +1 @@
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||||
rsa_workbench
|
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42
bc.html
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42
bc.html
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|
||||
<html>
|
||||
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
|
||||
<h1><title> BC - Bench Calculator </title></h1>
|
||||
<h1> BC - Bench Calculator </h1>
|
||||
|
||||
<h3>'bc' is a unix scripting tool that provides 'arbitary precision'
|
||||
mathematics.</h3>
|
||||
<p>
|
||||
It has a 'C' like syntax, supports recursion and allows
|
||||
variables and functions to
|
||||
be defined (although as the old bc only allowed single letter names
|
||||
I have carried on using this).
|
||||
</p>
|
||||
<p>
|
||||
An example of bc in action can be seen in <a href="pi.php"> calculate pi with arbitary precision </a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
In this project it is used via php scripts, to provide
|
||||
the mathematical muscle to deal with the very large numbers
|
||||
handled in RSA implementations.
|
||||
It is still a little slow, and the cpu load will
|
||||
regularly hit 95% as it calculates large exponents.
|
||||
Very large values may even cause the page to take minutes
|
||||
to complete calculations.
|
||||
However, the numbers used in RSA are so large that
|
||||
double precision, or floating point, is woefully inadequate.
|
||||
</p>
|
||||
Link to unix <a href="bc_man_page.html"> bc man page </a> converted to html.
|
||||
|
||||
|
||||
<br>
|
||||
<br>
|
||||
<center>
|
||||
<a href="javascript:history.back();">
|
||||
<img src=back.png align=center border=0> </a>
|
||||
</center>
|
||||
</body>
|
||||
</html>
|
||||
905
bc_man_page.html
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905
bc_man_page.html
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|
||||
Content-type: text/html
|
||||
|
||||
<HTML><HEAD><TITLE>Manpage of bc</TITLE>
|
||||
</HEAD><BODY>
|
||||
<H1>bc</H1>
|
||||
Section: User Commands (1)<BR>Updated: .<BR><A HREF="#index">Index</A>
|
||||
<A HREF="http://localhost/cgi-bin/man/man2html">Return to Main Contents</A><HR>
|
||||
|
||||
<A NAME="lbAB"> </A>
|
||||
<H2>NAME</H2>
|
||||
|
||||
bc - An arbitrary precision calculator language
|
||||
<A NAME="lbAC"> </A>
|
||||
<H2>SYNTAX</H2>
|
||||
|
||||
<B>bc</B> [ <B>-hlwsqv</B> ] [long-options] [ <I> file ...</I> ]
|
||||
<A NAME="lbAD"> </A>
|
||||
<H2>VERSION</H2>
|
||||
|
||||
This man page documents GNU bc version 1.06.
|
||||
<A NAME="lbAE"> </A>
|
||||
<H2>DESCRIPTION</H2>
|
||||
|
||||
<B>bc</B> is a language that supports arbitrary precision numbers
|
||||
with interactive execution of statements. There are some similarities
|
||||
in the syntax to the C programming language.
|
||||
A standard math library is available by command line option.
|
||||
If requested, the math library is defined before processing any files.
|
||||
<B>bc</B> starts by processing code from all the files listed
|
||||
on the command line in the order listed. After all files have been
|
||||
processed, <B>bc</B> reads from the standard input. All code is
|
||||
executed as it is read. (If a file contains a command to halt the
|
||||
processor, <B>bc</B> will never read from the standard input.)
|
||||
<P>
|
||||
|
||||
This version of <B>bc</B> contains several extensions beyond
|
||||
traditional <B>bc</B> implementations and the POSIX draft standard.
|
||||
Command line options can cause these extensions to print a warning
|
||||
or to be rejected. This
|
||||
document describes the language accepted by this processor.
|
||||
Extensions will be identified as such.
|
||||
<A NAME="lbAF"> </A>
|
||||
<H3>OPTIONS</H3>
|
||||
|
||||
<DL COMPACT>
|
||||
<DT>-h, --help<DD>
|
||||
Print the usage and exit.
|
||||
<DT>-i, --interactive<DD>
|
||||
Force interactive mode.
|
||||
<DT>-l, --mathlib<DD>
|
||||
Define the standard math library.
|
||||
<DT>-w, --warn<DD>
|
||||
Give warnings for extensions to POSIX <B>bc</B>.
|
||||
<DT>-s, --standard<DD>
|
||||
Process exactly the POSIX <B>bc</B> language.
|
||||
<DT>-q, --quiet<DD>
|
||||
Do not print the normal GNU bc welcome.
|
||||
<DT>-v, --version<DD>
|
||||
Print the version number and copyright and quit.
|
||||
</DL>
|
||||
<A NAME="lbAG"> </A>
|
||||
<H3>NUMBERS</H3>
|
||||
|
||||
The most basic element in <B>bc</B> is the number. Numbers are
|
||||
arbitrary precision numbers. This precision is both in the integer
|
||||
part and the fractional part. All numbers are represented internally
|
||||
in decimal and all computation is done in decimal. (This version
|
||||
truncates results from divide and multiply operations.) There are two
|
||||
attributes of numbers, the length and the scale. The length is the
|
||||
total number of significant decimal digits in a number and the scale
|
||||
is the total number of decimal digits after the decimal point. For
|
||||
example:
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD> .000001 has a length of 6 and scale of 6.
|
||||
1935.000 has a length of 7 and a scale of 3.
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
<A NAME="lbAH"> </A>
|
||||
<H3>VARIABLES</H3>
|
||||
|
||||
Numbers are stored in two types of variables, simple variables and
|
||||
arrays. Both simple variables and array variables are named. Names
|
||||
begin with a letter followed by any number of letters, digits and
|
||||
underscores. All letters must be lower case. (Full alpha-numeric
|
||||
names are an extension. In POSIX <B>bc</B> all names are a single
|
||||
lower case letter.) The type of variable is clear by the context
|
||||
because all array variable names will be followed by brackets ([]).
|
||||
<P>
|
||||
|
||||
There are four special variables, <B>scale, ibase, obase,</B> and
|
||||
<B>last</B>. <B>scale</B> defines how some operations use digits after the
|
||||
decimal point. The default value of <B>scale</B> is 0. <B>ibase</B>
|
||||
and <B>obase</B> define the conversion base for input and output
|
||||
numbers. The default for both input and output is base 10.
|
||||
<B>last</B> (an extension) is a variable that has the value of the last
|
||||
printed number. These will be discussed in further detail where
|
||||
appropriate. All of these variables may have values assigned to them
|
||||
as well as used in expressions.
|
||||
<A NAME="lbAI"> </A>
|
||||
<H3>COMMENTS</H3>
|
||||
|
||||
Comments in <B>bc</B> start with the characters <B>/*</B> and end with
|
||||
the characters <B>*/</B>. Comments may start anywhere and appear as a
|
||||
single space in the input. (This causes comments to delimit other
|
||||
input items. For example, a comment can not be found in the middle of
|
||||
a variable name.) Comments include any newlines (end of line) between
|
||||
the start and the end of the comment.
|
||||
<P>
|
||||
|
||||
To support the use of scripts for <B>bc</B>, a single line comment has been
|
||||
added as an extension. A single line comment starts at a <B>#</B>
|
||||
character and continues to the next end of the line. The end of line
|
||||
character is not part of the comment and is processed normally.
|
||||
<A NAME="lbAJ"> </A>
|
||||
<H3>EXPRESSIONS</H3>
|
||||
|
||||
The numbers are manipulated by expressions and statements. Since
|
||||
the language was designed to be interactive, statements and expressions
|
||||
are executed as soon as possible. There is no "main" program. Instead,
|
||||
code is executed as it is encountered. (Functions, discussed in
|
||||
detail later, are defined when encountered.)
|
||||
<P>
|
||||
|
||||
A simple expression is just a constant. <B>bc</B> converts constants
|
||||
into internal decimal numbers using the current input base, specified
|
||||
by the variable <B>ibase</B>. (There is an exception in functions.)
|
||||
The legal values of <B>ibase</B> are 2 through 16. Assigning a
|
||||
value outside this range to <B>ibase</B> will result in a value of 2
|
||||
or 16. Input numbers may contain the characters 0-9 and A-F. (Note:
|
||||
They must be capitals. Lower case letters are variable names.)
|
||||
Single digit numbers always have the value of the digit regardless of
|
||||
the value of <B>ibase</B>. (i.e. A = 10.) For multi-digit numbers,
|
||||
<B>bc</B> changes all input digits greater or equal to ibase to the
|
||||
value of <B>ibase</B>-1. This makes the number <B>FFF</B> always be
|
||||
the largest 3 digit number of the input base.
|
||||
<P>
|
||||
|
||||
Full expressions are similar to many other high level languages.
|
||||
Since there is only one kind of number, there are no rules for mixing
|
||||
types. Instead, there are rules on the scale of expressions. Every
|
||||
expression has a scale. This is derived from the scale of original
|
||||
numbers, the operation performed and in many cases, the value of the
|
||||
variable <B>scale</B>. Legal values of the variable <B>scale</B> are
|
||||
0 to the maximum number representable by a C integer.
|
||||
<P>
|
||||
|
||||
In the following descriptions of legal expressions, "expr" refers to a
|
||||
complete expression and "var" refers to a simple or an array variable.
|
||||
A simple variable is just a
|
||||
<DL COMPACT><DT><DD>
|
||||
<I>name</I>
|
||||
</DL>
|
||||
|
||||
and an array variable is specified as
|
||||
<DL COMPACT><DT><DD>
|
||||
<I>name</I>[<I>expr</I>]
|
||||
</DL>
|
||||
|
||||
Unless specifically
|
||||
mentioned the scale of the result is the maximum scale of the
|
||||
expressions involved.
|
||||
<DL COMPACT>
|
||||
<DT>- expr<DD>
|
||||
The result is the negation of the expression.
|
||||
<DT>++ var<DD>
|
||||
The variable is incremented by one and the new value is the result of
|
||||
the expression.
|
||||
<DT>-- var<DD>
|
||||
The variable
|
||||
is decremented by one and the new value is the result of the
|
||||
expression.
|
||||
<DT>var ++<DD>
|
||||
<BR> The result of the expression is the value of
|
||||
the variable and then the variable is incremented by one.
|
||||
<DT>var --<DD>
|
||||
The result of the expression is the value of the variable and then
|
||||
the variable is decremented by one.
|
||||
<DT>expr + expr<DD>
|
||||
The result of the expression is the sum of the two expressions.
|
||||
<DT>expr - expr<DD>
|
||||
The result of the expression is the difference of the two expressions.
|
||||
<DT>expr * expr<DD>
|
||||
The result of the expression is the product of the two expressions.
|
||||
<DT>expr / expr<DD>
|
||||
The result of the expression is the quotient of the two expressions.
|
||||
The scale of the result is the value of the variable <B>scale</B>.
|
||||
<DT>expr % expr<DD>
|
||||
The result of the expression is the "remainder" and it is computed in the
|
||||
following way. To compute a%b, first a/b is computed to <B>scale</B>
|
||||
digits. That result is used to compute a-(a/b)*b to the scale of the
|
||||
maximum of <B>scale</B>+scale(b) and scale(a). If <B>scale</B> is set
|
||||
to zero and both expressions are integers this expression is the
|
||||
integer remainder function.
|
||||
<DT>expr ^ expr<DD>
|
||||
The result of the expression is the value of the first raised to the
|
||||
second. The second expression must be an integer. (If the second
|
||||
expression is not an integer, a warning is generated and the
|
||||
expression is truncated to get an integer value.) The scale of the
|
||||
result is <B>scale</B> if the exponent is negative. If the exponent
|
||||
is positive the scale of the result is the minimum of the scale of the
|
||||
first expression times the value of the exponent and the maximum of
|
||||
<B>scale</B> and the scale of the first expression. (e.g. scale(a^b)
|
||||
= min(scale(a)*b, max( <B>scale,</B> scale(a))).) It should be noted
|
||||
that expr^0 will always return the value of 1.
|
||||
<DT>( expr )<DD>
|
||||
This alters the standard precedence to force the evaluation of the
|
||||
expression.
|
||||
<DT>var = expr<DD>
|
||||
The variable is assigned the value of the expression.
|
||||
<DT>var <op>= expr<DD>
|
||||
This is equivalent to "var = var <op> expr" with the exception that
|
||||
the "var" part is evaluated only once. This can make a difference if
|
||||
"var" is an array.
|
||||
</DL>
|
||||
<P>
|
||||
|
||||
<BR> Relational expressions are a special kind of expression
|
||||
that always evaluate to 0 or 1, 0 if the relation is false and 1 if
|
||||
the relation is true. These may appear in any legal expression.
|
||||
(POSIX bc requires that relational expressions are used only in if,
|
||||
while, and for statements and that only one relational test may be
|
||||
done in them.) The relational operators are
|
||||
<DL COMPACT>
|
||||
<DT>expr1 < expr2<DD>
|
||||
The result is 1 if expr1 is strictly less than expr2.
|
||||
<DT>expr1 <= expr2<DD>
|
||||
The result is 1 if expr1 is less than or equal to expr2.
|
||||
<DT>expr1 > expr2<DD>
|
||||
The result is 1 if expr1 is strictly greater than expr2.
|
||||
<DT>expr1 >= expr2<DD>
|
||||
The result is 1 if expr1 is greater than or equal to expr2.
|
||||
<DT>expr1 == expr2<DD>
|
||||
The result is 1 if expr1 is equal to expr2.
|
||||
<DT>expr1 != expr2<DD>
|
||||
The result is 1 if expr1 is not equal to expr2.
|
||||
</DL>
|
||||
<P>
|
||||
|
||||
Boolean operations are also legal. (POSIX <B>bc</B> does NOT have
|
||||
boolean operations). The result of all boolean operations are 0 and 1
|
||||
(for false and true) as in relational expressions. The boolean
|
||||
operators are:
|
||||
<DL COMPACT>
|
||||
<DT>!expr<DD>
|
||||
The result is 1 if expr is 0.
|
||||
<DT>expr && expr<DD>
|
||||
The result is 1 if both expressions are non-zero.
|
||||
<DT>expr || expr<DD>
|
||||
The result is 1 if either expression is non-zero.
|
||||
</DL>
|
||||
<P>
|
||||
|
||||
The expression precedence is as follows: (lowest to highest)
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD>|| operator, left associative
|
||||
&& operator, left associative
|
||||
! operator, nonassociative
|
||||
Relational operators, left associative
|
||||
Assignment operator, right associative
|
||||
+ and - operators, left associative
|
||||
*, / and % operators, left associative
|
||||
^ operator, right associative
|
||||
unary - operator, nonassociative
|
||||
++ and -- operators, nonassociative
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
|
||||
This precedence was chosen so that POSIX compliant <B>bc</B> programs
|
||||
will run correctly. This will cause the use of the relational and
|
||||
logical operators to have some unusual behavior when used with
|
||||
assignment expressions. Consider the expression:
|
||||
<DL COMPACT><DT><DD>
|
||||
a = 3 < 5
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
|
||||
Most C programmers would assume this would assign the result of "3 <
|
||||
5" (the value 1) to the variable "a". What this does in <B>bc</B> is
|
||||
assign the value 3 to the variable "a" and then compare 3 to 5. It is
|
||||
best to use parenthesis when using relational and logical operators
|
||||
with the assignment operators.
