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readme.txt
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IMPORTANT! See UPDATE.TXT for latest changes
Then read FIRST.TXT
The distribution media contains the following files
README.TXT - This file
FIRST.TXT - Read this next
MSVISUAL.TXT - Microsoft Visual C++ V6.0 quick-start instructions
VC2005.TXT - Microsoft Visual C++ V8.0 quick-start instructions
BORLAND.TXT - Borland C quick-start instructions
ARM.TXT - ARM processor advice
SPARC.TXT - SPARC processor advice
ITANIUM.TXT - ITANIUM processor advice
FASTGF2M.TXT - How to speed up methods based on the field GF(2^m)
WIN64.TXT - 64-bit Windows advice
DEVCPP.TXT - DEV-CPP quick-start instructions
TEXASDSP.TXT - Texas C6713 DSP advice
AMD64.TXT - AMD64 processor advice
SSE2.TXT - SSE2 extensions advice
PIC32.TXT - PIC32 processor advice
POWERPC.TXT - POWERPC processor advice
LINUX.TXT - Some advice for Linux users
CYGWIN.TXT - How to install MIRACL using Cygwin
MANUAL.DOC - The Manual - read it!
PROBLEMS.TXT - Known problems with MIRACL
UPDATE.TXT - MIRACL Update History
KCMCOMBA.TXT - Using super-fast techniques
MAKEMCS.TXT - How to create your own .mcs file
DOUBLE.TXT - Using a double underlying type
FLOAT.TXT - Multiprecision floating-point
DOUBIG.TXT - How to allow "Double Precision" big types
EDWARDS.TXT - How to use Edwards curves for Elliptic curve crypto over Fp
MANAGED.TXT - How to build a "managed code" version of MIRACL for .NET applications
AESGCM.TXT - New support for AES-GCM mode of operation
BLACKFIN.TXT - For information on Analog devices Blackfin processors
CONFIG.C - Program to automatically generate a mirdef.h file
MEX.C - Program to insert fast macros into mrcomba.c/mrkcm.c
FPE.PDF - Paper on Format Preserving Encryption
In the subdirectory SOURCE
MRMULDV.ANY - Contains assembly language versions of muldiv,muldvm,
muldvd and muldvd2
MRMULDV.S - Version of the above for Linux i386 GCC
MRMULDV.S64 - Version of the above for Linux x86_64 GCC
MRMULDV.W64 - Version of the above for Windows x86-64 Visual Studio
MRMULDV.GCC - GCC version of above - 32-bit
MRMULDV.G64 - GCC version of above - 64-bit
MRMULDV.C - Version of the above for Win32
MRMULDV.CCC - Standard C version
MRMULDV.GPP - Version of the above for DJGPP GCC
MR*.C - MIRACL library source files
MRCOMBA.TPL - Template file for fast Comba method
MRCOMBA2.TPL - Template file for fast Comba method for GF2 arithmetic
MRKCM.TPL - Template file for fast KCM method
C.MCS - C macros for use with above
C1.MCS - Alternate C macros
C2.MCS - Alternate C macros
CS.MCS - Alternate C macros
CLMUL.MCS - MSC Intrinsic macros to use PCLMULQDQ instruction
GCCLMUL.MCS - GCC assembly language to support PCLMULQDQ instruction
SMARTMIP.MCS - Macros for Smartmips smart-card processor
MIPS.MCS - Macros for 32-bit Mips processor
MS86.MCS - Microsoft/Borland 80*86/Pentium macros for use with above
GCC386.MCS - GCC compiler compatible Pentium macros
ARM.MCS - ARM processor macros
GCCARM.MCS - GCC compatable version of the above
AVR.MCS - Atmel Atmega128 processor macros
MSP430.MCS - TI msp430 support (uses hardware multiplier)
BLACKFIN.MCS - Analog Devices Blackfin processor support
GCCMSP430.MCS - GCC compatable version of the above
SPARC32.MCS - 32-bit Sparc processor macros
SPARC64.MCS - 64-bit Sparc processor macros
ITANIUM.MCS - 64-bit Itanium processor macros
WIN64.MCS - 64-bit x86-64 Windows macros
AMD64.MCS - 64-bit AMD64 procesor macros
SSE2.MCS - Pentium 4 SSE2 instructions for Microsoft compiler
GCCPPC.MCS - PowerPC processor macros
GCCSSE2.MCS - Pentium 4 SSE2 instructions for GCC compiler
BMARK.C - Benchmark program for Public Key methods
IMRATIO.C - Benchmark program. Calculates S/M, I/M and J/M ratios over GF(p)
IMRATIO2.C - Benchmark program. Calculates S/M and I/M ratios over GF(2^m)
MERSENNE.C - Mersenne primes
FACT.C - Factorials
BRUTE.C - Brute-force factorisation
BRENT.C - Brent-pollard factoring
BRENT_MT.C - Example of generic Multi-Threading
HAIL.C - Hailstone numbers
PALIN.C - Palindromic numbers
GENKEY.C - Generate Public and Private keys
ENCODE.C - Encode using RSA method
DECODE.C - Decode using RSA method
ENCIPH.C - Encipher using Probabalistic method
DECIPH.C - Decipher using Probabalistic method
PK-DEMO.C - Demo of RSA/El Gamal/Diffie-Hellman/Elliptic Curve...
