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December 24th, 2006
v0.40 -- Updated makefile to properly support LIBNAME
-- Fixed bug in fast_s_mp_mul_high_digs() which overflowed (line 83), thanks Valgrind!
April 4th, 2006
v0.39 -- Jim Wigginton pointed out my Montgomery examples in figures 6.4 and 6.6 were off by one, k should be 9 not 8
-- Bruce Guenter suggested I use --tag=CC for libtool builds where the compiler may think it's C++.
-- "mm" from sci.crypt pointed out that my mp_gcd was sub-optimal (I also updated and corrected the book)
-- updated some of the @@ tags in tommath.src to reflect source changes.
-- updated email and url info in all source files
Jan 26th, 2006
v0.38 -- broken makefile.shared fixed
-- removed some carry stores that were not required [updated text]
November 18th, 2005
v0.37 -- [Don Porter] reported on a TCL list [HEY SEND ME BUGREPORTS ALREADY!!!] that mp_add_d() would compute -0 with some inputs. Fixed.
-- [] reported the makefile.bcc was messed up. Fixed.
-- [Kevin Kenny] reported some issues with mp_toradix_n(). Now it doesn't require a min of 3 chars of output.
-- Made the make command renamable. Wee
August 1st, 2005
v0.36 -- LTM_PRIME_2MSB_ON was fixed and the "OFF" flag was removed.
-- [Peter LaDow] found a typo in the XREALLOC macro
-- [Peter LaDow] pointed out that mp_read_(un)signed_bin should have "const" on the input
-- Ported LTC patch to fix the prime_random_ex() function to get the bitsize correct [and the maskOR flags]
-- Kevin Kenny pointed out a stray //
-- David Hulton pointed out a typo in the textbook [mp_montgomery_setup() pseudo-code]
-- Neal Hamilton (Elliptic Semiconductor) pointed out that my Karatsuba notation was backwards and that I could use
unsigned operations in the routine.
-- Paul Schmidt pointed out a linking error in mp_exptmod() when BN_S_MP_EXPTMOD_C is undefined (and another for read_radix)
-- Updated makefiles to be way more flexible
March 12th, 2005
v0.35 -- Stupid XOR function missing line again... oops.
-- Fixed bug in invmod not handling negative inputs correctly [Wolfgang Ehrhardt]
-- Made exteuclid always give positive u3 output...[ Wolfgang Ehrhardt ]
-- [Wolfgang Ehrhardt] Suggested a fix for mp_reduce() which avoided underruns. ;-)
-- mp_rand() would emit one too many digits and it was possible to get a 0 out of it ... oops
-- Added montgomery to the testing to make sure it handles 1..10 digit moduli correctly
-- Fixed bug in comba that would lead to possible erroneous outputs when "pa < digs"
-- Fixed bug in mp_toradix_size for "0" [Kevin Kenny]
-- Updated chapters 1-5 of the textbook ;-) It now talks about the new comba code!
February 12th, 2005
v0.34 -- Fixed two more small errors in mp_prime_random_ex()
-- Fixed overflow in mp_mul_d() [Kevin Kenny]
-- Added mp_to_(un)signed_bin_n() functions which do bounds checking for ya [and report the size]
-- Added "large" diminished radix support. Speeds up things like DSA where the moduli is of the form 2^k - P for some P < 2^(k/2) or so
Actually is faster than Montgomery on my AMD64 (and probably much faster on a P4)
-- Updated the manual a bit
-- Ok so I haven't done the textbook work yet... My current freelance gig has landed me in France till the
end of Feb/05. Once I get back I'll have tons of free time and I plan to go to town on the book.
As of this release the API will freeze. At least until the book catches up with all the changes. I welcome
bug reports but new algorithms will have to wait.
December 23rd, 2004
v0.33 -- Fixed "small" variant for mp_div() which would munge with negative dividends...