|
||||
<P>
|
||||
|
||||
There are a few more special expressions that are provided in <B>bc</B>.
|
||||
These have to do with user defined functions and standard
|
||||
functions. They all appear as "<I>name</I><B>(</B><I>parameters</I><B>)</B>".
|
||||
See the section on functions for user defined functions. The standard
|
||||
functions are:
|
||||
<DL COMPACT>
|
||||
<DT>length ( expression )<DD>
|
||||
The value of the length function is the number of significant digits in the
|
||||
expression.
|
||||
<DT>read ( )<DD>
|
||||
The read function (an extension) will read a number from the standard
|
||||
input, regardless of where the function occurs. Beware, this can
|
||||
cause problems with the mixing of data and program in the standard input.
|
||||
The best use for this function is in a previously written program that
|
||||
needs input from the user, but never allows program code to be input
|
||||
from the user. The value of the read function is the number read from
|
||||
the standard input using the current value of the variable
|
||||
<B>ibase</B> for the conversion base.
|
||||
<DT>scale ( expression )<DD>
|
||||
The value of the scale function is the number of digits after the decimal
|
||||
point in the expression.
|
||||
<DT>sqrt ( expression )<DD>
|
||||
The value of the sqrt function is the square root of the expression. If
|
||||
the expression is negative, a run time error is generated.
|
||||
</DL>
|
||||
<A NAME="lbAK"> </A>
|
||||
<H3>STATEMENTS</H3>
|
||||
|
||||
Statements (as in most algebraic languages) provide the sequencing of
|
||||
expression evaluation. In <B>bc</B> statements are executed "as soon
|
||||
as possible." Execution happens when a newline in encountered and
|
||||
there is one or more complete statements. Due to this immediate
|
||||
execution, newlines are very important in <B>bc</B>. In fact, both a
|
||||
semicolon and a newline are used as statement separators. An
|
||||
improperly placed newline will cause a syntax error. Because newlines
|
||||
are statement separators, it is possible to hide a newline by using
|
||||
the backslash character. The sequence "\<nl>", where <nl> is the
|
||||
newline appears to <B>bc</B> as whitespace instead of a newline. A
|
||||
statement list is a series of statements separated by semicolons and
|
||||
newlines. The following is a list of <B>bc</B> statements and what
|
||||
they do: (Things enclosed in brackets ([]) are optional parts of the
|
||||
statement.)
|
||||
<DL COMPACT>
|
||||
<DT>expression<DD>
|
||||
This statement does one of two things. If the expression starts with
|
||||
"<variable> <assignment> ...", it is considered to be an assignment
|
||||
statement. If the expression is not an assignment statement, the
|
||||
expression is evaluated and printed to the output. After the number
|
||||
is printed, a newline is printed. For example, "a=1" is an assignment
|
||||
statement and "(a=1)" is an expression that has an embedded
|
||||
assignment. All numbers that are printed are printed in the base
|
||||
specified by the variable <B>obase</B>. The legal values for <B>
|
||||
obase</B> are 2 through BC_BASE_MAX. (See the section LIMITS.) For
|
||||
bases 2 through 16, the usual method of writing numbers is used. For
|
||||
bases greater than 16, <B>bc</B> uses a multi-character digit method
|
||||
of printing the numbers where each higher base digit is printed as a
|
||||
base 10 number. The multi-character digits are separated by spaces.
|
||||
Each digit contains the number of characters required to represent the
|
||||
base ten value of "obase-1". Since numbers are of arbitrary
|
||||
precision, some numbers may not be printable on a single output line.
|
||||
These long numbers will be split across lines using the "\" as the
|
||||
last character on a line. The maximum number of characters printed
|
||||
per line is 70. Due to the interactive nature of <B>bc</B>, printing
|
||||
a number causes the side effect of assigning the printed value to the
|
||||
special variable <B>last</B>. This allows the user to recover the
|
||||
last value printed without having to retype the expression that
|
||||
printed the number. Assigning to <B>last</B> is legal and will
|
||||
overwrite the last printed value with the assigned value. The newly
|
||||
assigned value will remain until the next number is printed or another
|
||||
value is assigned to <B>last</B>. (Some installations may allow the
|
||||
use of a single period (.) which is not part of a number as a short
|
||||
hand notation for for <B>last</B>.)
|
||||
<DT>string<DD>
|
||||
The string is printed to the output. Strings start with a double quote
|
||||
character and contain all characters until the next double quote character.
|
||||
All characters are take literally, including any newline. No newline
|
||||
character is printed after the string.
|
||||
<DT><B>print</B> list<DD>
|
||||
The print statement (an extension) provides another method of output.
|
||||
The "list" is a list of strings and expressions separated by commas.
|
||||
Each string or expression is printed in the order of the list. No
|
||||
terminating newline is printed. Expressions are evaluated and their
|
||||
value is printed and assigned to the variable <B>last</B>. Strings
|
||||
in the print statement are printed to the output and may contain
|
||||
special characters. Special characters start with the backslash
|
||||
character (\). The special characters recognized by <B>bc</B> are
|
||||
"a" (alert or bell), "b" (backspace), "f" (form feed), "n" (newline),
|
||||
"r" (carriage return), "q" (double quote), "t" (tab), and "\" (backslash).
|
||||
Any other character following the backslash will be ignored.
|
||||
<DT>{ statement_list }<DD>
|
||||
This is the compound statement. It allows multiple statements to be
|
||||
grouped together for execution.
|
||||
<DT><B>if</B> ( expression ) statement1 [<B>else</B> statement2]<DD>
|
||||
The if statement evaluates the expression and executes statement1 or
|
||||
statement2 depending on the value of the expression. If the expression
|
||||
is non-zero, statement1 is executed. If statement2 is present and
|
||||
the value of the expression is 0, then statement2 is executed. (The
|
||||
else clause is an extension.)
|
||||
<DT><B>while</B> ( expression ) statement<DD>
|
||||
The while statement will execute the statement while the expression
|
||||
is non-zero. It evaluates the expression before each execution of
|
||||
the statement. Termination of the loop is caused by a zero
|
||||
expression value or the execution of a break statement.
|
||||
<DT><B>for</B> ( [expression1] ; [expression2] ; [expression3] ) statement<DD>
|
||||
The for statement controls repeated execution of the statement.
|
||||
Expression1 is evaluated before the loop. Expression2 is evaluated
|
||||
before each execution of the statement. If it is non-zero, the statement
|
||||
is evaluated. If it is zero, the loop is terminated. After each
|
||||
execution of the statement, expression3 is evaluated before the reevaluation
|
||||
of expression2. If expression1 or expression3 are missing, nothing is
|
||||
evaluated at the point they would be evaluated.
|
||||
If expression2 is missing, it is the same as substituting
|
||||
the value 1 for expression2. (The optional expressions are an
|
||||
extension. POSIX <B>bc</B> requires all three expressions.)
|
||||
The following is equivalent code for the for statement:
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD>expression1;
|
||||
while (expression2) {
|
||||
statement;
|
||||
expression3;
|
||||
}
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
<DT><B>break</B><DD>
|
||||
This statement causes a forced exit of the most recent enclosing while
|
||||
statement or for statement.
|
||||
<DT><B>continue</B><DD>
|
||||
The continue statement (an extension) causes the most recent enclosing
|
||||
for statement to start the next iteration.
|
||||
<DT><B>halt</B><DD>
|
||||
The halt statement (an extension) is an executed statement that causes
|
||||
the <B>bc</B> processor to quit only when it is executed. For example,
|
||||
"if (0 == 1) halt" will not cause <B>bc</B> to terminate because the halt is
|
||||
not executed.
|
||||
<DT><B>return</B><DD>
|
||||
Return the value 0 from a function. (See the section on functions.)
|
||||
<DT><B>return</B> ( expression )<DD>
|
||||
Return the value of the expression from a function. (See the section on
|
||||
functions.) As an extension, the parenthesis are not required.
|
||||
</DL>
|
||||
<A NAME="lbAL"> </A>
|
||||
<H3>PSEUDO STATEMENTS</H3>
|
||||
|
||||
These statements are not statements in the traditional sense. They are
|
||||
not executed statements. Their function is performed at "compile" time.
|
||||
<DL COMPACT>
|
||||
<DT><B>limits</B><DD>
|
||||
Print the local limits enforced by the local version of <B>bc</B>. This
|
||||
is an extension.
|
||||
<DT><B>quit</B><DD>
|
||||
When the quit statement is read, the <B>bc</B> processor
|
||||
is terminated, regardless of where the quit statement is found. For
|
||||
example, "if (0 == 1) quit" will cause <B>bc</B> to terminate.
|
||||
<DT><B>warranty</B><DD>
|
||||
Print a longer warranty notice. This is an extension.
|
||||
</DL>
|
||||
<A NAME="lbAM"> </A>
|
||||
<H3>FUNCTIONS</H3>
|
||||
|
||||
Functions provide a method of defining a computation that can be executed
|
||||
later. Functions in
|
||||
<B>bc</B>
|
||||
|
||||
always compute a value and return it to the caller. Function definitions
|
||||
are "dynamic" in the sense that a function is undefined until a definition
|
||||
is encountered in the input. That definition is then used until another
|
||||
definition function for the same name is encountered. The new definition
|
||||
then replaces the older definition. A function is defined as follows:
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD><B>define </B><I>name </I><B>( </B><I>parameters </I><B>) { </B><I>newline
|
||||
auto_list statement_list </I><B>}</B>
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
A function call is just an expression of the form
|
||||
"<I>name</I><B>(</B><I>parameters</I><B>)</B>".
|
||||
<P>
|
||||
|
||||
Parameters are numbers or arrays (an extension). In the function definition,
|
||||
zero or more parameters are defined by listing their names separated by
|
||||
commas. Numbers are only call by value parameters. Arrays are only
|
||||
call by variable. Arrays are specified in the parameter definition by
|
||||
the notation "<I>name</I><B>[]</B>". In the function call, actual parameters
|
||||
are full expressions for number parameters. The same notation is used
|
||||
for passing arrays as for defining array parameters. The named array is
|
||||
passed by variable to the function. Since function definitions are dynamic,
|
||||
parameter numbers and types are checked when a function is called. Any
|
||||
mismatch in number or types of parameters will cause a runtime error.
|
||||
A runtime error will also occur for the call to an undefined function.
|
||||
<P>
|
||||
|
||||
The <I>auto_list</I> is an optional list of variables that are for
|
||||
"local" use. The syntax of the auto list (if present) is "<B>auto
|
||||
</B><I>name</I>, ... ;". (The semicolon is optional.) Each <I>name</I> is
|
||||
the name of an auto variable. Arrays may be specified by using the
|
||||
same notation as used in parameters. These variables have their
|
||||
values pushed onto a stack at the start of the function. The
|
||||
variables are then initialized to zero and used throughout the
|
||||
execution of the function. At function exit, these variables are
|
||||
popped so that the original value (at the time of the function call)
|
||||
of these variables are restored. The parameters are really auto
|
||||
variables that are initialized to a value provided in the function
|
||||
call. Auto variables are different than traditional local variables
|
||||
because if function A calls function B, B may access function
|
||||
A's auto variables by just using the same name, unless function B has
|
||||
called them auto variables. Due to the fact that auto variables and
|
||||
parameters are pushed onto a stack, <B>bc</B> supports recursive functions.
|
||||
<P>
|
||||
|
||||
The function body is a list of <B>bc</B> statements. Again, statements
|
||||
are separated by semicolons or newlines. Return statements cause the
|
||||
termination of a function and the return of a value. There are two
|
||||
versions of the return statement. The first form, "<B>return</B>", returns
|
||||
the value 0 to the calling expression. The second form,
|
||||
"<B>return ( </B><I>expression </I><B>)</B>", computes the value of the expression
|
||||
and returns that value to the calling expression. There is an implied
|
||||
"<B>return (0)</B>" at the end of every function. This allows a function
|
||||
to terminate and return 0 without an explicit return statement.
|
||||
<P>
|
||||
|
||||
Functions also change the usage of the variable <B>ibase</B>. All
|
||||
constants in the function body will be converted using the value of
|
||||
<B>ibase</B> at the time of the function call. Changes of <B>ibase</B>
|
||||
will be ignored during the execution of the function except for the
|
||||
standard function <B>read</B>, which will always use the current value
|
||||
of <B>ibase</B> for conversion of numbers.
|
||||
<P>
|
||||
|
||||
As an extension, the format of the definition has been slightly relaxed.
|
||||
The standard requires the opening brace be on the same line as the
|
||||
<B>define</B> keyword and all other parts must be on following lines.
|
||||
This version of <B>bc</B> will allow any number of newlines before and
|
||||
after the opening brace of the function. For example, the following
|
||||
definitions are legal.
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD><TT>
|
||||
define d (n) { return (2*n); }
|
||||
define d (n)
|
||||
{ return (2*n); }
|
||||
</TT>
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
<A NAME="lbAN"> </A>
|
||||
<H3>MATH LIBRARY</H3>
|
||||
|
||||
If <B>bc</B> is invoked with the <B>-l</B> option, a math library is preloaded
|
||||
and the default scale is set to 20. The math functions will calculate their
|
||||
results to the scale set at the time of their call.
|
||||
The math library defines the following functions:
|
||||
<DL COMPACT>
|
||||
<DT>s (<I>x</I>)<DD>
|
||||
The sine of x, x is in radians.
|
||||
<DT>c (<I>x</I>)<DD>
|
||||
The cosine of x, x is in radians.
|
||||
<DT>a (<I>x</I>)<DD>
|
||||
The arctangent of x, arctangent returns radians.
|
||||
<DT>l (<I>x</I>)<DD>
|
||||
The natural logarithm of x.
|
||||
<DT>e (<I>x</I>)<DD>
|
||||
The exponential function of raising e to the value x.
|
||||
<DT>j (<I>n,x</I>)<DD>
|
||||
The bessel function of integer order n of x.
|
||||
</DL>
|
||||
<A NAME="lbAO"> </A>
|
||||
<H3>EXAMPLES</H3>
|
||||
|
||||
In /bin/sh, the following will assign the value of "pi" to the shell
|
||||
variable <B>pi</B>.
|
||||
<DL COMPACT><DT><DD>
|
||||
<TT>
|
||||
pi=$(echo "scale=10; 4*<A HREF="http://localhost/cgi-bin/man/man2html?1+a">a</A>(1)" | bc -l)
|
||||
</TT>
|
||||
</DL>
|
||||
|
||||
<P>
|
||||
|
||||
The following is the definition of the exponential function used in the
|
||||
math library. This function is written in POSIX <B>bc</B>.