IDENTITY.C - ID based key exchange program
HILBERT.C - Solve special system of equations
SAMPLE.C - Example of Flash arithmetic
ROOTS.C - Square roots
POLLARD.C - Pollard's factoring method
WILLIAMS.C - William's factoring method
LENSTRA.C - Lenstra's factoring method
QSIEVE.C - The Quadratic Sieve
RATCALC.C - Rational Scientific Calculator
FACTOR.C - Factoring Program source
KANGAROO.C - Pollards Lambda method for discrete logs
INDEX.C - Pollards rho method for discrete logs
GENPRIME.C - Generates prime for above
LIMLEE.C - Lim-Lee prime generation
DSSETUP.C - Digital Signature Standard setup program
DSSGEN.C - Digital Signature Standard key generator program
DSSIGN.C - Digital Signature Standard signature program
DSSVER.C - Digital Signature Standard verification program
ECDH2M.C - Example EC Diffie-Hellman program for 32-bit constrained environments (static stack-only)
ECDH2M16.C - 16-bit version of the above
ECDH2M8.c - 8-bit version of the above
ROMAKER2.C - Program to automatically generate ROMS for above programs
ECDHP.C - ditto, over GF(p) - 32-bit
ECDHP32.C - ditto, over GF(p) - Nice ARM example (32-bits)
ECDHP8.C - ditto, over GF(p), 8-bit version
ECDHP16.C - ditto, over GF(p), 16-bit version
ROMAKER.C - Program to automatically generate ROMS for above programs
ECSGEN.C - DSS (Elliptic Curve GF(p) variation) key generator program
ECSIGN.C - DSS (Elliptic Curve GF(p) variation) signature program
ECSVER.C - DSS (Elliptic Curve GF(p) variation) verification program
ECSGEN_S.C - DSS (Elliptic Curve GF(p) variation) key generator program (static stack-only version)
ECSIGN_S.C - DSS (Elliptic Curve GF(p) variation) signature program (static stack-only version)
ECSVER_S.C - DSS (Elliptic Curve GF(p) variation) verification program (static stack-only version)
ECSGEN2.C - DSS (Elliptic Curve GF(2^m) variation) key generator program
ECSIGN2.C - DSS (Elliptic Curve GF(2^m) variation) signature program
ECSVER2.C - DSS (Elliptic Curve GF(2^m) variation) verification program
ECSGEN2S.C - DSS (Elliptic Curve GF(2^m) variation) key generator program (static stack-only version)
ECSIGN2S.C - DSS (Elliptic Curve GF(2^m) variation) signature program (static stack-only version)
ECSVER2S.C - DSS (Elliptic Curve GF(2^m) variation) verification program (static stack-only version)
BRICK.C - Brickell's method for fast exponentiation
EBRICK.C - Same for GF(p) Elliptic Curves
EBRICK2.C - Same for GF(2^m) Elliptic Curves
BIG.CPP - Big function implementations
ZZN.CPP - ZZn function implementations
ECN.CPP - ECn function implementations
ECNZZN.CPP - ECn <-> ZZn functions
EC2.CPP - EC2 function implementations
GF2M.CPP - GF(2^m) function implementations
CRT.CPP - Crt function implementations
FLASH.CPP - Flash function implementations
FLOATING.CPP - Float function implementations
PAL_ENC.CPP - Paillier Homomorphic Encryption Program
PAL_DEC.CPP - Paillier Homomorphic Decryption Program
THREADWN.CPP - Example of Windows Multi-threading
THREADUX.CPP - Example of Unix Multi-Threading
THREADMP.CPP - Example of openMP Multi-Threading
FINDBASE.CPP - Find irreducible polynomial for GF(2^m) programs