-- Fixed bug in mp_prime_random_ex() which would set the most significant byte to zero when
no special flags were set
-- Fixed overflow [minor] bug in fast_s_mp_sqr()
-- Made the makefiles easier to configure the group/user that ltm will install as
-- Fixed "final carry" bug in comba multipliers. (Volkan Ceylan)
-- Matt Johnston pointed out a missing semi-colon in mp_exptmod
October 29th, 2004
v0.32 -- Added "makefile.shared" for shared object support
-- Added more to the build options/configs in the manual
-- Started the Depends framework, wrote to scan deps and
produce "callgraph.txt" ;-)
-- Wrote SC_RSA_1 which will enable close to the minimum required to perform
RSA on 32-bit [or 64-bit] platforms with LibTomCrypt
-- Merged in the small/slower mp_div replacement. You can now toggle which
you want to use as your mp_div() at build time. Saves roughly 8KB or so.
-- Renamed a few files and changed some comments to make depends system work better.
(No changes to function names)
-- Merged in new Combas that perform 2 reads per inner loop instead of the older
3reads/2writes per inner loop of the old code. Really though if you want speed
learn to use TomsFastMath ;-)
August 9th, 2004
v0.31 -- "profiled" builds now :-) new timings for Intel Northwoods
-- Added "pretty" build target
-- Update mp_init() to actually assign 0's instead of relying on calloc()
-- "Wolfgang Ehrhardt" <> found a bug in mp_mul() where if
you multiply a negative by zero you get negative zero as the result. Oops.
-- J Harper from PeerSec let me toy with his AMD64 and I got 60-bit digits working properly
[this also means that I fixed a bug where if sizeof(int) < sizeof(mp_digit) it would bug]
April 11th, 2004
v0.30 -- Added "mp_toradix_n" which stores upto "n-1" least significant digits of an mp_int
-- Johan Lindh sent a patch so MSVC wouldn't whine about redefining malloc [in weird dll modes]
-- Henrik Goldman spotted a missing OPT_CAST in mp_fwrite()
-- Tuned tommath.h so that when MP_LOW_MEM is defined MP_PREC shall be reduced.
[I also allow MP_PREC to be externally defined now]
-- Sped up mp_cnt_lsb() by using a 4x4 table [e.g. 4x speedup]
-- Added mp_prime_random_ex() which is a more versatile prime generator accurate to
exact bit lengths (unlike the deprecated but still available mp_prime_random() which
is only accurate to byte lengths). See the new LTM_PRIME_* flags ;-)
-- Alex Polushin contributed an optimized mp_sqrt() as well as mp_get_int() and mp_is_square().
I've cleaned them all up to be a little more consistent [along with one bug fix] for this release.
-- Added mp_init_set and mp_init_set_int to initialize and set small constants with one function
-- Removed /etclib directory [um LibTomPoly deprecates this].
-- Fixed mp_mod() so the sign of the result agrees with the sign of the modulus.
++ N.B. My semester is almost up so expect updates to the textbook to be posted to the
Jan 25th, 2004
v0.29 ++ Note: "Henrik" from the v0.28 changelog refers to Henrik Goldman ;-)
-- Added fix to mp_shrink to prevent a realloc when used == 0 [e.g. realloc zero bytes???]
-- Made the mp_prime_rabin_miller_trials() function internal table smaller and also
set the minimum number of tests to two (sounds a bit safer).
-- Added a mp_exteuclid() which computes the extended euclidean algorithm.
-- Fixed a memory leak in s_mp_exptmod() [called when Barrett reduction is to be used] which would arise
if a multiplication or subsequent reduction failed [would not free the temp result].
-- Made an API change to mp_radix_size(). It now returns an error code and stores the required size
through an "int star" passed to it.
Dec 24th, 2003
v0.28 -- Henrik Goldman suggested I add casts to the montomgery code [stores into mu...] so compilers wouldn't
spew [erroneous] diagnostics... fixed.