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD><TT>
|
||||
scale = 20
|
||||
|
||||
/* Uses the fact that e^x = (e^(x/2))^2
|
||||
When x is small enough, we use the series:
|
||||
e^x = 1 + x + x^2/2! + x^3/3! + ...
|
||||
*/
|
||||
|
||||
define e(x) {
|
||||
auto a, d, e, f, i, m, v, z
|
||||
|
||||
/* Check the sign of x. */
|
||||
if (x<0) {
|
||||
m = 1
|
||||
x = -x
|
||||
}
|
||||
|
||||
/* Precondition x. */
|
||||
z = scale;
|
||||
scale = 4 + z + .44*x;
|
||||
while (x > 1) {
|
||||
f += 1;
|
||||
x /= 2;
|
||||
}
|
||||
|
||||
/* Initialize the variables. */
|
||||
v = 1+x
|
||||
a = x
|
||||
d = 1
|
||||
|
||||
for (i=2; 1; i++) {
|
||||
e = (a *= x) / (d *= i)
|
||||
if (e == 0) {
|
||||
if (f>0) while (f--) v = v*v;
|
||||
scale = z
|
||||
if (m) return (1/v);
|
||||
return (v/1);
|
||||
}
|
||||
v += e
|
||||
}
|
||||
}
|
||||
</TT>
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
|
||||
The following is code that uses the extended features of <B>bc</B> to
|
||||
implement a simple program for calculating checkbook balances. This
|
||||
program is best kept in a file so that it can be used many times
|
||||
without having to retype it at every use.
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD><TT>
|
||||
scale=2
|
||||
print "\nCheck book program!\n"
|
||||
print " Remember, deposits are negative transactions.\n"
|
||||
print " Exit by a 0 transaction.\n\n"
|
||||
|
||||
print "Initial balance? "; bal = read()
|
||||
bal /= 1
|
||||
print "\n"
|
||||
while (1) {
|
||||
"current balance = "; bal
|
||||
"transaction? "; trans = read()
|
||||
if (trans == 0) break;
|
||||
bal -= trans
|
||||
bal /= 1
|
||||
}
|
||||
quit
|
||||
</TT>
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
<P>
|
||||
|
||||
The following is the definition of the recursive factorial function.
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD><TT>
|
||||
define f (x) {
|
||||
if (x <= 1) return (1);
|
||||
return (f(x-1) * x);
|
||||
}
|
||||
</TT>
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
<A NAME="lbAP"> </A>
|
||||
<H3>READLINE AND LIBEDIT OPTIONS</H3>
|
||||
|
||||
GNU <B>bc</B> can be compiled (via a configure option) to use the GNU
|
||||
<B>readline</B> input editor library or the BSD <B>libedit</B> library.
|
||||
This allows the user to do editing of lines before sending them
|
||||
to <B>bc</B>. It also allows for a history of previous lines typed.
|
||||
When this option is selected, <B>bc</B> has one more special variable.
|
||||
This special variable, <B>history</B> is the number of lines of history
|
||||
retained. For <B>readline</B>, a value of -1 means that an unlimited
|
||||
number of history lines are retained. Setting the value of
|
||||
<B>history</B> to a positive number restricts the number of history
|
||||
lines to the number given. The value of 0 disables the history
|
||||
feature. The default value is 100. For more information, read the
|
||||
user manuals for the GNU <B>readline</B>, <B>history</B> and BSD <B>libedit</B>
|
||||
libraries. One can not enable both <B>readline</B> and <B>libedit</B>
|
||||
at the same time.
|
||||
<A NAME="lbAQ"> </A>
|
||||
<H3>DIFFERENCES</H3>
|
||||
|
||||
This version of
|
||||
<B>bc</B>
|
||||
|
||||
was implemented from the POSIX P1003.2/D11 draft and contains
|
||||
several differences and extensions relative to the draft and
|
||||
traditional implementations.
|
||||
It is not implemented in the traditional way using
|
||||
<I><A HREF="http://localhost/cgi-bin/man/man2html?1+dc">dc</A>(1).</I>
|
||||
|
||||
This version is a single process which parses and runs a byte code
|
||||
translation of the program. There is an "undocumented" option (-c)
|
||||
that causes the program to output the byte code to
|
||||
the standard output instead of running it. It was mainly used for
|
||||
debugging the parser and preparing the math library.
|
||||
<P>
|
||||
|
||||
A major source of differences is
|
||||
extensions, where a feature is extended to add more functionality and
|
||||
additions, where new features are added.
|
||||
The following is the list of differences and extensions.
|
||||
<DL COMPACT>
|
||||
<DT>LANG<DD>
|
||||
This version does not conform to the POSIX standard in the processing
|
||||
of the LANG environment variable and all environment variables starting
|
||||
with LC_.
|
||||
<DT>names<DD>
|
||||
Traditional and POSIX
|
||||
<B>bc</B>
|
||||
|
||||
have single letter names for functions, variables and arrays. They have
|
||||
been extended to be multi-character names that start with a letter and
|
||||
may contain letters, numbers and the underscore character.
|
||||
<DT>Strings<DD>
|
||||
Strings are not allowed to contain NUL characters. POSIX says all characters
|
||||
must be included in strings.
|
||||
<DT>last<DD>
|
||||
POSIX <B>bc</B> does not have a <B>last</B> variable. Some implementations
|
||||
of <B>bc</B> use the period (.) in a similar way.
|
||||
<DT>comparisons<DD>
|
||||
POSIX <B>bc</B> allows comparisons only in the if statement, the while
|
||||
statement, and the second expression of the for statement. Also, only
|
||||
one relational operation is allowed in each of those statements.
|
||||
<DT>if statement, else clause<DD>
|
||||
POSIX <B>bc</B> does not have an else clause.
|
||||
<DT>for statement<DD>
|
||||
POSIX <B>bc</B> requires all expressions to be present in the for statement.
|
||||
<DT>&&, ||, !<DD>
|
||||
POSIX <B>bc</B> does not have the logical operators.
|
||||
<DT>read function<DD>
|
||||
POSIX <B>bc</B> does not have a read function.
|
||||
<DT>print statement<DD>
|
||||
POSIX <B>bc</B> does not have a print statement .
|
||||
<DT>continue statement<DD>
|
||||
POSIX <B>bc</B> does not have a continue statement.
|
||||
<DT>return statement<DD>
|
||||
POSIX <B>bc</B> requires parentheses around the return expression.
|
||||
<DT>array parameters<DD>
|
||||
POSIX <B>bc</B> does not (currently) support array parameters in full.
|
||||
The POSIX grammar allows for arrays in function definitions, but does
|
||||
not provide a method to specify an array as an actual parameter. (This
|
||||
is most likely an oversight in the grammar.) Traditional implementations
|
||||
of <B>bc</B> have only call by value array parameters.
|
||||
<DT>function format<DD>
|
||||
POSIX <B>bc</B> requires the opening brace on the same line as the
|
||||
<B>define</B> key word and the <B>auto</B> statement on the next line.
|
||||
<DT>=+, =-, =*, =/, =%, =^<DD>
|
||||
POSIX <B>bc</B> does not require these "old style" assignment operators to
|
||||
be defined. This version may allow these "old style" assignments. Use
|
||||
the limits statement to see if the installed version supports them. If
|
||||
it does support the "old style" assignment operators, the statement
|
||||
"a =- 1" will decrement <B>a</B> by 1 instead of setting <B>a</B> to the
|
||||
value -1.
|
||||
<DT>spaces in numbers<DD>
|
||||
Other implementations of <B>bc</B> allow spaces in numbers. For example,
|
||||
"x=1 3" would assign the value 13 to the variable x. The same statement
|
||||
would cause a syntax error in this version of <B>bc</B>.
|
||||
<DT>errors and execution<DD>
|
||||
This implementation varies from other implementations in terms of what
|
||||
code will be executed when syntax and other errors are found in the
|
||||
program. If a syntax error is found in a function definition, error
|
||||
recovery tries to find the beginning of a statement and continue to
|
||||
parse the function. Once a syntax error is found in the function, the
|
||||
function will not be callable and becomes undefined.
|
||||
Syntax errors in the interactive execution code will invalidate the
|
||||
current execution block. The execution block is terminated by an
|
||||
end of line that appears after a complete sequence of statements.
|
||||
For example,
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD>a = 1
|
||||
b = 2
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
has two execution blocks and
|
||||
<PRE>
|
||||
<DL COMPACT><DT><DD>{ a = 1
|
||||
b = 2 }
|
||||
</DL>
|
||||
</PRE>
|
||||
|
||||
has one execution block. Any runtime error will terminate the execution
|
||||
of the current execution block. A runtime warning will not terminate the
|
||||
current execution block.
|
||||
<DT>Interrupts<DD>
|
||||
During an interactive session, the SIGINT signal (usually generated by
|
||||
the control-C character from the terminal) will cause execution of the
|
||||
current execution block to be interrupted. It will display a "runtime"
|
||||
error indicating which function was interrupted. After all runtime
|
||||
structures have been cleaned up, a message will be printed to notify the
|
||||
user that <B>bc</B> is ready for more input. All previously defined functions
|
||||
remain defined and the value of all non-auto variables are the value at
|
||||
the point of interruption. All auto variables and function parameters
|
||||
are removed during the
|
||||
clean up process. During a non-interactive
|
||||
session, the SIGINT signal will terminate the entire run of <B>bc</B>.
|
||||
</DL>
|
||||
<A NAME="lbAR"> </A>
|
||||
<H3>LIMITS</H3>
|
||||
|
||||
The following are the limits currently in place for this
|
||||
<B>bc</B>
|
||||
|
||||
processor. Some of them may have been changed by an installation.
|
||||
Use the limits statement to see the actual values.
|
||||
<DL COMPACT>
|
||||
<DT>BC_BASE_MAX<DD>
|
||||
The maximum output base is currently set at 999. The maximum input base
|
||||
is 16.
|
||||
<DT>BC_DIM_MAX<DD>
|
||||
This is currently an arbitrary limit of 65535 as distributed. Your
|
||||
installation may be different.
|
||||
<DT>BC_SCALE_MAX<DD>
|
||||
The number of digits after the decimal point is limited to INT_MAX digits.
|
||||
Also, the number of digits before the decimal point is limited to INT_MAX
|
||||
digits.
|
||||
<DT>BC_STRING_MAX<DD>
|
||||
The limit on the number of characters in a string is INT_MAX characters.
|
||||
<DT>exponent<DD>
|
||||
The value of the exponent in the raise operation (^) is limited to LONG_MAX.
|
||||
<DT>variable names<DD>
|
||||
The current limit on the number of unique names is 32767 for each of
|
||||
simple variables, arrays and functions.
|
||||
</DL>
|
||||
<A NAME="lbAS"> </A>
|
||||
<H2>ENVIRONMENT VARIABLES</H2>
|
||||
|
||||
The following environment variables are processed by <B>bc</B>:
|
||||
<DL COMPACT>
|
||||
<DT>POSIXLY_CORRECT<DD>
|
||||
This is the same as the <B>-s</B> option.
|
||||
<DT>BC_ENV_ARGS<DD>
|
||||
This is another mechanism to get arguments to <B>bc</B>. The
|
||||
format is the same as the command line arguments. These arguments
|
||||
are processed first, so any files listed in the environent arguments
|
||||
are processed before any command line argument files. This allows
|
||||
the user to set up "standard" options and files to be processed
|
||||
at every invocation of <B>bc</B>. The files in the environment
|
||||
variables would typically contain function definitions for functions
|
||||
the user wants defined every time <B>bc</B> is run.
|
||||
<DT>BC_LINE_LENGTH<DD>
|
||||
This should be an integer specifing the number of characters in an
|
||||
output line for numbers. This includes the backslash and newline characters
|
||||
for long numbers.
|
||||
</DL>
|
||||
<A NAME="lbAT"> </A>
|
||||
<H2>DIAGNOSTICS</H2>
|
||||
|
||||
If any file on the command line can not be opened, <B>bc</B> will report
|
||||
that the file is unavailable and terminate. Also, there are compile
|
||||
and run time diagnostics that should be self-explanatory.
|
||||
<A NAME="lbAU"> </A>
|
||||
<H2>BUGS</H2>
|
||||
|
||||
Error recovery is not very good yet.
|
||||
<P>
|
||||
|
||||
Email bug reports to
|
||||
<B><A HREF="mailto:bug-bc@gnu.org">bug-bc@gnu.org</A></B>.
|
||||
|
||||
Be sure to include the word ``bc'' somewhere in the ``Subject:'' field.
|
||||
<A NAME="lbAV"> </A>
|
||||
<H2>AUTHOR</H2>
|
||||
|
||||
<PRE>
|
||||
Philip A. Nelson
|
||||
<A HREF="mailto:philnelson@acm.org">philnelson@acm.org</A>
|
||||
</PRE>
|
||||
|
||||
<A NAME="lbAW"> </A>
|
||||
<H2>ACKNOWLEDGEMENTS</H2>
|
||||
|
||||
The author would like to thank Steve Sommars (<A HREF="mailto:Steve.Sommars@att.com">Steve.Sommars@att.com</A>) for
|
||||
his extensive help in testing the implementation. Many great suggestions
|
||||
were given. This is a much better product due to his involvement.