IRP.CPP - Generates code to implement irreducible polynomial
NEWBASIS.CPP - Converts from one irreducible polynomial representation to another
FACT.CPP - Example C++ source (uses BIG.H)
HAIL.CPP - " "
PALIN.CPP - " "
BRUTE.CPP - " "
MERSENNE.CPP - " "
QSIEVE.CPP - " "
GENKEY.CPP - " "
ENCODE.CPP - " "
DECODE.CPP - " "
ENCIPH.CPP - " "
DECIPH.CPP - " "
PK-DEMO.CPP - " "
LIMLEE.CPP - " "
DSSETUP.CPP - " "
DSSGEN.CPP - " "
DSSIGN.CPP - " "
DSSVER.CPP - " "
KANGAROO.CPP - " "
INDEX.CPP - " "
GENPRIME.CPP - " "
BRICK.CPP - " "
EBRICK.CPP - Example C++ source (uses ECN.H)
ECSGEN.CPP - " "
ECSIGN.CPP - " "
ECSVER.CPP - " "
EBRICK2.CPP - Example C++ source (uses EC2.H)
ECSGEN2.CPP - " "
ECSIGN2.CPP - " "
ECSVER2.CPP - " "
POLLARD.CPP - Example C++ source (uses ZZN.H)
WILLIAMS.CPP - " "
LENSTRA.CPP - " "
BRENT.CPP - " "
SAMPLE.CPP - Example C++ source (uses FLASH.H)
ROOTS.CPP - " "
HILBERT.CPP - " "
FSAMPLE.CPP - Example C++ source (uses FLOATING.H)
CARDANO.CPP - Example C++ source (uses ZZn2.H)
BP160.ECS - Brainpool 160-bit GF(p) curve
BPT160.ECS - Brainpool 160-bit GF(p) twisted curve
SECP160/192/224/256/521.ecs - Parameter files for some standard GF(p) elliptic curves
NIST163/233/283/571.ecs - Parameter files for standard GF(2^m) elliptic curves
KOB163/233/283/571.ecs - Parameter files for GF(2^m) Koblitz curves
EDWARDS.ECS - Parameter file for an Edwards GF(p) elliptic curve
Note how readable the C++ versions of the example programs look.
In the subdirectory SOURCE\CURVE
CM.CPP - Complex Multiplication - creates elliptic curves
VARIABLE.H - Dummy Variable class
POLY.H - Polynomial Class definition, elements from ZZn
POLY.CPP - Polynomial Arithmetic with ZZn coefficients
POLY2.H - Polynomial Class definition, elements from GF(2^m)
POLY2.CPP - Polynomial Arithmetic with GF(2^m) coefficients
FLPOLY.H - Polynomial Class definition, float elements
FLPOLY.CPP - Polynomial arithmetic with float coefficients
COMPLEX.H - Complex Float class definition
COMPLEX.CPP - Complex Float class arithmetic
CM.TXT - How to build the CM application
POLYMOD.H - Polynomials mod a Polynomial - Class Definition
POLYMOD.CPP - ZZn Polynomial arithmetic wrt a Polynomial Modulus
POLY2MOD.H - Polynomials mod a Polynomial - Class Definition
POLY2MOD.CPP - GF(2^m) Polynomial arithmetic wrt a Polynomial Modulus
TRANS.CPP - A simple utility to convert elliptic curve to Weierstrass
SCHOOF.CPP - Schoof's method for counting points on a GF(p) elliptic curve
SCHOOF2.CPP - Schoof's method for counting points on a GF(2^m) elliptic curve
SCHOOF.TXT - How to build the schoof Application
SCHOOF2.TXT - How to build the schoof2 Application
PS_BIG.H - Power series with Big coefficients - Class Definition
PS_BIG.CPP - Power Series Arithmetic
PS_ZZN.H - Power series with ZZN coefficients - Class Definition
PS_ZZN.CPP - Power Series Arithmetic
POLYXY.H - Bivariate Polynomials - Class Definition
POLYXY.CPP - Bivariate Polynomilas - Implementation
POLY2XY.H - Bivariate Polynomials - Class Definition
POLY2XY.CPP - Bivariate Polynomilas - Implementation
MUELLER.CPP - Program to generate Modular Polynomials
