| From: mrr@scss3.cl.msu.edu (Mark Riordan)
Newsgroups: sci.crypt,sci.math
Subject: List of Bignum packages (updated)
Date: 12 May 92 20:01:00 GMT
Organization: Michigan State University
Lines: 277
This is the file BIGNUMS.TXT from cl-next2.cl.msu.edu.
In response to Email requests, I have assembled this list of
large-integer arithmetic packages of which I have heard.
Last updated: 12 May 1992
For your convenience, I have placed copies of
some of these on cl-next2.cl.msu.edu (35.8.4.22). They are
available for anonymous FTP in the directory "bignum".
However, what I have may not be the most current version in all cases.
Also, this server does not allow connections from outside the
USA and Canada. (Sorry.)
Here they are, in no particular order:
mp
Multiple Precision package that comes with some Unixes
Multiple precision package accessed via -lmp flag on your
compiler. Provides +, -, *, /, gcd, exponentiation,
sqrt. Comes with SunOS, NeXT Mach, BBN Mach 1000,
and probably a few others. See "man mp".
Object code only, of course.
PARI
Henri Cohen, et al., Universite Bordeaux I, Paris, FRANCE
Multiple precision desk calculator and library routines.
Contains optimized assembly code for Motorola 68020,
semi-optimized code for SPARC, and apparently rather slow
generic C version. Does both integers and reals.
Does vectors and matrices as well as scalars.
Contains a number of advanced functions, some of which I've
never heard of. ("Weber's function"?)
Has a factorization function, primality test, & other related stuff.
Plenty of TEX documentation.
Public domain, but you can't distribute modified versions.
Available via anonymous FTP from math.ucla.edu. There seem to
be Mac- and NeXT-specific versions there in addition to:
Filename: pari-1.35a.tar.Z
Arithmetic in Global Fields (Arith)
Kevin R. Coombes, David R. Grant
Package of routines for arbitrary precision integers or
polynomials over finite fields. Includes basic +, -, *, /
and a few others like gcd. Source code in C.
Distributed under the terms of the GNU public license.
Includes man pages and TEX documentation.
Filename: arith.tar.Z
Arbitrary Precision Math Library
Lloyd Zusman Los Gatos, CA
C package which supports basic +, -, *, /. Provides for radix
points (i.e., non-integers). Not as polished as the others here.
Posted to comp.sources.misc in October 1988.
Filename: apml.tar.Z
BigNum
J. Vuillemin, INRIA, FRANCE, and others.
Distributed by Digital Equipment Paris Research Lab (DECPRL)
A "portable and efficient arbitrary-precision integer" package.
C code, with generic C "kernel", plus assembly "kernels" for
MC680x0, Intel i960, MIPS, NS32032, Pyramid, and of course VAX.
This is probably one of the better-known packages of this type.
Implements +, -, *, /, mod, plus logical operations OR, AND, XOR.
Both signed and unsigned arithmetic available.
Available via email from librarian@decprl.dec.com.
You will receive 5 shell archives. Give your postal address
and you will also receive printed documentation from France.
Package includes TEX documentation.
Publicly available for non-commercial use.
I removed this from my archive when I heard a rumor that PRL
doesn't like others to distribute it. Send to the email address above.
Lenstra's package
Arjen Lenstra Bellcore
Portable unsigned integer package written entirely in C.
Includes +, -, *, /, exponentiation, mod, primality testing,
sqrt, random number generator, and a few others. The package
was uncommented and undocumented; I have tried to add enough
comments to get by. This is the only of these packages that I
have actually used. It works well and is very portable.
I haven't done any benchmarks against the others, but the code
looks clever & Lenstra is an accomplished number theorist.
Unlike the other packages here, this one requires you to allocate
storage statically--only a problem if your numbers are really huge.
Arjen has placed the code in the public domain.
Filename: lenstra.tar.Z
lenstra_3
Arjen Lenstra, Bellcore
An improved version of Arjen's package above. This one
does signed arithmetic and can do dynamic memory management as
an option. Has a few new routines, too. "lenstra_3" contains
minor bugfixes to the previously-available "lenstra_2".
Filename: lenstra_3.c
bmp (Brent's Multiple Precision?)
R. P. Brent
1981 vintage FORTRAN code to do extended precision floating &
fixed point arithmetic. Includes most of the mathematical
functions you'd find in a FORTRAN run-time library.
This code is an ACM algorithm, number 524.
To obtain, send a mail message to netlib@ornl.gov
containing the line "send mp.f from bmp" or better yet, perhaps
just start with "help".
SPX
Kannan Alagappan & Joseph Tardo, DEC
This is a huge prototype public key authentication system
based on RSA. I mention it here because those who have heard
of SPX have probably correctly guessed that it contains a large
integer package and I want to inform you that the large integer
package it contains is indeed DEC's BigNum from France.
You can get a beta test copy of SPX from crl.dec.com (192.58.206.2).
Use it only for testing, as it "may" expire on a certain date.
amp (Antti's Multiple Precision?)
Antti Louko alo@kampi.hut.fi
Multiple precision integer package in C. Includes +, -, *, /, %,
pow, mod, 1/x mod y, random, sqrt, gcd. Available for non-commercial
use. The package includes "share-secret", a public key system based
on the Diffie-Hellman algorithm.