-- Henrik Goldman also spotted two typos. One in mp_radix_size() and another in mp_toradix().
-- Added fix to mp_shrink() to avoid a memory leak.
-- Added mp_prime_random() which requires a callback to make truly random primes of a given nature
(idea from chat with Niels Ferguson at Crypto'03)
-- Picked up a second wind. I'm filled with Gooo. Mission Gooo!
-- Removed divisions from mp_reduce_is_2k()
-- Sped up mp_div_d() [general case] to use only one division per digit instead of two.
-- Added the heap macros from LTC to LTM. Now you can easily [by editing four lines of tommath.h]
change the name of the heap functions used in LTM [also compatible with LTC via MPI mode]
-- Added bn_prime_rabin_miller_trials() which gives the number of Rabin-Miller trials to achieve
a failure rate of less than 2^-96
-- fixed bug in fast_mp_invmod(). The initial testing logic was wrong. An invalid input is not when
"a" and "b" are even it's when "b" is even [the algo is for odd moduli only].
-- Started a new manual [finally]. It is incomplete and will be finished as time goes on. I had to stop
adding full demos around half way in chapter three so I could at least get a good portion of the
manual done. If you really need help using the library you can always email me!
-- My Textbook is now included as part of the package [all Public Domain]
Sept 19th, 2003
v0.27 -- Removed changes.txt~ which was made by accident since "kate" decided it was
a good time to re-enable backups... [kde is fun!]
-- In mp_grow() "a->dp" is not overwritten by realloc call [re: memory leak]
Now if mp_grow() fails the mp_int is still valid and can be cleared via
mp_clear() to reclaim the memory.
-- Henrik Goldman found a buffer overflow bug in mp_add_d(). Fixed.
-- Cleaned up mp_mul_d() to be much easier to read and follow.
Aug 29th, 2003
v0.26 -- Fixed typo that caused warning with GCC 3.2
-- Martin Marcel noticed a bug in mp_neg() that allowed negative zeroes.
Also, Martin is the fellow who noted the bugs in mp_gcd() of 0.24/0.25.
-- Martin Marcel noticed an optimization [and slight bug] in mp_lcm().
-- Added fix to mp_read_unsigned_bin to prevent a buffer overflow.
-- Beefed up the comments in the baseline multipliers [and montgomery]
-- Added "mont" demo to the makefile.msvc in etc/
-- Optimized sign compares in mp_cmp from 4 to 2 cases.
Aug 4th, 2003
v0.25 -- Fix to mp_gcd again... oops (0,-a) == (-a, 0) == a
-- Fix to mp_clear which didn't reset the sign [Greg Rose]
-- Added mp_error_to_string() to convert return codes to strings. [Greg Rose]
-- Optimized fast_mp_invmod() to do the test for invalid inputs [both even]
first so temps don't have to be initialized if it's going to fail.
-- Optimized mp_gcd() by removing mp_div_2d calls for when one of the inputs
is odd.
-- Tons of new comments, some indentation fixups, etc.
-- mp_jacobi() returns MP_VAL if the modulus is less than or equal to zero.
-- fixed two typos in the header of each file :-)
-- LibTomMath is officially Public Domain [see LICENSE]
July 15th, 2003
v0.24 -- Optimized mp_add_d and mp_sub_d to not allocate temporary variables
-- Fixed mp_gcd() so the gcd of 0,0 is 0. Allows the gcd operation to be chained
e.g. (0,0,a) == a [instead of 1]
-- Should be one of the last release for a while. Working on LibTomMath book now.
-- optimized the pprime demo [/etc/pprime.c] to first make a huge table of single
digit primes then it reads them randomly instead of randomly choosing/testing single
digit primes.
July 12th, 2003
v0.23 -- Optimized mp_prime_next_prime() to not use mp_mod [via is_divisible()] in each
iteration. Instead now a smaller table is kept of the residues which can be updated
without division.