|
||||
<P>
|
||||
|
||||
<HR>
|
||||
<A NAME="index"> </A><H2>Index</H2>
|
||||
<DL>
|
||||
<DT><A HREF="#lbAB">NAME</A><DD>
|
||||
<DT><A HREF="#lbAC">SYNTAX</A><DD>
|
||||
<DT><A HREF="#lbAD">VERSION</A><DD>
|
||||
<DT><A HREF="#lbAE">DESCRIPTION</A><DD>
|
||||
<DL>
|
||||
<DT><A HREF="#lbAF">OPTIONS</A><DD>
|
||||
<DT><A HREF="#lbAG">NUMBERS</A><DD>
|
||||
<DT><A HREF="#lbAH">VARIABLES</A><DD>
|
||||
<DT><A HREF="#lbAI">COMMENTS</A><DD>
|
||||
<DT><A HREF="#lbAJ">EXPRESSIONS</A><DD>
|
||||
<DT><A HREF="#lbAK">STATEMENTS</A><DD>
|
||||
<DT><A HREF="#lbAL">PSEUDO STATEMENTS</A><DD>
|
||||
<DT><A HREF="#lbAM">FUNCTIONS</A><DD>
|
||||
<DT><A HREF="#lbAN">MATH LIBRARY</A><DD>
|
||||
<DT><A HREF="#lbAO">EXAMPLES</A><DD>
|
||||
<DT><A HREF="#lbAP">READLINE AND LIBEDIT OPTIONS</A><DD>
|
||||
<DT><A HREF="#lbAQ">DIFFERENCES</A><DD>
|
||||
<DT><A HREF="#lbAR">LIMITS</A><DD>
|
||||
</DL>
|
||||
<DT><A HREF="#lbAS">ENVIRONMENT VARIABLES</A><DD>
|
||||
<DT><A HREF="#lbAT">DIAGNOSTICS</A><DD>
|
||||
<DT><A HREF="#lbAU">BUGS</A><DD>
|
||||
<DT><A HREF="#lbAV">AUTHOR</A><DD>
|
||||
<DT><A HREF="#lbAW">ACKNOWLEDGEMENTS</A><DD>
|
||||
</DL>
|
||||
<HR>
|
||||
This document was created by
|
||||
<A HREF="http://localhost/cgi-bin/man/man2html">man2html</A>,
|
||||
using the manual pages.<BR>
|
||||
Time: 21:31:33 GMT, March 20, 2004
|
||||
</BODY>
|
||||
</HTML>
|
||||
BIN
blu_bullet_half.gif
Normal file
BIN
blu_bullet_half.gif
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 193 B |
44
calc_big_expon.bc
Normal file
44
calc_big_expon.bc
Normal file
@ -0,0 +1,44 @@
|
||||
|
||||
|
||||
# recursive routine to calculate c^d%n
|
||||
# by reaking it down. Works only where
|
||||
# d is a power of 2.
|
||||
#
|
||||
define x ( c,d,n) {
|
||||
#-1; d; -1;
|
||||
if ( d == 1 ) return (c^d%n);
|
||||
return x(c^2,d/2,n)%n;
|
||||
}
|
||||
|
||||
r = 1;
|
||||
|
||||
# recursive routine to break d into powers of 2
|
||||
# and then to collect multiply the results
|
||||
# of the 2^n exponents.
|
||||
#
|
||||
define t(c,d,n) {
|
||||
auto i
|
||||
i = 0;
|
||||
|
||||
# find biggest power of 2 left in exponentiation
|
||||
#
|
||||
while(d >= (2^i)) { i = i+1; }
|
||||
|
||||
#
|
||||
# subtract from exponent
|
||||
#
|
||||
d = (d - (2^(i-1)));
|
||||
|
||||
|
||||
if (d>0) {
|
||||
r=(r*x(c,2^(i-1),n))%n; # calculate this large exponentiation
|
||||
t(c,d,n); # recurse with new d value
|
||||
return (2^(i-1));
|
||||
}
|
||||
if (d == 0) {
|
||||
r = (r*x(c,2^(i-1),n))%n; # last one
|
||||
return (2^(i-1));
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
16
calc_big_expon.sh
Executable file
16
calc_big_expon.sh
Executable file
@ -0,0 +1,16 @@
|
||||
#!/bin/bash
|
||||
|
||||
# Calculate large exponent
|
||||
# $1 = c $2 = d $3 = n
|
||||
#
|
||||
# calculate c^d%n
|
||||
date=`date | sed 's\:\_\g' | sed 's\ \_\g'`
|
||||
# create a bc script to calculate this.
|
||||
# php5 is sopposed to have bc embedded...
|
||||
#
|
||||
cat calc_big_expon.bc > calc_big_expon.$$.$date.bc
|
||||
|
||||
echo "t($1,$2,$3)" >> calc_big_expon.$$.$date.bc
|
||||
echo "r;" >> calc_big_expon.$$.$date.bc
|
||||
bc < calc_big_expon.$$.$date.bc | tail -1
|
||||
rm -rf calc_big_expon.$$.$date.bc
|
||||
17
calc_big_num.php
Normal file
17
calc_big_num.php
Normal file
@ -0,0 +1,17 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<h1> The Numbers </h1>
|
||||
<?
|
||||
echo " p $p q $q";
|
||||
$big_num = `echo $p^$q | bc | sed -f /var/www/html/rsa/nlhtml.sed `;
|
||||
//$big_num = `echo $p^$q | bc | sed -f /home/robin/scripts/nlhtml.sed `;
|
||||
//$big_num = `echo $p^$q | bc`;
|
||||
|
||||
printf("<p> <h2> the big number </h2> %s ",$big_num);
|
||||
printf(" <h2> which is the result of %s^%s </h2> \n", $p,$q);
|
||||
?>
|
||||
<p>
|
||||
<a href="javascript:history.back();"> <img src=back.gif align=center border=0> </a>
|
||||
</p>
|
||||
</body>
|
||||
</html>
|
||||
27
calc_pi.php
Normal file
27
calc_pi.php
Normal file
@ -0,0 +1,27 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<h1> PI - calculated to required precision </h1>
|
||||
<?
|
||||
|
||||
if ( $precision < 1 ) { $precision = 100; }
|
||||
|
||||
$date = `date`;
|
||||
printf("<p> Start Time == %s </p>\n",$date);
|
||||
$big_num = `echo 'scale=$precision; a(1)*4' | bc -l | sed -f ./nlhtml.sed `;
|
||||
printf("<p> <h2> Pi is approximately </h2> %s ",$big_num);
|
||||
printf(" <h2> which is the result of %d decimal places </h2> \n", $precision);
|
||||
|
||||
$date = `date`;
|
||||
printf(" <p>End Time == %s </p>\n",$date);
|
||||
?>
|
||||
<p>
|
||||
|
||||
<center>
|
||||
<a href="index.php" border=0> <img src="home.png" border=0> </a>
|
||||
</center>
|
||||
|
||||
|
||||
<center>
|
||||
<a href="javascript:history.back();">
|
||||
<img src=back.png align=center border=0> </a>
|
||||
</center>
|
||||
28
cbe.php
Normal file
28
cbe.php
Normal file
@ -0,0 +1,28 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<?
|
||||
echo "arggggh why wont you call this script $m $e $n<p>";
|
||||
echo `echo " a(1)*4" | bc -l `;
|
||||
echo "A<p>";
|
||||
$ccc = `./cbe.sh $m $e $n`;
|
||||
echo "B<p>";
|
||||
echo $ccc;
|
||||
$ln2 = `./ln2 5623765365325`;
|
||||
echo "C<p>";
|
||||
echo $ln2;
|
||||
echo "D<p>";
|
||||
// this is due to php safe mode. the paramters are passed as the first arg. God dag yxe skaft !
|
||||
$ccc = system("./cbe.sh A$mB$eC$nD");
|
||||
echo "E $ccc <p>";
|
||||
$e = 1233;
|
||||
$m = 177;
|
||||
$n = 9999;
|
||||
$ddd = system("./cbe.sh 'A $m B $e C $n D'");
|
||||
echo "F $ddd <p>";
|
||||
|
||||
$dddd = `./cbe.sh 'A $m B $e C $n D'`;
|
||||
echo "G $dddd <p>";
|
||||
|
||||
?>
|
||||
</body>
|
||||
</html>
|
||||
46
cbe.sh
Executable file
46
cbe.sh
Executable file
@ -0,0 +1,46 @@
|
||||
#!/bin/bash
|
||||
|
||||
# Calculate large exponent
|
||||
|
||||
# php in 'safe mode' (god dag yx skaft)
|
||||
# passes the parameters sent in one string
|
||||
# turning off safe mode in the php.ini file
|
||||
# does not seem to change this behaviour.
|
||||
|
||||
# to overcome this sed will extract the variables
|
||||
#echo $1
|
||||
#
|
||||
c=`echo $1 | sed 's/.*A \([0-9]*\) B.*/\1/'`
|
||||
d=`echo $1 | sed 's/.*B \([0-9]*\) C.*/\1/'`
|
||||
n=`echo $1 | sed 's/.*C \([0-9]*\) D.*/\1/'`
|
||||
|
||||
args=`echo "<p> c " $c " d " $d " n " $n "</p>"`
|
||||
|
||||
#
|
||||
# calculate c^d%n
|
||||
|
||||
date=`date | sed 's\:\_\g' | sed 's\ \_\g'`
|
||||
|
||||
#echo $date
|
||||
|
||||
# create a bc script to calculate this.
|
||||
# php5 is sopposed to have bc embedded...
|
||||
#
|
||||
cat calc_big_expon.bc > calc_big_expon.$$.$date.bc
|
||||
|
||||
#echo " calc_big_expon.bc > calc_big_expon.$$.$date.bc ";
|
||||
|
||||
echo "r=1;" >> calc_big_expon.$$.$date.bc
|
||||
echo "t($c,$d,$n);" >> calc_big_expon.$$.$date.bc
|
||||
echo "r;" >> calc_big_expon.$$.$date.bc
|
||||
|
||||
#echo "invoking bc "
|
||||
#more calc_big_expon.$$.$date.bc
|
||||
#bc < calc_big_expon.$$.$date.bc
|
||||
#echo "bc invoked "
|
||||
|
||||
#ls -l calc_big_expon.$$.$date.bc
|
||||
result=`bc < calc_big_expon.$$.$date.bc | tail -1`
|
||||
#echo $args $result
|
||||
echo $result
|
||||
rm -rf calc_big_expon.$$.$date.bc
|
||||
16
checkd
Executable file
16
checkd
Executable file
@ -0,0 +1,16 @@
|
||||
#!/bin/bash
|
||||
|
||||
# R.P. Clark : 02APR2004
|
||||
#
|
||||
# Takes three args
|
||||
# $1 d
|
||||
# $2 e
|
||||
# $3 phi
|
||||
|
||||
# returns d.e % phi, which if
|
||||
# 1 satisfies the criteria for being a
|
||||
# private key..
|
||||
|
||||
|
||||
echo " ( $1 * $2 ) % $3 " | bc
|
||||
|
||||
BIN
create_rsa_key_set.png
Normal file
BIN
create_rsa_key_set.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 3.6 KiB |
69
decode.php
Normal file
69
decode.php
Normal file
@ -0,0 +1,69 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<h1> Encode integer 'm' </h1>
|
||||
<?
|
||||
echo "<h1> Decodes the ciphered integer using the secret 'd' key : m = c^d mod n. </h1>\n";
|
||||
|
||||
//echo "d == $d <p>";
|
||||
//echo "c == $c <p>";
|
||||
//echo "digits = $digits<p>";
|
||||
//echo "\n\n\n\n\n";
|
||||
//$gt100k = `./gt100k $digits`;
|
||||
//if ($gt100k != 1)
|
||||
//echo "<h3>c^d == </h3>";
|
||||
|
||||
|
||||
// check here that the exponentiation can actually be displayed
|
||||
// and use the recursive algorithms if it cannot
|
||||
// along with a warning about the length of time it could take.
|
||||
$digits = `./pow_digits $c $d `;
|
||||
$gt100_k = `./gt100k $digits`;
|
||||
//echo "./gt100k $digits";
|
||||
//echo " gt100_k == $gt100_k";
|
||||
|
||||
$date = `date`;
|
||||
printf("<p> Start Time == %s </p>\n",$date);
|
||||
if ($gt100_k != 1) {
|
||||
echo " <h3> The predicted number of digits from the exponentiation is less than 100,000. </h3></h3>It can therefore be shown in full </h3><p>";
|
||||
$c_to_d = `echo " $c ^ $d " | bc | sed -f ./nlhtml.sed `;
|
||||
echo $c_to_d;
|
||||
`echo " $c ^ $d " | bc | sed -f ./nlhtml.sed `;
|
||||
echo " % $n <p>";
|
||||
echo "<h3> this gives the 'in clear' result </h3>";
|
||||
$clear = `echo " ( $c ^ $d ) % $n " | bc | sed -f ./nlhtml.sed `;
|
||||
echo $clear;
|
||||
}
|
||||
else {
|
||||
echo "<h3> The number of digits produced by the exponentiation of c^d is greater than 100,0000 </h3>";
|
||||
|
||||
echo "<h3> The resursive (see <a href=\"maths.html\"> recursive exponentiation break down </a>) routines will be applied instead to calculate c^d%n </h3>";
|
||||
$clear = `./cbe.sh 'A $c B $d C $n D'`; // php is very nasty about sending multiple args to scripts
|
||||
echo "<h3> this gives the 'in clear' result </h3>";
|
||||
echo $clear;
|
||||
|
||||
}
|
||||
$date = `date`;
|
||||
printf("<p> End Time == %s</p> \n",$date);
|
||||
printf("<form enctype=\"multipart/form-data\" method=\"post\"
|
||||
action=\"encode_pub.php#KEYS\">");
|
||||
?>
|
||||
|
||||
<input type="hidden" name=d value=<? echo $d ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
<input type="hidden" name=c value=<? echo $c ?>>
|
||||
<input type="hidden" name=m value=<? echo $m ?>>
|
||||
<input type="hidden" name=digits value=<? echo $digits ?>>
|
||||
<table>
|
||||
<tr>
|
||||
<td>
|
||||
<input type="submit" name="submit" value="Next">
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
53
encode.php
Normal file
53
encode.php
Normal file
@ -0,0 +1,53 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<h1> Encode integer 'm' </h1>
|
||||
<?
|
||||
echo "<h1> Computes the cipher text c = m^e mod n.</h1>";
|
||||
echo "<h3> $m^$e%$n </h3>";
|
||||
$digits = `./pow_digits $m $e`;
|
||||
$gt100_k = `./gt100k $digits`;
|
||||
echo "digits",$digits;
|
||||
echo "<h3>m^e for this equation will produce a number with approx $digits digits</h3>";
|
||||
|
||||
|
||||
if ( $gt100_k != 1 ) {
|
||||
$m_to_e = `echo " $m ^ $e " | bc | sed -f ./nlhtml.sed `;
|
||||
echo $m_to_e;
|
||||
echo " % $n <p>";
|
||||
echo "<h3> this gives the'public key encoded' cipher result </h3>";
|
||||
echo "</p>";
|
||||
$c = `echo " ( $m ^ $e ) % $n " | bc`;
|
||||
echo $c;
|
||||
}
|
||||
else {
|
||||
echo "<h3> The number of digits produced by the exponentiation of m^e is greater than 100,0000 </h3>";
|
||||
echo "<h3> The resursive (see <a href=\"maths.html\"> recursive exponentiation break down </a>) ";
|
||||
echo "routines will be applied instead of direct implementation to calculate m^e%n </h3>";
|
||||
$c = `./cbe.sh 'A $m B $e C $n D'`; // php is very nasty about sending multiple args to scripts
|
||||
echo "<h3> this gives the 'public key encoded' cipher result </h3>";
|
||||
echo $c;
|
||||
|
||||
}
|
||||
|
||||
printf("<form enctype=\"multipart/form-data\" method=\"post\"
|
||||
action=\"encode_pub.php#DECODE\">");
|
||||
?>
|
||||
|
||||
<input type="hidden" name=d value=<? echo $d ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
<input type="hidden" name=c value=<? echo $c ?>>
|
||||
<input type="hidden" name=m value=<? echo $m ?>>
|
||||
<table>
|
||||
<tr>
|
||||
<td>
|
||||
<input type="submit" name="submit" value="Next">
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
183
encode_pub.php
Normal file
183
encode_pub.php
Normal file
@ -0,0 +1,183 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
<title> RSA Interactive Simulator : Encoding data with the public Key </title>
|
||||
|
||||
<h1> RSA Interactive Simulator / Work Bench : Encoding data with the public Key </h1>
|
||||
|
||||
<?