PROCESS.CPP - Program to process Modular Polynomials wrt a prime modulus
SEA.CPP - Schoof-Elkies-Atkin-Mueller algorithm
SEA.TXT - How to build the MUELLER/PROCESS/SEA applications
WEIL.CPP - Calculates number of points on curve over extension field
GLV.CPP - Calculates a GLV decomposition
In the subdirectory SOURCE\P1363
P1363.H - P1363 Header File
P1363.C - P1363 implementation file
TEST1363.c - test driver for P1363 implementation
RSA.C - quick start RSA application
OCTET.C - OCTET string handler
OCTET.H - OCTET header
ECDH.C - Elliptic Curve Code
ECDH.H - Elliptic Curve Header
TESTECC.C - Typical MIRACL Elliptic Curve API Implementation - thread-safe - no heap
In the subdirectory SOURCE\CURVE\PAIRING
BLS_SIGN.CPP - Boneh-Lynn-Shacham signature
BLS_VER.CPP - Boneh-Lynn-Shacham signature verification
GF2M4X.H - GF(2^4m) arithmetic - Header file
GF2M4X.CPP - GF(2^4m) arithmetic - Implementation file
GF2M6X.H - GF(2^6m) arithmetic - Header file
GF2M6X.CPP - GF(2^6m) arithmetic - Implementation file
GF2M12X.H - GF(2^12m) arithmetic - Header file
GF2M12X.CPP - GF(2^12m) arithmetic - Implementation file
SF2M12X.H - GF(2^12m) special extension arithmetic - Header file
SF2M12X.CPP - GF(2^12m) special extension arithmetic - Implementation file
ECN2.H - Elliptic curves over Fp2 - Header file
ECN2.CPP - Elliptic curves over Fp2 - Implementation file
ECN4.H - Elliptic curves over Fp4 - Header file
ECN4.CPP - Elliptic curves over Fp4 - Implementation file
ECN6.H - Elliptic curves over Fp6 - Header file
ECN6.CPP - Elliptic curves over Fp6 - Implementation file
ECN8.H - Elliptic curves over Fp8 - Header file
ECN8.CPP - Elliptic curves over Fp8 - Implementation file
ZZN2.H - Fp2 arithmetic - Header file
ZZN2.CPP - Fp2 arithmetic - Implementation file
ZZN3.H - Fp3 arithmetic - Header file
ZZN3.CPP - Fp3 arithmetic - Implementation file
ZZN4.H - Fp4 arithmetic - Header file
ZZN4.CPP - Fp4 arithmetic - Implementation file
ZZN8.H - Fp8 arithmetic - Header file
ZZN8.CPP - Fp8 arithmetic - Implementation file
ECN3.H/.CPP - Elliptic curves over Fp3
ZZN6.H/.CPP - Fp6 arithmetic - 2 over 3
ZZN6a.H/.CPP - Fp6 arithmetic - 3 over 2
ZZN12.H/.CPP - Fp12 arithmetic - 2 over 3 over 2
ZZN12a.H/.CPP- Fp12 arithmetic - 3 over 2 over 2
ZZN12b.H/.CPP- Fp12 arithmetic - 2 over 2 over 3
ZZN18.H/.CPP - Fp18 arithmetic - 3 over 2 over 3
ZZN24.H/.CPP - Fp24 arithmetic - 3 over 2 over 2 over 2
ZZN36.H/.CPP - Fp36 arithmetic - 3 over 2 over 2 over 3
MNT.CPP - Program to generate MNT elliptic curves
MNT.ECS - Non-supersingular curve, k=6, created by CM from MNT output
FREEMAN.CPP - Program to generate k=10 Freeman curves
FOLKLORE.CPP - program to create pairing-friendly non-SS curves
IRRED.CPP - Finds irreducible polynomial - Experimental!
AKE.TXT - Some explanation for these programs.
AKE6MNTT.CPP - Authenticated Key Exchange, MNT k=6 curve - Experimental! 1-3-6 tower
AKE6MNTX.CPP - Authenticated Key Exchange, MNT k=6 curve - Experimental! Uses "compositum" tower.
AKE6MNTA.CPP - Authenticated Key Exchange, MNT k=6 curve - Experimental! Uses "compositum" tower.