This is normally part of the well-known "des-dist.tar.Z",
but I have removed the DES part to avoid having to deal with
cryptographic export laws, and have named the result:
Filename: amp.tar.Z
gennum
Per Bothner U of Wisconsin-Madison
C++ routines and classes to do generic arithmetic, both
integer and rational.
Obtain from sevenlayer.cs.wis.edu.
MIRACL
(By someone in Dublin, Ireland)
Integer and fractional multiple precision package.
Includes factorization, primality testing, encryption.
Not public domain, apparently. It is available from the Austin
Code Works. (See ads in Byte Magazine or Dr. Dobbs.)
precision
Dave Barrett barrettd@tigger.colorado.edu
Multiple precision integer package in C with +,-,*,/, sqrt, rand,
mod, pow, log. Simple vector support. Does dynamic allocation of memory.
Free as long as you don't sell it or any program that uses it.
Filename: precision.tar.Z
UBASIC
Unknown (to me)
Multiple-precision version of the BASIC programming language,
for MS-DOS. Includes floating point. Said (by Keith Briggs)
to be pretty fast. Object only, I think. ervin@morekypr.bitnet
says: "This is the best package that I know of for
fast arithmetic. Has a version optimized for 386 machines. Includes
routines to do MPQS, the fastest currently known general factoring
algorithm. An additional file is at both sites to allow MPQS to use
hard drives so that it can factor up to 80 digits. Many number
theoretical functions are included in UBASIC. It allows over 2500
digits of precision."
Available via anonymous FTP from shape.mps.ohio-state.edu,
or simtel20.army.mil, or wuarchive.wustl.edu.
calc_v22
Unknown
MS-DOS C-like language that allows "infinite" precision.
Nice intrinsic functions. ervin@morekypr.bitnet reports problems
when changing precision on the fly.
See simtel20 or wuarchive.
briggs_arith
Keith Briggs (kbriggs@mundoe.maths.mu.oz.au)
Turbo Pascal 5 source for routines that do multiple-precision
+, -, *, /, sqrt, gcd, factoring, rand for integers; also includes
+, -, *, / and rand for rational numbers.
Filename: briggs_arith.pas
Institute fur Experimentelle Mathematik
Dr Gerhard Schneider (?)
Fast C multiple-precision subroutine library.
I don't know anything about it; sl25@ely.cl.cam.ac.uk says
to contact MAT420@DE0HRZ1A.BITNET for more info.
Postal Address:
Institute fur Experimentelle Mathematik
EllernStr 29
D4300 Essen-12 GERMANY
LongInt
Markus Mueller (mueller@komsys.tik.ethz.ch)
"Multi precision arithmetic written in MODULA-2, with the most time critical
parts written in Assembler. Includes basic arithmetics (+, -, *, /, %) as
well as arithmetics MODULO a number. An additional module provides a
collection of procedures for primality testing, gcd, multiplicative
inverse and more. The package is part of a Privacy Enhanced Mail (PEM)
package which includes a PEM mailer, RSA key generator and Certificate
generation tools."
Source is in Modula-2, C, and assembler for Sun 3. LongInt has
also been ported to MS-DOS under Logitech Modula-2 and Turbo
Assembler. Availability: free for university use (research and
education); otherwise, a source license is required. To obtain,
write or email to:
Markus Mueller
Bertastrasse 7
CH-8953 Dietikon
Switzerland
email: mueller@komsys.tik.ethz.ch
bignum-1.2
Henrik.Johansson@Nexus.Comm.SE
Bignum package written in portable C. Will in the future
conform to the Common Lisp functions that handles integers.
Currently includes +, -, *, /, exponentiation, "exptmod",
comparison, random numbers, and gcd.
Filename: bignum-1.2
GNU Multiple Precision
GNU (Free Software Foundation) multiple precision package.
I haven't looked at it yet. This is current as of April 1992,
but there may be a more recent version by the time you read
this. This package is very widely available on FTP sites.
Filename: gmp-1.2.tar.Z
Elliptic Curve Primality Proving
By Francois Morian, France.
Large package to prove the primality of any prime.
Includes Inria's BIGNUM package.
Obtained from ftp.inria.fr (128.93.1.26).
Filename: ecpp.V3.4.1.tar.Z
Bell's Arbitrary Precision Calculator
David I. Bell, Australia (dbell@pdact.pd.necisa.oz.au)
Arbitrary-precision calculator with good online help, C-like
language, many builtin functions, support for integers,
rational numbers (they work like floating point), complex numbers,
matrices, strings, lists, files, "objects". Includes
gcd, primality testing, even trig functions. Recommended.
(Large package, though.) Obtained from alt.sources.
Free for personal use.
Filename: bell-calc.tar.Z
Built-in support in other languages
Various
Multiple precision arithmetic is available in a number of
programming languages, such as Lisp and ABC (cf. mcsun.eu.net).
Perl (by Larry Wall, available from devvax.jpl.nasa.gov)
includes source, in Perl, for such a package, but it's probably
not suitable for serious use.
For some of these, source code may be available. This list is
long enough, so I'm not going to pursue it aggressively.
Thanks to Ed Vielmetti and several others who contributed to this list.
Mark Riordan riordanmr@clvax1.cl.msu.edu
Michigan State University
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