|
||||
|
||||
If ( $n < 1 || $e < 1 || $d < 1 ) {
|
||||
|
||||
printf("<h2> Error, you have got to this page without defining all of the RSA keys</h2>");
|
||||
printf("<h2> You must go back and generate a full RSA key </h2>");
|
||||
printf("<a href=\"generate_key.php\"><img src=\"create_rsa_key_set.png\" border=0></a>");
|
||||
|
||||
}
|
||||
else {
|
||||
?>
|
||||
|
||||
<h3> Here a user is encoding data to send to third party which
|
||||
has published a public key. The user
|
||||
takes the public key, and encodes the message. Only
|
||||
the third party can decode the message, using its private key
|
||||
</h3>
|
||||
|
||||
<p>
|
||||
The encoding is simply performed by taking the number to be encrypted
|
||||
to the power of e, and then applying the modulus for n (i.e. p times q).
|
||||
</p>
|
||||
|
||||
<A name="KEYS">
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="encode.php">
|
||||
|
||||
<strong>Encode Data using the following key set</strong>
|
||||
|
||||
|
||||
<table border=2>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>Modulus (used by both public and private key) </strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="n" size=120 value="<? echo $n ?>">
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong> e - the public key </strong>
|
||||
</td>
|
||||
<td width>
|
||||
<input type=text name="e" size=120 value="<? echo $e ?>">
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong> m - the number to encrypt </strong>
|
||||
</td>
|
||||
<td width>
|
||||
<input type=text name="m" size=120 value="<? echo $m ?>">
|
||||
</td>
|
||||
</tr>
|
||||
<input type="hidden" name=d value=<? echo $d ?>>
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<tr><td><input type="submit" name="submit" value="Encode"> </td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
</table>
|
||||
</form>
|
||||
|
||||
<? if ( $m ) { ?>
|
||||
|
||||
<br> <br>
|
||||
<hr>
|
||||
<h2> DECODE : Decode with your secret key (n,d) </h2>
|
||||
<A name="DECODE">
|
||||
<hr>
|
||||
|
||||
<? $digits = `./pow_digits $c $d ` ?>
|
||||
|
||||
<p>
|
||||
The decoding process calculates the value of c ^ d % n.
|
||||
</p>
|
||||
<p>
|
||||
The value c ^ d <i> ( <? printf(" %s ^ %s ",$c,$d); ?> ) </i>
|
||||
in this case
|
||||
would produce a number with approx
|
||||
<b> <? echo $digits ?> </b> decimal digits !
|
||||
</p>
|
||||
|
||||
<? $gt100k = `./gt100k $digits`;
|
||||
if ( $gt100k == 1 ) { ?>
|
||||
<p>
|
||||
Obviously this is unacceptable and would cause memory and processing time problems.
|
||||
Mathematical techniques for algebraically breaking this problem into
|
||||
smaller pieces, are described <a href="maths.html"> here </a>
|
||||
</p>
|
||||
<p> Note that for this very large value,
|
||||
the bc script may take up to
|
||||
<? $mins_est = (($digits/1000000) * ($digits/1000000)) * 1.5;
|
||||
printf("%2.2f",$mins_est); ?>
|
||||
minutes to finish this calculation.
|
||||
</P>
|
||||
<? } ?>
|
||||
<br>
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="decode.php">
|
||||
|
||||
<strong>De-code Data using the key set</strong>
|
||||
|
||||
|
||||
<p> Note that to encode with the private key, you may type a value in for 'c' and press decode. Cut and paste the 'in clear' value into the m of encode to verify correct reverse operation (de-coding with the private key ).
|
||||
</p>
|
||||
<p> The purpose of encoding with the private key is one of verifying identity (i.e. anyone can decode it using your published public key, but it is stamped with your RSA identity)</p>
|
||||
<table border=2>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>Modulus (used by both public and private key) </strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="n" size=120 value="<? echo $n ?>">
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>d - the private key</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="d" size=120 value="<? echo $d ?>" >
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong> c - the number to de-crypt </strong>
|
||||
</td>
|
||||
<td width>
|
||||
<input type=text name="c" size=120 value="<? echo $c ?>">
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
|
||||
|
||||
<input type="hidden" name=digits value=<? echo $digits ?>
|
||||
<input type="hidden" name=m value=<? echo $m ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<tr><td><input type="submit" name="submit" value="Decode"> </td></tr>
|
||||
</table>
|
||||
|
||||
</form>
|
||||
|
||||
<? } // if to hide decode menu until a value has been coded
|
||||
?>
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="generate_key.php">
|
||||
<input type="hidden" name=digits value=<? echo $digits ?>
|
||||
<input type="hidden" name=m value=<? echo $m ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
<input type="hidden" name=d value=<? echo $d ?>>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="submit" name="submit" value="Back to Generate Key">
|
||||
</form>
|
||||
|
||||
<? } // all RSA key components defined
|
||||
?>
|
||||
<center> <a href="index.php" border=0> <img src="home.png" border=0> </a> </center>
|
||||
</body>
|
||||
</html>
|
||||
50
files.html
Normal file
50
files.html
Normal file
@ -0,0 +1,50 @@
|
||||
<html>
|
||||
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
|
||||
<title> RSA workbench assignment - Files used with brief description </title>
|
||||
|
||||
<h1> Files used to implement this assignment </h1>
|
||||
|
||||
|
||||
<br><img src="red_bullet_half.gif"> bc.html <img src="blu_bullet_half.gif"> A brief description of the bc scripting language.
|
||||
<br><img src="red_bullet_half.gif"> bc_man_page.html <img src="blu_bullet_half.gif"> The unix man page for the bc scripting language
|
||||
<br><img src="red_bullet_half.gif"> calc_big_expon.bc <img src="blu_bullet_half.gif"> source code for the 'residue' optimised c^d%n equation script.
|
||||
<br><img src="red_bullet_half.gif"> calc_pi.php <img src="blu_bullet_half.gif"> Calculate pi to arbitary precision.
|
||||
<br><img src="red_bullet_half.gif"> cbe.sh <img src="blu_bullet_half.gif"> Script to take parameters from php to create and run a bc script based on the source code from calc_big_expon.bc.
|
||||
<br><img src="red_bullet_half.gif"> checkd <img src="blu_bullet_half.gif"> Script to check that a value of d, is valid aginst known values of phi and e.
|
||||
<br><img src="red_bullet_half.gif"> decode.php <img src="blu_bullet_half.gif"> PHP page to decode a value encoded with a public key -or- to encode a value using the private key.
|
||||
<br><img src="red_bullet_half.gif"> encode.php <img src="blu_bullet_half.gif"> PHP page to decode a value encoded with a private key -or- to encode a value using the public key.
|
||||
<br><img src="red_bullet_half.gif"> encode_pub.php <img src="blu_bullet_half.gif"> PHP page to guide a user into encrypting a value with a newly created RSA keyset.
|
||||
<br><img src="red_bullet_half.gif"> findd <img src="blu_bullet_half.gif"> Script to find a suitable value of d.
|
||||
<br><img src="red_bullet_half.gif"> find_d.html <img src="blu_bullet_half.gif"> Description of the algorithm used to calculate the private key value 'd'
|
||||
<br><img src="red_bullet_half.gif"> find_d.php <img src="blu_bullet_half.gif"> PHP page that calls the bc scripts to iterate to find a correct value for d.
|
||||
<br><img src="red_bullet_half.gif"> find_phi.php <img src="blu_bullet_half.gif"> PHP page to find the value for phi.
|
||||
<br><img src="red_bullet_half.gif"> gcd.php <img src="blu_bullet_half.gif"> Greatest common denominator PHP page, calls a BC script, which recursively finds the gcd.
|
||||
<br><img src="red_bullet_half.gif"> generate_key.php <img src="blu_bullet_half.gif"> A large PHP page which guides the user through all stage of creating an RSA key set.
|
||||
<br><img src="red_bullet_half.gif"> gt100k <img src="blu_bullet_half.gif"> script to decide whether a number is larger than 100,000. Note this has to be done via bc, as PHP/floating point cannot deal with large numbers.
|
||||
<br><img src="red_bullet_half.gif"> hints_to_choosing_e.html <img src="blu_bullet_half.gif"> HTML page offering advice on values of e to choose for the public key.
|
||||
<br><img src="red_bullet_half.gif"> index.php <img src="blu_bullet_half.gif"> Main page, introduction and links to descriptions and generate key/ encryption pages.
|
||||
<br><img src="red_bullet_half.gif"> ln2 <img src="blu_bullet_half.gif"> Script (using bc) to find the log to base 2 of very very large numbers. Useful for determining maximum key set lenghts possible with the chosen modulus (n value)
|
||||
<br><img src="red_bullet_half.gif"> maths.html <img src="blu_bullet_half.gif"> Description of the mathematical method used to break very large equations of the form c^d%n down recursively into more manageable calculations.
|
||||
<br><img src="red_bullet_half.gif"> multiply.php <img src="blu_bullet_half.gif"> Multiplies the two prime numbers chosen to form the modulus (n value)
|
||||
<br><img src="red_bullet_half.gif"> nlhtml.sed <img src="blu_bullet_half.gif"> A 'sed' script to tidy up raw bc output
|
||||
<br><img src="red_bullet_half.gif"> pi.php <img src="blu_bullet_half.gif"> A PHP page offering an arbitary precision calculation of pi, part of the general description of the bc scripting language.
|
||||
<br><img src="red_bullet_half.gif"> pow_digits <img src="blu_bullet_half.gif">
|
||||
<br><img src="red_bullet_half.gif"> primes.php <img src="blu_bullet_half.gif"> A PHP page to calculate prime numbers on the fly, to be chosen for creating an RSA key.
|
||||
<br><img src="red_bullet_half.gif"> rsa_explanations_list.html <img src="blu_bullet_half.gif"> A list of web pages germane to RSA.
|
||||
<br><img src="red_bullet_half.gif"> rsa_workbench.tar.gz <img src="blu_bullet_half.gif"> All the files that comprise this assignment. Unpacking this on a PHP/bc/unix machine, should allow this project to be run on other servers.
|
||||
<br><img src="red_bullet_half.gif"> searchd <img src="blu_bullet_half.gif"> Calculate a possible value of 'd' using bc with a bash wrapper
|
||||
<br><img src="red_bullet_half.gif"> 21255511to266511.txt <img src="blu_bullet_half.gif"> A clear text example of a very large number produced by an eight and six digit exponent.
|
||||
|
||||
<br>
|
||||
<br>
|
||||
<br>
|
||||
<center>
|
||||
<a href="javascript:history.back();">
|
||||
<br><img src=back.png align=center border=0> </a>
|
||||
</center>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
44
find_d.html
Normal file
44
find_d.html
Normal file
@ -0,0 +1,44 @@
|
||||
|
||||
<html>
|
||||
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
|
||||
<title> Algorithm used to find 'd' </title>
|
||||
|
||||
<h1> Algorithm used to find 'd' </h1>
|
||||
|
||||
The variable 'd' must obey the equation
|
||||
<center> <b> d.e % phi = 1 </b> </center>
|
||||
This can be re-written as :
|
||||
|
||||
<center> <b> d.e = 1 + k.phi </b> </center>
|
||||
<p>
|
||||
And further
|
||||
<center> <b> d = (1+k.phi)/e </b> </center>
|
||||
<p>
|
||||
Iterating though with values for k, a correct value
|
||||
for d is found when a whole number result for d (no fractional part)
|
||||
is found.
|
||||
<p>
|
||||
The algorithm used is to first test the user entered value
|
||||
in the form. If this satisfies the equation, it is the d value used.
|
||||
If it does not, it is used as the seed value for 'k'.
|
||||
If the 'd' value is left blank in the form, the algorithm
|
||||
will iterate using k==1 as its start value.
|
||||
<p>
|
||||
Note that if the value 'e' is not co-prime to phi,
|
||||
this script may never find a valid value for 'd'.
|
||||
A limit of 10,000 iterations has been placed on this for the time being.
|
||||
It has been left this way to show the importance of these
|
||||
numbers being co-prime, for the RSA system.
|
||||
<br>
|
||||
<br>
|
||||
<br>
|
||||
<center>
|
||||
<a href="javascript:history.back();">
|
||||
<img src=back.png align=center border=0> </a>
|
||||
|
||||
|
||||
</body>
|
||||
</html>
|
||||
78
find_d.php
Normal file
78
find_d.php
Normal file
@ -0,0 +1,78 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<h1> Find d, the private key </h1>
|
||||
<?
|
||||
|
||||
//echo "debug n==$n";
|
||||
|
||||
$max_search = 10000;
|
||||
|
||||
// first find out whether the value typed in by the user
|
||||
// satisfies the equation
|
||||
$result = `./checkd $d $e $phi`;
|
||||
echo " result of checkd $result";
|
||||
$too_large=0;
|
||||
printf("initial result %s <p>\n",$result);
|
||||
if ( $result == "") { $result=0; $d=0; }
|
||||
|
||||
if ( $result == 1 ) {
|
||||
echo " <h3> value $d matches the <strong> de % phi == 1 </strong> criteria </h3>";
|
||||
printf("<form enctype=\"multipart/form-data\" method=\"post\"
|
||||
action=\"generate_key.php#KEYS\">");
|
||||
}
|
||||
|
||||
|
||||
|
||||
else {
|
||||
|
||||
|
||||
echo " Iterating with start seed d $d";
|
||||
for ($i=0; $i<$max_search; $i++) {
|
||||
$y = $d + $i;
|
||||
$result = `./searchd $y $phi $e `;
|
||||
$dd = `./findd $y $phi $e`;
|
||||
|
||||
printf("Trying %s \n",$dd);
|
||||
if ( $result == 0 ) {
|
||||
// found one !
|
||||
$d = $dd;
|
||||
echo " matches criteria <p>";
|
||||
break;
|
||||
}
|
||||
else {
|
||||
echo " does not match <strong> de % phi == 1 </strong> criteria <p>\n";
|
||||
}
|
||||
|
||||
}
|
||||
|
||||
if ( $i > $max_search || $too_large == 1) {
|
||||
echo "<h1>d not found, try another seed, and check e is co-prime to phi </h1>";
|
||||
printf("<form enctype=\"multipart/form-data\" method=\"post\"
|
||||
action=\"generate_key.php#D\">");
|
||||
|
||||
}
|
||||
else {
|
||||
echo "<h1> Acceptable value for 'd' found after $i iterations </h1>\n";
|
||||
printf("<form enctype=\"multipart/form-data\" method=\"post\"
|
||||
action=\"generate_key.php#KEYS\">");
|
||||
}
|
||||
|
||||
}
|
||||
?>
|
||||
|
||||
<input type="hidden" name=d value=<? echo $d ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
<table>
|
||||
<tr>
|
||||
<td>
|
||||
<input type="submit" name="submit" value="Next">
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
42
find_phi.php
Normal file
42
find_phi.php
Normal file
@ -0,0 +1,42 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<h1> Generating PHI the secret Modulus </h1>
|
||||
<?