AKE6MNTT.C - Partial C version of the above
AKE4MNTT.CPP - Authenticated Key Exchange, k=4 - Experimental!
AKE4MNTT.C - Partial C version of the above
AKE4MNTA.CPP - Authenticated Key Exchange, k=4 - Experimental! - Ate pairing
AKE4MNTT.C - Partial C version of the above
AKE6FSTA.CPP - Authenticated Key Exchange, k=6, Ate pairing, sextic twist!
BN.CPP - Program to generate BN k=12 curves
KSS8.CPP - Program to generate KSS k=8 curves
KSS18.CPP - Program to generate KSS k=18 curves
BLS12.CPP - Program to generate BLS k=12 curves
BLS24.CPP - Program to generate BLS k=24 curves
BESTPAIR.CPP - Program to generate nice pairing-friendly curves
AKE12BNE.CPP - Authenticated Key Exchange, k=12, BN curve - Experimental!
AKE12BNA.CPP - Authenticated Key Exchange, k=12, BN curve, Ate pairing, sextic twist!
AKE12BNR.CPP - Authenticated Key Exchange, k=12, BN curve, R-ate pairing, sextic twist! 1-2-6-12 tower
AKE12BNX.CPP - Authenticated Key Exchange, k=12, BN curve, R-ate pairing, sextic twist! 1-2-4-12 tower
AKE12BLSA.CPP - Authenticated Key Exchange, k=12, BLS curve, ate pairing, sextic twist!
AKE18KSSX.CPP - Authenticated Key Exchange, k=18, KSS curve, R-ate pairing, sextic twist!
AKE24BLSA.CPP - Authenticated Key Exchange, k=18, BLS curve, ate pairing, sextic twist!
AKE2CPT.CPP - Same as above, but k=2 Cocks-Pinch curve
AKE2SST.CPP - Same as above, but uses a supersingular curve
AKE4CPT.CPP - Same as above, but k=4
AKEW4.CPP - Variation on the above
AKE8CPT.CPP - Same as above, but k=8 based
AKE8BWT.CPP - Variation on the above - uses Brezing-Weng curve
K2.ECS - Non-supersingular curve, k=2
K2SS.ECS - Supersingular curve, k=2
K4.ECS - Non-supersingular curve, k=4
K4MNT.ECS - MNT k=4 curve
K8.ECS - Non-supersingular curve, k=8
WENG.ECS - Non-supersingular curve, k=8
DL.CPP - Duursma-Lee Char 2 pairings
DL2.CPP - Truncnated-loop eta_T char 2 pairings
ETAT271.c - C version of eta_T pairing
BANDW.CPP - Brezing & Weng curves
AKE2NSST.CPP - Faster k=2 key exchange program - Not Superingular Curves
AKE2CPW.CPP - Uses New Weil pairing, k=2
AKE1KMT.CPP - Key Exchange program, for k=1 Koblitz-Menezes curve
MAKE_K1.CPP - Creates curves for the above
XK1.ECS - k=1 curve details
PAIRINGS.TXT - Details of pairing-based resources
PAIRING_1.H - High level type 1 pairings interface header
PAIRING_3.H - High level type 3 pairings interface header
AKE.CPP - Pairing-based Authentiated Key Exchange
BLS.CPP - Pairing-based Short Signature Scheme
DAA.CPP - Pairing-based Direct Anonymous Attestation
BMC.CPP - Pairing-based Signcryption scheme
BLMQ.CPP - Another pairing-based signcryption scheme
BB1.CPP - Boneh & Boyen BB1 IBE
FUZZY.CPP - Sahai & Waters Fuzzy IBE
PEKS.CPP - PKE with keyword search
HIBE.CPP - Hierarchical IBE (Lewko & Waters)
SK_1.CPP - Sakai-Kasahara IBE - type 1 pairing
SK_3.CPP - Sakai-Kasahara IBE - type 3 pairing
CPABE.CPP - Waters Attribute Based Cryptography
SOK.CPP - Sakai-Ohgishi-Kasahara key exchange (Type 1 pairing)
BGW.CPP - Boneh-Gentry-Waters Broadcast encryption
IPE.CPP - Inner Product Predicate Encryption
WANG.CPP - Key Exchange Protocol
CP_PAIR - AES-80 security from a Cocks-Pinch k=2 curve
MNT_PAIR.CPP - AES-80 security from an MNT k=6 curve
BN_PAIR.CPP - AES-128 security from a BN k=12 curve
KSS_PAIR.CPP - AES-192 security from a KSS k=18 curve
BLS_PAIR.CPP - AES-256 security from a BLS k=24 curve
SS2_PAIR.CPP - AES-80/128 security from a Supersingular k=4 curve over GF(2^m)
SSP_PAIR.CPP - AES-80/128 security from a Supersingular k=2 curve over GF(p)
