COMMAND-LINE MODULAR ARITHMETIC PROGRAMS
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1. bd_ModExp.exe computes the modular exponentiation a^e mod m
2. bd_ModInv.exe computes the modular inversion a^{-1} mod m
3. bd_ModMult.exe computes the modular multiplication a*b mod m
4. bd_Convert.exe converts a number in decimal format to hexadecimal and vice versa

To install
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Copy the EXE files into a directory on your current search path, such as C:\WINDOWS. Alternatively, copy to any directory and open the command prompt in that directory.

Syntax
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bd_ModExp [-x] a e m
calculates b = a^e mod m
Options:
-x = use hex numbers (default = decimal).

bd_ModInv [-x] a m
calculates b = a^{-1} mod m.
Options:
-x = use hex numbers (default = decimal).

bd_ModMult [-x] a b m
calculates c = a*b mod m
Options:
-x = use hex numbers (default = decimal).

bd_Convert [-x2d|-d2x] b
converts number b in decimal format to hexadecimal and vice versa
Options:
-d = b is in decimal, convert to hex (default)
-x = b is in hex, convert to decimal

Examples
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bd_modexp 14313 3 17947
13366

bd_modinv 3 17680
11787

bd_modexp 13366 11787 17947
14313

bd_modexp -x 3436 2e0b 461b
37e9 (i.e. the same calculation as before but in hex)

bd_convert -x 37e9
14313

bd_convert 65537
10001

Show that (m^e mod n).z^e mod n == (m.z)^e mod n 
for m=0xdead, z=0xbeef, n=0xcafefacade:
LHS:
bd_modexp -x dead 3 cafefacade
dead^3 mod cafefacade = 5ecc612b9d

bd_modexp -x beef 3 cafefacade
beef^3 mod cafefacade = bf65886479

bd_modmult -x 5ecc612b9d bf65886479 cafefacade
5ecc612b9d*bf65886479 mod cafefacade = c8b85f8ae9  --[1]

RHS:
bd_modmult -x dead beef cafefacade
dead*beef mod cafefacade = a6144983

bd_modexp -x a6144983 3 cafefacade
a6144983^3 mod cafefacade = c8b85f8ae9   --[2]
Thus LHS == RHS.

Limits
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The bd_mod functions accept in theory positive numbers of unlimited size. 
This may be limited by the character limit of your command line interpreter.


Written by David Ireland
Copyright (c) 2002-11 DI Management Services Pty Limited
Report bugs to http://www.di-mgt.com.au
First published: 14 November 2002
Last updated:    11 November 2011
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