|
||||
|
||||
$big_num = `echo "($p-1)*($q-1)" | bc `;
|
||||
|
||||
printf("<p> <h2> Phi == %s </h2>",$big_num);
|
||||
$phi = $big_num;
|
||||
printf(" <h2> which is the result of (%s-1)*(%s-1) </h2> \n", $p,$q);
|
||||
//
|
||||
// of the number. To convert log x = ln(x) / ln(a)
|
||||
// a
|
||||
//
|
||||
|
||||
//$k = `./ln2 $phi`;
|
||||
|
||||
//printf("<h2> The large number here, as a rough guide ",strlen($big_num)-1);
|
||||
//printf(" is capable of encrypting a %s bit length key </h2>",$k-1);
|
||||
?>
|
||||
|
||||
<h2> Note this is part of the secret key ! <h2>
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="generate_key.php#GCD">
|
||||
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
|
||||
<table>
|
||||
<tr>
|
||||
<td>
|
||||
<input type="submit" name="submit" value="Next">
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
14
findd
Executable file
14
findd
Executable file
@ -0,0 +1,14 @@
|
||||
#!/bin/bash
|
||||
|
||||
# R.P. Clark : 02APR2004
|
||||
#
|
||||
# Takes three args
|
||||
# $1 y - the multiplier for phi
|
||||
# $2 phi
|
||||
# $3 e
|
||||
|
||||
# returns (1 + phi.y) / e, which is
|
||||
# a value of d to use.
|
||||
|
||||
echo " ( 1 + ( $1 * $2 ) ) / $3 + 0.5" | bc | sed 's/\..*//'
|
||||
|
||||
37
gcd.php
Normal file
37
gcd.php
Normal file
@ -0,0 +1,37 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<h1> The Numbers </h1>
|
||||
<?
|
||||
//echo " gcd($e,$phi) == ";
|
||||
|
||||
$big_num = `echo "a=$e; b=$phi; while(b) {a=a%b; r=b; b=a; a=r;}; a;" | bc `;
|
||||
|
||||
printf(" <h2> gcd($e,$phi) == %s </h2>",$big_num);
|
||||
|
||||
if ($big_num == 1) {
|
||||
printf("<h2>So these numbers are co-prime</h2><h2> the value for e is therefore acceptable </h2>\n");
|
||||
printf("<form enctype=\"multipart/form-data\" method=\"post\" action=\"generate_key.php#D\">");
|
||||
}
|
||||
else {
|
||||
printf("<h1>e is not coprime to M</h1><h1> go back and try another value for e</h1>\n");
|
||||
printf("<form enctype=\"multipart/form-data\" method=\"post\" action=\"generate_key.php#GCD\">");
|
||||
}
|
||||
|
||||
|
||||
?>
|
||||
|
||||
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
<input type="hidden" name=d value=<? echo $d ?>>
|
||||
<table>
|
||||
<tr><td><input type="submit" name="submit" value="Back"> </td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
|
||||
</body>
|
||||
</html>
|
||||
382
generate_key.php
Normal file
382
generate_key.php
Normal file
@ -0,0 +1,382 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
<title> RSA Interactive Simulator : Key Generation </title>
|
||||
|
||||
<h1> RSA Interactive Simulator / Work Bench : Key Generation </h1>
|
||||
|
||||
<h3>
|
||||
This RSA key generator, will lead you though making a key set.
|
||||
You may at anytime enter your own values into the forms, or
|
||||
use the ones calculated for you.
|
||||
</h3>
|
||||
|
||||
<h3>
|
||||
Use the BACK button on your browser
|
||||
at your peril !
|
||||
</h3>
|
||||
|
||||
<p>
|
||||
The first stage of RSA key generation is to choose two large
|
||||
prime numbers,
|
||||
p and q.
|
||||
|
||||
A php utility to find prime numbers up to
|
||||
2 Billion (i.e. 2 000 000 000 ) is provided below.
|
||||
|
||||
This is adequate for 56 bit RSA encryption simulations.
|
||||
This script has a 30 second processing time
|
||||
limitation which will interrupt the program if a
|
||||
very large range is given. Best to play with this a little...
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Pick some two of the prime numbers offered and cut and
|
||||
paste them into the form for further use.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
For full RSA simulations a <a href="bc.html"> bc </a>
|
||||
based prime number finder is provided as
|
||||
<a href="bc_primes.zip"> source code </a>
|
||||
and on-line <a href="bc_primes.php"> here </a>.
|
||||
</p>
|
||||
|
||||
<br> <br> <A name="PRIME">
|
||||
<hr>
|
||||
<h2> FIND SUITABLE PRIMES </h2>
|
||||
<hr> <br> <br>
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="primes.php">
|
||||
|
||||
|
||||
<strong>Prime Number Finder</strong>
|
||||
<small>Taken (and modified slightly) from
|
||||
<a href="http://www.planet-source-code.com/vb/scripts/ShowCode.asp?txtCodeId=1273&lngWId=8"> Prime Number finder 2 </a></small>
|
||||
|
||||
<table border=2>
|
||||
<tr>
|
||||
<td>
|
||||
<strong>Min</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="x" size=120 value="100" colspan=2>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>max</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="i" size=120 value="1000" colspan=2>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
|
||||
<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
</form>
|
||||
<br> <br><a name="MUL">
|
||||
<hr>
|
||||
<h2> FIND THE MODULUS OF THE PRIMES </h2>
|
||||
<hr>
|
||||
|
||||
These when multiplied together,
|
||||
should be as large as the encryption
|
||||
key being used (for instance a 128 bit key has
|
||||
approx ln(2^128)/ln(10) == 39 decimal digits), note
|
||||
that this has already exceeded the 52 bits of
|
||||
precision of <b> double precision </b>
|
||||
maths as defined by the
|
||||
<a href="http://www.freesoft.org/CIE/RFC/1832/10.htm"> IEEE </a>
|
||||
<p>
|
||||
Test your values of P and Q here
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="multiply.php">
|
||||
|
||||
<strong>Multiply P and Q </strong>
|
||||
|
||||
<table border=2>
|
||||
<tr>
|
||||
<td>
|
||||
<strong>Min</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="p" size=120 value="<? echo $p ?>" >
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>max</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="q" size=120 value="<? echo $q ?>" >
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
<input type="hidden" name=mprivate value=<? echo $mprivate ?>>
|
||||
<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
|
||||
</table>
|
||||
</form>
|
||||
|
||||
</p>
|
||||
|
||||
|
||||
<br> <br> <A NAME="PHI">
|
||||
<hr>
|
||||
<h2> FIND PHI</h2>
|
||||
<hr>
|
||||
|
||||
|
||||
<p>
|
||||
When you have chosen your two prime numbers.....we need to find <strong> phi == (p-1)(q-1) </strong>
|
||||
</p>
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="find_phi.php">
|
||||
|
||||
<strong>RSA p and q</strong>
|
||||
|
||||
<table border=2>
|
||||
<tr>
|
||||
<td>
|
||||
<strong>p</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="p" size=120 value="<? echo $p ?>" >
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>q</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="q" size=120 value="<? echo $q ?>" >
|
||||
</td>
|
||||
</tr>
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
|
||||
|
||||
<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
</table>
|
||||
</form>
|
||||
|
||||
<br> <br> <A name="GCD">
|
||||
<hr>
|
||||
<h2> GREATEST COMMON DENOMINATOR </h2>
|
||||
<hr>
|
||||
|
||||
<p>
|
||||
We now need to find a small number 'e' which is co-prime to phi.
|
||||
This number may therefore be any number you choose, (except 1, which would be unsafe cryptographically) as long as it is <b> co-prime to phi </b>.
|
||||
This number forms the second part of your public key.
|
||||
Hints to <a href="hints_to_choosing_e.html"> choosing e </a>.
|
||||
</p>
|
||||
<p>
|
||||
Note that this calls the gcd (greatest common denominator) function
|
||||
which returns 1 when co-prime values are entered.
|
||||
</p>
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="gcd.php">
|
||||
|
||||
<strong>RSA e and phi </strong>
|
||||
|
||||
<table border=2>
|
||||
<tr>
|
||||
<td>
|
||||
<strong>e</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="e" size=120 value="<? echo $e ?>">
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>phi</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="phi" size=120 value="<? echo $phi ?>">
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
|
||||
<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
|
||||
</table>
|
||||
</form>
|
||||
|
||||
<br> <br>
|
||||
<hr>
|
||||
<h2> FIND D </h2>
|
||||
<hr>
|
||||
<p>
|
||||
We now need to find a number 'd' so that <strong> d.e % phi == 1 </strong>
|
||||
This number will be your private key.</p>
|
||||
Enter a seed value for D or calculate it yourself.
|
||||
If the number typed obeys <strong> d.e % phi == 1 </strong>
|
||||
it will be used, otherwise it will be used as a start seed value.
|
||||
Leave blank to iterate to find lowest d value.
|
||||
Note on the algorithm used are <a href="find_d.html"> here </a>
|
||||
<A name="D">
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="find_d.php">
|
||||
|
||||
<strong>RSA find 'd'</strong>
|
||||
|
||||
<table border=2>
|
||||
<tr>
|
||||
<td>
|
||||
<strong>d</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="d" size=120 value="<? echo $d ?>" >
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>phi</strong>
|
||||
</td>
|
||||
<td width>
|
||||
<input type=text name="phi" size=120 value="<? echo $phi ?>">
|
||||
</td>
|
||||
</tr>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
</table>
|
||||
</form>
|
||||
|
||||
<br> <br> <A name="KEYS">
|
||||
<hr>
|
||||
<h2> RSA KEYSET </h2>
|
||||
<hr>
|
||||
|
||||
<table>
|
||||
<tr>
|
||||
<td>
|
||||
<table border=4>
|
||||
<tr>
|
||||
<td colspan=2>
|
||||
<strong> PUBLIC KEY </strong>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
MODULUS (n)
|
||||
</td>
|
||||
<td>
|
||||
<? echo $n ?>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
Public Key (e)
|
||||
</td>
|
||||
|
||||
<td>
|
||||
<? echo $e ?>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
</td>
|
||||
<td>
|
||||
<table border=4>
|
||||
<tr>
|
||||
<td colspan=2>
|
||||
<strong> PRIVATE KEY </strong>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
MODULUS (n)
|
||||
</td>
|
||||
<td>
|
||||
<? echo $n ?>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>
|
||||
Private Key (d)
|
||||
</td>
|
||||
|
||||
<td>
|
||||
<? echo $d ?>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
</table>
|
||||
</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
<h3>
|
||||
Now we have an RSA key set, we can use these
|
||||
to send encrypted data both ways. A user seeing the
|
||||
public key can encrypt using it, and the receiving party
|
||||
de-crypts with the private key. Note that no other user
|
||||
can de-crypt the message without knowing (or finding by brute force)
|
||||
the private key.
|
||||
</h3>
|
||||
|
||||
<table>
|
||||
<tr>
|
||||
<td>
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="encode_pub.php">
|
||||
|
||||
|
||||
<input type="hidden" name=phi value=<? echo $phi ?>>
|
||||
<input type="hidden" name=d value=<? echo $d ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
<tr><td><input type="submit" name="submit" value="Encode Using Public Key"> </td></tr>
|
||||
</table>
|
||||
</form>
|
||||
</td>
|
||||
<td>
|
||||
|
||||
|
||||
|
||||
<center> <a href="index.php" border=0> <img src="home.png" border=0> </a> </center>
|
||||
<center>
|
||||
<a href="javascript:history.back();">
|
||||
<img src=back.png align=center border=0> </a>
|
||||
</center>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
|
||||
10
gt100k
Executable file
10
gt100k
Executable file
@ -0,0 +1,10 @@
|
||||
#!/bin/bash
|
||||
|
||||
# R.P. Clark : 11APR2004
|
||||
#
|
||||
# Takes one arg, the number to
|
||||
# check. Thisfunction returns 1 if the
|
||||
# number is .gt. 100000
|
||||
|
||||
echo "if ( $1 > 100000 ) { 1; } else { 0; } " | bc
|
||||
|
||||
46
hints_to_choosing_e.html
Normal file
46
hints_to_choosing_e.html
Normal file
@ -0,0 +1,46 @@
|
||||
<html>
|
||||
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
|
||||
<h1><title> Hints to Choosing 'e' </title></h1>
|
||||
<h1> Hints to Choosing 'e' </h1>
|
||||
The 'e' value along with the Modulus 'n' forms the public key.
|
||||
<p>
|
||||
It is used to encode information by taking the data to encode 'm',
|
||||
to the power of 'e' and then applying the mod operator
|
||||
(remainder of division) between that result and the modulus value 'n'.
|
||||
<p>
|
||||
|
||||
<h3>encoded = m<sup>e</sup>%n</h3>
|
||||
|
||||
As it is part of the public key, (and therefore published)
|
||||
there is no point in it being a large number. Values like 3,5,7,11
|
||||
are all acceptable. The only restriction is that they should be co-prime
|
||||
to the phi value.
|
||||
<p>
|
||||
Some automatic algorithms for choosing 'e', simply start at 3, test
|
||||
for co-prime against phi, and on failure, increment 'e' by two and try again
|
||||
until they hit a co-prime combination.
|
||||
<p>
|
||||
If a non co-prime number is used, you may find it impossible
|
||||
to calculate the secret key in the next stage...
|
||||
<p>
|
||||
If 1 is chosen for 'e', it will be co-prime to any value of
|
||||
phi, but this will mean that the secret key will be 1 also, not very secure !
|
||||
|
||||
<p>
|
||||
Hit the back button and try some values for 'e' until you have a co-prime
|
||||
value....
|
||||
|
||||
|
||||
|
||||
<br>
|
||||
<br>
|
||||
<br>
|
||||
<center>
|
||||
<a href="javascript:history.back();">
|
||||
<img src=back.png align=center border=0> </a>
|
||||
</center>
|
||||
</body>
|
||||
</html>
|
||||
48
index.html
Normal file
48
index.html
Normal file
@ -0,0 +1,48 @@
|
||||
|
||||
<html>
|
||||
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
|
||||
<title> Web Mastery Course : Assignment Work </title>
|
||||
|
||||
<h1> Web Mastery Course : Assignment Work </h1>
|
||||
|
||||
This web site is a submission for the <b> Web Mastery </b>
|
||||
course held at Brighton University from the 15th of March to
|
||||
the 19th of March 2003.