In the subdirectory INCLUDE
MIRDEF.H16 - Standard hardware specific header file for 16-bit computer
MIRDEF.H32 - Header file for full 32-bit Computer
MIRDEF.H - Same as above
MIRDEF.H64 - Header file for full 64-bit Computer
MIRDEF.W64 - Header file for Microsoft 64-bit compiler
MIRDEF.HPC - Header file for pseudo-32 bit computer
MIRDEF.HAF - Header file for 16 bit use of 32 bit computer
MIRDEF.HIO - Integer-Only 32-bit header file
MIRDEF.HPP - Header file for full 64-bit Computer - C++ Library Build - see linux64_cpp
MIRDEF.MGW - Header file for 64-bit mingw build
MIRACL.H - Main MIRACL header
BIG.H - C++ header for 'big' numbers
FLASH.H - C++ header for 'flash' numbers
FLOATING.H - C++ header for 'float' numbers
ZZN.H - C++ header for 'big' numbers mod n
CRT.H - C++ header for chinese remainder thereom
ECN.H - C++ header for GF(p) Elliptic Curves
ECNZZN.H - ECn <-> ZZn functions
EC2.H - C++ header for GF(2^m) Elliptic Curves
GF2M.H - C++ header for GF(2^m)
BRICK.H - C++ header for Brickell's method
EBRICK.H - C++ header for Brickell's method (Elliptic Curve GF(p) version)
EBRICK2.H - C++ header for Brickell's method (Elliptic Curve GF(2^m) version)
In the subdirectory LIB
*DOIT.BAT - Batch files for constructing libraries and sample progs.
MINGW.BAT - Batch file to build library for 64-bit MINGW
MIRACL.MAK - John Kennedy's UNIX make file
LINUX - Linux bash script to build library - 32-bit
LINUX64 - Linux bash script to build library - 64-bit - C Library Build
LINUX64_CPP - Linux bash script to build library - 64-bit - C++ Library Build
To build the standard library on a standard OS, dump all of the MIRACL files
into a single directory, and move to that directory
(1) If using Windows and the Microsoft compiler, open a command window,
ensure paths are set correctly by executing the microsoft-supplied
vcvars32.bat or vcvars64.bat, and then execute either ms32doit.bat
or ms64doit.bat, depending on your system being 32-bits or 64-bits
(2) If using Linux, open a terminal window and simply execute either
"bash linux", or "bash linux64" for 64-bit systems
Otherwise
(1) Determine which of
mirdef.h64/mirdef.w64/mirdef.h32/mirdef.h16/mirdef.haf/mirdef.hpc etc
is suitable for you, and/or compile and run config.c to automatically
generate a suitable mirdef.h.
(2) If for performance reasons a non-portable version is to be built,
select suitable assembly language routines from mrmuldv.any, or
write them yourself (send us a copy!). Even better - produce a
.mcs file for the processor and use either the KCM or Comba method.
(3) Compile and link together the mr*.c components into an object library.
Also assemble and link in the assemble language component from
mrmuldv.any (if needed).
In the subdirectory EXE some precompiled example programs
FACT.EXE - Factorial program
ENCIPH.EXE - Enciphering program
DECIPH.EXE - Deciphering program
PUBLIC.KEY - Public key for use by enciphering program
PRIVATE.KEY - Private key for use by deciphering program
In the sub-directory FREE some FREEWARE 32-bit IBM PC Command prompt
specific applications. CM.EXE is free as well, but omitted here for space
reasons.
READ.TXT - Read this first
RATCALC.EXE - Rational Calculator
FACTOR.EXE - General purpose Factoring Program (80386+ only)
For maximum speed this is compiled as a true 32-bit
and runs in a 32-bit DOS Window
These files (ONLY!!) are FREEWARE, and may be freely copied
and distributed, unmodified. Copyright remains with CertiVox.