|
||||
<p>
|
||||
This is the course work submission for R.P. Clark (part time student).
|
||||
|
||||
<h2> Course Work Presentation </h2>
|
||||
|
||||
A presentation on the mechanics of DNS look up <a href="dns.ppt"> here </a>
|
||||
|
||||
<h2> Course Assignment </h2>
|
||||
|
||||
A web based tool, to run through RSA encryption. This tool uses PHP
|
||||
as a web server scripting language, which calls bash and bc scripts to
|
||||
perform the mathematics of RSA. The intention is to produce an interactive
|
||||
tutorial for RSA. Each stage in key generation and encryption is shown, with
|
||||
(where practical) intermediate results.
|
||||
<p>
|
||||
This tool allows simulations of small RSA implementations. Even
|
||||
with some algorithmic optimisation to the de-cryption routines
|
||||
(see <a href=maths.html> maths of large exponents)</a>. If
|
||||
simulations larger than 128 bits are simulated, the de-cryption
|
||||
private key parts may take several minutes to calculate.
|
||||
<p>
|
||||
|
||||
The assignment web application <a href="index.php"> RSA Work Bench / Simulator </a>
|
||||
<p>
|
||||
|
||||
|
||||
<br>
|
||||
<br>
|
||||
<br>
|
||||
|
||||
<hr>
|
||||
<img SRC="red_bullet_half.gif">Last updated 16Apr2004 <img SRC="blu_bullet_half.gif"> R.P.Clark.
|
||||
<hr>
|
||||
</body>
|
||||
</html>
|
||||
92
index.php
Normal file
92
index.php
Normal file
@ -0,0 +1,92 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
<title> RSA Interactive Simulator </title>
|
||||
|
||||
<h1> RSA Interactive Simulator / Work Bench </h1>
|
||||
|
||||
<p>
|
||||
This tutorial seeks not to specifically explain the RSA algorithm,
|
||||
but provides a web
|
||||
based tool to run though the algorithm step by step.
|
||||
|
||||
</p>
|
||||
<p>
|
||||
By doing this the very large numbers
|
||||
used in 'real' RSA connections can be run though,
|
||||
also simulations of bad RSA implementations
|
||||
can be tried
|
||||
</p>
|
||||
<p>
|
||||
for instance:
|
||||
<ul>
|
||||
<li> Small Prime Numbers to follow the algorithm through </li>
|
||||
<li> No co-prime public key/phi combinations (impossible to find 'd')</li>
|
||||
<li> Unsafe values for public key 'e' value (i.e. 1)</li>
|
||||
<li> Attemtping to encode numbers larger than the modulus</li>
|
||||
<li> Oversize values (>n) for d and e and subsequent effects </li>
|
||||
<li> Intermediate results seen (where practical) </li>
|
||||
</ul>
|
||||
|
||||
</p>
|
||||
|
||||
<p>
|
||||
It is easy to find thousands of <i> RSA explanations </i> on the Web,
|
||||
(for instance google currently lists 195,000 for searching on
|
||||
<b> rsa algorithm </b> ) a list of a few useful
|
||||
reviewed sites with guide notes is included
|
||||
<a href="rsa_explanations_list.html"> here </a>.
|
||||
</p>
|
||||
|
||||
|
||||
<p>
|
||||
This series of web pages has been written in PHP, running on a RedHat
|
||||
Linux server with a moderately fast processor (1.4GHz athlon), principally
|
||||
to use the unix <a href="bc.html"> bc </a> utility
|
||||
to deal with the very large numbers used
|
||||
in the RSA encryption technique.
|
||||
Javascript with double precision floating point
|
||||
provides for instance around 12 places of decimals.
|
||||
With <a href="bc.html"> bc </a>
|
||||
the only practical limitation is server side processing time
|
||||
and memory.
|
||||
</p>
|
||||
|
||||
|
||||
<p>
|
||||
The first stage of RSA encryption is to
|
||||
<a href="generate_key.php"><img src="create_rsa_key_set.png" border=0></a>.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
This key is used in the start up sequences of a secure connection, to pass
|
||||
and encryption/or scambling key. This key is then used to encode
|
||||
the subsequent transmission.
|
||||
</p>
|
||||
|
||||
<p>
|
||||
When a key has been chosen, the
|
||||
encryption and decryption processes can be simulated.
|
||||
The final decryption process
|
||||
involves very large exponentiation.
|
||||
This was beyond the abilities of bc for practical
|
||||
values.
|
||||
To allow bc scripts to process these very large
|
||||
numbers mathematical breakdowns
|
||||
of the equations, resulting in
|
||||
recursive routines was required. These are described
|
||||
<a href="maths.html"> here </a>.
|
||||
|
||||
</p>
|
||||
All the scripts and php source are available in a <a href="rsa_workbench.tar.gz"> gzipped tar file here</a>
|
||||
A brief description of all files, PHP pages, HTML pages bc, sed and bash scripts used is <a href="files.html"> here </a>
|
||||
|
||||
<br>
|
||||
<br>
|
||||
<hr>
|
||||
<img SRC="red_bullet_half.gif">Last updated 12Apr2004 <img SRC="blu_bullet_half.gif"> R.P.Clark.
|
||||
<hr>
|
||||
</body>
|
||||
</html>
|
||||
|
||||
|
||||
14
ln
Executable file
14
ln
Executable file
@ -0,0 +1,14 @@
|
||||
#!/bin/bash
|
||||
|
||||
# R.P. Clark : 10APR2004
|
||||
#
|
||||
# Takes one arg, the number to be converted
|
||||
# to log base e.
|
||||
|
||||
# script to take a very large interger number
|
||||
# and return a rounded up log to base 2 of it.
|
||||
# this corresponds to the number of bits needed
|
||||
# to represent the number in binary.
|
||||
|
||||
echo "l($1)" | bc -l | sed 's/\..*//'
|
||||
|
||||
14
ln2
Executable file
14
ln2
Executable file
@ -0,0 +1,14 @@
|
||||
#!/bin/bash
|
||||
|
||||
# R.P. Clark : 02APR2004
|
||||
#
|
||||
# Takes one arg, the number to be converted
|
||||
# to log base 2.
|
||||
|
||||
# script to take a very large interger number
|
||||
# and return a rounded up log to base 2 of it.
|
||||
# this corresponds to the number of bits needed
|
||||
# to represent the number in binary.
|
||||
|
||||
echo "l($1)/l(2)+0.5" | bc -l | sed 's/\..*//'
|
||||
|
||||
239
maths.html
Normal file
239
maths.html
Normal file
@ -0,0 +1,239 @@
|
||||
<html>
|
||||
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
|
||||
<h1><title> Mathematics of Large Exponents : Algorithms for Tackling extremely large intermediate results </title></h1>
|
||||
<h1>Mathematics of Large Exponents : Algorithms for Tackling extremely large intermediate results </h1>
|
||||
|
||||
|
||||
Consider a 256 bit capable key.
|
||||
<p>
|
||||
The Modulus (n) must be greater than 2<sup>256</sup>.
|
||||
<p>
|
||||
This number represented in decimal is very large.
|
||||
90 odd decimal digits !
|
||||
<p>
|
||||
2^256 == 115792089237316195423570985008687907853269984665640564039457584007913129639936
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Compared to the numbers generated by raising large numbers to large exponents,
|
||||
though, 2<sup>256</sup> seems quite trivial.
|
||||
</p>
|
||||
|
||||
The RSA encryption algorithms are based on taking large numbers
|
||||
to the power of a key value, and then applying the modulus
|
||||
of that result with a large pre-calculated value (n) based on a
|
||||
prime number multiplication.
|
||||
|
||||
<h3>encoded = c<sup>d</sup>%n</h3>
|
||||
|
||||
<p>
|
||||
For instance 2<sup>256</sup> to the power of a 6 digit key (say 5,000,000)
|
||||
produces a number of approximately <b> 385,318,394 </b> digits !
|
||||
</p>
|
||||
|
||||
<p>
|
||||
Obviously, such large intermediate results are impractical.
|
||||
For the purpose of this tool, intermediate values with up to
|
||||
100,000 digits are shown (and can be dealt with directly using the
|
||||
<a href="bc.html"> unix bc utility </a>).
|
||||
</p>
|
||||
|
||||
<p>
|
||||
An effective way to break this problem down is to use results from
|
||||
<a href="http://mathworld.wolfram.com/Residue.html"> residue theory </a>.
|
||||
|
||||
From
|
||||
<a href="http://mathworld.wolfram.com/Residue.html"> residue theory </a>
|
||||
we can state that where d is even:
|
||||
<p>
|
||||
<center> <b> c<sup>d</sup>%n == ((c^2%n)<sup>d/2</sup>)%n </b> </center>
|
||||
</p>
|
||||
If d is an integer power of 2, (i.e. d == 2<sup>n</sup> where
|
||||
n is a positive integer) this can be extended to a recursive algorithm.
|
||||
|
||||
<h3> Recursive algorithm for simplifying equations of the form
|
||||
c<sup>d</sup>%n where d is an integer power of 2 </h3>
|
||||
|
||||
<hr>
|
||||
<pre>
|
||||
calc_residue ( bigint c, bigint d, bigint n ) {
|
||||
if ( d == 1 ) return ( c ^ d % n );
|
||||
return calc_residue ( c^2, d/2, n ) % n; # recursion
|
||||
}
|
||||
</pre>
|
||||
<hr>
|
||||
|
||||
This is all very well, and solves the large exponentiation problem.
|
||||
But most exponents used in RSA are not integer powers of 2 !
|
||||
Some way of breaking the exponent up and handling each integer power
|
||||
of 2 part is required.
|
||||
|
||||
<h3>Breaking down exponent to Powers of 2 As pseudo code</h3>
|
||||
|
||||
|
||||
Consider for instance the number 323
|
||||
can be represented by
|
||||
<p>
|
||||
<center> <b> 323 == 2<sup>8</sup> + 2<sup>6</sup> + 2<sup>1</sup> + 2<sup>0</sup> </b> </center>
|
||||
<p>
|
||||
|
||||
Thus 'c' to the power of 323, could be written as
|
||||
(where ^ means to the power of, as in c and bc scripts)
|
||||
|
||||
<p>
|
||||
<center> <b>c<sup>(2^8+2^6+2^1+2^0)</sup></b> </center>
|
||||
<p>
|
||||
<br>
|
||||
|
||||
<p>
|
||||
or written as
|
||||
<p>
|
||||
<center> <b>c<sup>2^8</sup>*c<sup>2^6</sup>*c<sup>2^1</sup>*c<sup>2^0</sup></b> </center>
|
||||
<p>
|
||||
In this form it is easy to see that any exponent can be broken down into
|
||||
powers of two for processing by the <b>calc_residues</b> algorithm.
|
||||
|
||||
<p>
|
||||
The following pseudo code takes the variable d, and breaks it down into
|
||||
into its integer power of 2 parts.
|
||||
</P>
|
||||
|
||||
<hr>
|
||||
<pre>
|
||||
|
||||
break_down_into_powers_of_two ( bigint d ) {
|
||||
|
||||
|
||||
integer i = 0;
|
||||
|
||||
# find biggest power of 2 left in exponentiation
|
||||
#
|
||||
while(d >= (2^i)) { i = i+1; }
|
||||
|
||||
# subtract highest power of 2 possible from d
|
||||
#
|
||||
d = (d - (2^(i-1)));
|
||||
|
||||
PRINT (2^(i-1));
|
||||
|
||||
if (d>0) {
|
||||
# d is greater than 0 so we need to break this down further
|
||||
#
|
||||
break_down_into_powers_of_two(d); # recurse with new d value
|
||||
return (2^(i-1));
|
||||
}
|
||||
if (d == 0) {
|
||||
# d is 0, we have found the last power of 2 required
|
||||
#
|
||||
return (2^(i-1);
|
||||
}
|
||||
}
|
||||
</pre>
|
||||
<hr>
|
||||
|
||||
In order to implement code that can process any
|
||||
d exponent in a c^d%n equation in a <a href="bc.html">bc</a>
|
||||
script the problem has been divided into two distinct
|
||||
but linked stages:
|
||||
<ul>
|
||||
<li> Recursively break down the exponent into powers of two </li>
|
||||
<li> Recursively process each power of two c<sup>d</sup>%n equation </li>
|
||||
</ul>
|
||||
|
||||
|
||||
<h3> Script to calculate c<sup>d</sup>%n equations without incredibly large intermediate results</h3>
|
||||
|
||||
Integrating these together produces the following
|
||||
<a href="bc.html">bc</a> program.
|
||||
<hr>
|
||||
<pre>
|
||||
# bc program. Call with -q parameter
|
||||
# R.P. Clark 10APR2004
|
||||
|
||||
# recursive routine to calculate c^d%n
|
||||
# by breaking it down. Works only where
|
||||
# d is a power of 2.
|
||||
#
|
||||
define x ( c,d,n) {
|
||||
if ( d == 1 ) return (c^d%n);
|
||||
return x(c^2,d/2,n)%n;
|
||||
}
|
||||
|
||||
r = 1;
|
||||
|
||||
# recursive routine to break d into powers of 2
|
||||
# and then to collect multiply the results
|
||||
# of the 2^n exponents.
|
||||
#
|
||||
define t(c,d,n) {
|
||||
auto i
|
||||
i = 0;
|
||||
|
||||
# find biggest power of 2 left in exponentiation
|
||||
#
|
||||
while(d >= (2^i)) { i = i+1; }
|
||||
|
||||
# subtract from exponent
|
||||
#
|
||||
d = (d - (2^(i-1)));
|
||||
|
||||
|
||||
if (d>0) {
|
||||
r=(r*x(c,2^(i-1),n))%n; # calculate this large exponentiation
|
||||
t(c,d,n); # recursion with new d value
|
||||
return (2^(i-1));
|
||||
}
|
||||
if (d == 0) {
|
||||
r = (r*x(c,2^(i-1),n))%n; # last one
|
||||
return (2^(i-1));
|
||||
}
|
||||
}
|
||||
</pre>
|
||||
<hr>
|
||||
<p>
|
||||
Thus the function t(c,d,n), will break down the exponent,
|
||||
and pass it on as powers of 2, to calculate the residues using
|
||||
the 'x' function. Thus very large
|
||||
exponentiation and mod
|
||||
equations,will be calculated without having to handle
|
||||
incredibly large intermediate results.
|
||||
</p>
|
||||
|
||||
Some results, of timings for the equation
|
||||
<b>21255511<sup>266511</sup>%999999</b> run
|
||||
on a 1 Ghz Celeron laptop (Redhat 8.0 : <a href="bc.html">bc</a> version 1.06).
|
||||
Note that larger numbers than
|
||||
this in the exponent
|
||||
are rejected by bc.
|
||||
<p>
|
||||
To see how large <b>21255511<sup>266511</sup></b> is,
|
||||
a text file containing it is included <a href="21255511to266511.txt"> here </a>.
|
||||
</p>
|
||||
<pre>
|
||||
[robin@localhost bc]$ date; bc < calc_big_expon.bc | tail -1; date
|
||||
Sun Apr 11 17:21:10 BST 2004
|
||||
407926
|
||||
Sun Apr 11 17:26:37 BST 2004
|
||||
[robin@localhost bc]$ date ; echo "21255511^266511%999999" | bc ; date
|
||||
Sun Apr 11 17:36:13 BST 2004
|
||||
407926
|
||||
Sun Apr 11 17:43:29 BST 2004
|
||||
[robin@localhost bc]$ bc -v
|
||||
bc 1.06
|
||||
</pre>
|
||||
|
||||
|
||||
Thus the recursive algorithm is faster, and large exponents are
|
||||
not rejected.
|
||||
|
||||
<br>
|
||||
<br>
|
||||
<center>
|
||||
<a href="javascript:history.back();">
|
||||
<img src=back.png align=center border=0> </a>
|
||||
</center>
|
||||
</body>
|
||||
</html>
|
||||
33
multiply.php
Normal file
33
multiply.php
Normal file
@ -0,0 +1,33 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<h1> Public Key 'Modulus' Generation </h1>
|
||||
<?
|
||||
$p = trim($p);
|
||||
$q = trim($q);
|
||||
|
||||
|
||||
$n = $big_num = `echo $p*$q | bc`;
|
||||
|
||||
$k = `./ln2 $n`;
|
||||
|
||||
printf("<p> <h2> the result is </h2> %s ",$big_num);
|
||||
printf(" <h2> which is the result of %s * %s </h2> <h2> which forms part of the public key (n) </h2> \n", $p,$q);
|
||||
|
||||
printf("<h2> The large number here, as a rough guide ",strlen($big_num)-1);
|
||||
printf(" is capable of encrypting a %s bit length key </h2>",$k-1);
|
||||
|
||||
?>
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="generate_key.php#PHI">
|
||||
<input type="hidden" name=p value=<? echo $p ?>>
|
||||
<input type="hidden" name=q value=<? echo $q ?>>
|
||||
<input type="hidden" name=n value=<? echo $n ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<table>
|
||||
<tr><td><input type="submit" name="submit" value="Back"> </td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
</body>
|
||||
</html>
|
||||
2
nlhtml.sed
Normal file
2
nlhtml.sed
Normal file
@ -0,0 +1,2 @@
|
||||
s/^/<BR>/g
|
||||
s/\\//g
|
||||
49
pi.php
Normal file
49
pi.php
Normal file
@ -0,0 +1,49 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
<title> Pi to an arbitary precision </title>
|
||||
|
||||
<h1> Pi to an arbitary precision </h1>
|
||||
|
||||
Pi can be calculated by taking the arctangent of one
|
||||
radian and multiplying it by four.
|
||||
<p>
|
||||
This php page
|
||||
will pass the required precision to a bc script, and calculate
|
||||
pi to as many places as you like.More than 10,000 places
|
||||
may require a bit of a wait though....
|
||||
<p>
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="calc_pi.php">
|
||||
|
||||
<strong>Calculate pi on the fly</strong>
|
||||
|
||||
<table border=2>
|
||||
<tr>
|
||||
<td>
|
||||
<strong>required precision</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="precision" cols=80 value="" colspan=2>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
</table>
|
||||
|
||||
|
||||
<input type="hidden" name=luid value=<? echo $luid ?>>
|
||||
</form>
|
||||
|
||||
<center>
|
||||
<a href="javascript:history.back();">
|
||||
<img src=back.png align=center border=0> </a>
|
||||
</center>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
|
||||
|
||||
10
pow_digits
Executable file
10
pow_digits
Executable file
@ -0,0 +1,10 @@
|
||||
#!/bin/bash
|
||||
|
||||
# R.P. Clark : 10APR2004
|
||||
#
|
||||
# Takes two args, c and d.
|
||||
# returns approx number of decimal
|
||||
# digits that c^d would cause.
|
||||
|
||||
echo "(l($1)*$2)/l(10)" | bc -l | sed 's/\..*//'
|
||||
|
||||
36
primes.html
Normal file
36
primes.html
Normal file
@ -0,0 +1,36 @@
|
||||
<html>
|
||||
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="primes.php">
|
||||
|
||||
<strong>Prime Number Finder</strong>
|
||||
|
||||
<table border=2>
|
||||
<tr>
|
||||
<td>
|
||||
<strong>p</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="x" cols=80 value="1000" colspan=2>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>q</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="i" cols=80 value="2000" colspan=2>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
|
||||
</table>
|
||||
|
||||
|
||||
</table>
|
||||
|
||||
|
||||
</form>
|
||||
76
primes.php
Normal file
76
primes.php
Normal file
@ -0,0 +1,76 @@
|
||||
<html>
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
<?
|
||||
// Find Primes From $i to $x
|
||||
|
||||
|
||||
// if they put they parameters the wrong way round...
|
||||
|
||||
if ( $i > $x ) {
|
||||
$t = $i;
|
||||
$i = $x;
|
||||
$x = $t;
|
||||
}
|
||||
|
||||
|
||||
$max_search = 2000000001;
|
||||
|
||||
$counter = 0;
|
||||
if ( $i < $max_search && $x < $max_search && $x > 0 && $i > 0 ) {
|
||||
for($i;$i<=$x;$i++) {
|
||||
$f=sqrt($i);
|
||||
for($z=1;$z<=$f;$z++) {
|
||||
$y=$i%$z;
|
||||
if($y==0)
|
||||
$l++;
|
||||
if($l>=2)
|
||||
break;
|
||||
}
|
||||
if ($l<=1){
|
||||
echo "$i ";
|
||||
$b++;
|
||||
}
|
||||
$l=0;
|
||||
}
|
||||
}
|
||||
else {
|
||||
printf(" Parameter(s) with incorrect value. Use Values between 1 and %d",$max_search);
|
||||
}
|
||||
|
||||
|
||||
?>
|
||||
|
||||
<h3> Choose the prime numbers to use and then Cut and paste into the form </h3>
|
||||
|
||||
<form enctype="multipart/form-data" method="post"
|
||||
action="generate_key.php#MUL">
|
||||
|
||||
<input type="hidden" name=m value=<? echo $m ?>>
|
||||
<input type="hidden" name=e value=<? echo $e ?>>
|
||||
<input type="hidden" name=npublic value=<? echo $npublic ?>>
|
||||
<input type="hidden" name=nprivate value=<? echo $nprivate ?>>
|
||||
<table>
|
||||
<tr>
|
||||
<td>
|
||||
<strong>p</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="p" cols=80 value="<? echo $p ?>" colspan=2>
|
||||
</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>
|
||||
<strong>q</strong>
|
||||
</td>
|
||||
<td>
|
||||
<input type=text name="q" cols=80 value="<? echo $q ?>" colspan=2>
|
||||
</td>
|
||||
</tr>
|
||||
<tr><td><input type="submit" name="submit" value="Next"> </td></tr>
|
||||
</table>
|
||||
|
||||
</form>
|
||||
</body>
|
||||
</html>
|
||||
BIN
red_bullet_half.gif
Normal file
BIN
red_bullet_half.gif
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 894 B |
BIN
review.gif
Normal file
BIN
review.gif
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 165 B |
128
rsa_explanations_list.html
Normal file
128
rsa_explanations_list.html
Normal file
@ -0,0 +1,128 @@
|
||||
<html>
|
||||
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
|
||||
<title> RSA web resources </title>
|
||||
|
||||
<h1> A selected list of RSA WEB References </h1>
|
||||
|
||||
<h3> Organisations / Standards Bodies </h3>
|
||||
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://www.rsasecurity.com/"
|
||||
> RSA Security web site </a> <img SRC="blu_bullet_half.gif">
|
||||
RSA the holders of the patent, now a company offering
|
||||
security consultancy and products. well linked and kept up to date.
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://www.pgp.com/"
|
||||
> Pretty Good Privacy </a> <img SRC="blu_bullet_half.gif">
|
||||
Encrypted emails and authentication using SSL/RSA technologies.
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://www.openssl.org/"
|
||||
> Open SSL </a> <img SRC="blu_bullet_half.gif">
|
||||
The OPEN SSL project provides libraries and interfaces
|
||||
allowing industrial strength SSL to be incorporated into products
|
||||
and systems.
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://www.apache-ssl.org/"
|
||||
> Apache SSL </a> <img SRC="blu_bullet_half.gif">
|
||||
Apache-SSL is a secure Webserver, based on Apache and SSLeay/OpenSSL.
|
||||
It is licensed under a BSD-style licence, which means, in short,
|
||||
that you are free to use it for commercial or non-commercial purposes,
|
||||
so long as you retain the copyright notices.
|
||||
|
||||
|
||||
<h3> Implementation Notes </h3>
|
||||
|
||||
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://www.linuxjournal.com/article.php?sid=6826"
|
||||
> Exploring RSA Encryption in OpenSSL </a> <img SRC="blu_bullet_half.gif">
|
||||
Unsurprisingly, source code and implementation details for what is
|
||||
the basis for secure transactions and identification on the web are
|
||||
hard to come by. This page, however, describes coding details and
|
||||
is linked to discussions on RSA implementation.
|
||||
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://wp.netscape.com/eng/security/SSL_2.html"
|
||||
> SSL Protocol description </a> <img SRC="blu_bullet_half.gif">
|
||||
A description of the protocol surrounding encryption and identity verification.
|
||||
Essential reading for those implementing (and not just looking at the mathematical theory)
|
||||
of the SSL/RSA.
|
||||
|
||||
|
||||
<h3> Algorithms </h3>
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://www.di-mgt.com.au/rsa_alg.html"
|
||||
> DI Management RSA description </a> <img SRC="blu_bullet_half.gif">
|
||||
A Mathematically Terse description encompassing Key Generation, encryption,
|
||||
Digital Signing, Signature verification, practical notes (choosing primes etc),
|
||||
Computational Efficiency and a formal proof of RSA.
|
||||
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://mathworld.wolfram.com/RSAEncryption.html"
|
||||
> Pure Mathematical description of RSA </a> <img SRC="blu_bullet_half.gif">
|
||||
A pure mathematical description without examples. Very well hyper-linked to all mathematical terms used.
|
||||
|
||||
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://pajhome.org.uk/crypt/rsa/"
|
||||
> Algorithm run though </a> <img SRC="blu_bullet_half.gif">
|
||||
A run though a complete key generation and encryption sequence
|
||||
using small numbers. Uses the variable 'm' where most texts
|
||||
use 'phi'. Also a Java implementation example.
|
||||
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://world.std.com/~franl/crypto/rsa-example.html"
|
||||
> Simplified Algorithm run though </a> <img SRC="blu_bullet_half.gif">
|
||||
An example for a < 10 bit encrypted sequence. Misses out the phase of
|
||||
finding co-prime keys, but gives an overview of how RSA works.
|
||||
|
||||
|
||||
<h3> Social Impact </h3>
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://www.atmmarketplace.com/news_story.htm?i=16578"
|
||||
> ATM Market watch rates RSA technology in top ten inventions in Money </a> <img SRC="blu_bullet_half.gif">
|
||||
The financial world recognises the importance of RSA as a concept rating it
|
||||
alongside credit cards, electronic money transfer, bar codes and the spreadsheet.
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://www.stand.org.uk/dearjack/photostory.php3"
|
||||
> Open Letter to Jack Straw : Legal de-cryption Issue </a> <img SRC="blu_bullet_half.gif">
|
||||
A proposed ill-thought out law, forcing people to give up encryption keys (or be jailed)
|
||||
if it were even suspected they had them
|
||||
is mocked in this amusing photo-story.
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a HREF="http://news.bbc.co.uk/1/hi/special_report/1998/encryption/58499.stm"
|
||||
> Government unsure how to regulate encryption </a> <img SRC="blu_bullet_half.gif">
|
||||
An old link, but highlighting the dilemma of the pace of technology, and the
|
||||
difficulties in legislating for it.
|
||||
|
||||
<br><img SRC="red_bullet_half.gif">
|
||||
<a href="http://www.geocerts.com/?GoogleFRGN"
|
||||
> A Site selling RSA certificates </a> <img SRC="blu_bullet_half.gif">
|
||||
One commercial side of RSA and SSL. Certificates from 'trusted' authorities for sale.
|
||||
|
||||
<br>
|
||||
<br>
|
||||
<br>
|
||||
<center>
|
||||
<a href="javascript:history.back();">
|
||||
<img src=back.png align=center border=0> </a>
|
||||
</center>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
16
searchd
Executable file
16
searchd
Executable file
@ -0,0 +1,16 @@
|
||||
#!/bin/bash
|
||||
|
||||
# R.P. Clark : 02APR2004
|
||||
#
|
||||
# Takes three args
|
||||
# $1 y - the multiplier for phi
|
||||
# $2 phi
|
||||
# $3 e
|
||||
|
||||
# returns (1 + phi.y) % e, which if
|
||||
# 0 satisfies the criteria for being a
|
||||
# private key..
|
||||
|
||||
|
||||
echo " ( 1 + ( $1 * $2 ) ) % $3 " | bc
|
||||
|
||||
28
security.html
Normal file
28
security.html
Normal file
@ -0,0 +1,28 @@
|
||||
<html>
|
||||
|
||||
<body BGCOLOR="#00E0E0" link="#001fC0" vlink="#000080" text="#00000f">
|
||||
|
||||
|
||||
<title>Security considerations</title>
|
||||
|
||||
<h1>Security Considerations </h1>
|
||||
|
||||
This series of web pages uses direct calls to the unix shell
|
||||
and is therefore potentially vunerable to tampering and
|
||||
spoofing unix commands to be run as part of the typed in data.
|
||||
<br>
|
||||
<br>
|
||||
<br><br><img SRC="red_bullet_half.gif"> The Apache server is configured to run PHP and unix command shell as user 'apache' and has
|
||||
limited privilages.
|
||||
<br><br><img SRC="red_bullet_half.gif"> All input fields from forms and hidden variables are syntax checked (they must only contain digits).
|
||||
<br><br><img SRC="red_bullet_half.gif"> The processing requirements on this server are very high.
|
||||
The processor load will regularly go to 99% when performing RSA size calculations.
|
||||
The size of input values are therefore checked. If extremely large values
|
||||
were requested for instance, the server would appear to hang.
|
||||
<br>
|
||||
<br>
|
||||
<p>
|
||||
<a href="javascript:history.back();"> <img src=back.gif align=center border=0> </a>
|
||||
</p>
|
||||
</body>
|
||||
</html>
|
||||
Loading…
Reference in New Issue
Block a user