-- Fixed a bug in next_prime() where an input of zero would be treated as odd and
have two added to it [to move to the next odd].
-- fixed a bug in prime_fermat() and prime_miller_rabin() which allowed the base
to be negative, zero or one. Normally the test is only valid if the base is
greater than one.
-- changed the next_prime() prototype to accept a new parameter "bbs_style" which
will find the next prime congruent to 3 mod 4. The default [bbs_style==0] will
make primes which are either congruent to 1 or 3 mod 4.
-- fixed mp_read_unsigned_bin() so that it doesn't include both code for
the case DIGIT_BIT < 8 and >= 8
-- optimized div_d() to easy out on division by 1 [or if a == 0] and use
logical shifts if the divisor is a power of two.
-- the default DIGIT_BIT type was not int for non-default builds. Fixed.
July 2nd, 2003
v0.22 -- Fixed up mp_invmod so the result is properly in range now [was always congruent to the inverse...]
-- Fixed up s_mp_exptmod and mp_exptmod_fast so the lower half of the pre-computed table isn't allocated
which makes the algorithm use half as much ram.
-- Fixed the install script not to make the book :-) [which isn't included anyways]
-- added mp_cnt_lsb() which counts how many of the lsbs are zero
-- optimized mp_gcd() to use the new mp_cnt_lsb() to replace multiple divisions by two by a single division.
-- applied similar optimization to mp_prime_miller_rabin().
-- Fixed a bug in both mp_invmod() and fast_mp_invmod() which tested for odd
via "mp_iseven() == 0" which is not valid [since zero is not even either].
June 19th, 2003
v0.21 -- Fixed bug in mp_mul_d which would not handle sign correctly [would not always forward it]
-- Removed the #line lines from [was in violation of ISO C]
June 8th, 2003
v0.20 -- Removed the book from the package. Added the TDCAL license document.
-- This release is officially pure-bred TDCAL again [last officially TDCAL based release was v0.16]
June 6th, 2003
v0.19 -- Fixed a bug in mp_montgomery_reduce() which was introduced when I tweaked mp_rshd() in the previous release.
Essentially the digits were not trimmed before the compare which cause a subtraction to occur all the time.
-- Fixed up etc/tune.c a bit to stop testing new cutoffs after 16 failures [to find more optimal points].
Brute force ho!
May 29th, 2003
v0.18 -- Fixed a bug in s_mp_sqr which would handle carries properly just not very elegantly.
(e.g. correct result, just bad looking code)
-- Fixed bug in mp_sqr which still had a 512 constant instead of MP_WARRAY
-- Added Toom-Cook multipliers [needs tuning!]
-- Added efficient divide by 3 algorithm mp_div_3
-- Re-wrote mp_div_d to be faster than calling mp_div
-- Added in a donated BCC makefile and a single page LTM poster (
-- Added mp_reduce_2k which reduces an input modulo n = 2**p - k for any single digit k
-- Made the exptmod system be aware of the 2k reduction algorithms.
-- Rewrote mp_dr_reduce to be smaller, simpler and easier to understand.
May 17th, 2003
v0.17 -- Benjamin Goldberg submitted optimized mp_add and mp_sub routines. A new as well
as several smaller suggestions. Thanks!
-- removed call to mp_cmp in inner loop of mp_div and put mp_cmp_mag in its place :-)
-- Fixed bug in mp_exptmod that would cause it to fail for odd moduli when DIGIT_BIT != 28
-- mp_exptmod now also returns errors if the modulus is negative and will handle negative exponents
-- mp_prime_is_prime will now return true if the input is one of the primes in the prime table
-- Damian M Gryski ( found a index out of bounds error in the
mp_fast_s_mp_mul_high_digs function which didn't come up before. (fixed)
-- Refactored the DR reduction code so there is only one function per file.
-- Fixed bug in the mp_mul() which would erroneously avoid the faster multiplier [comba] when it was
allowed. The bug would not cause the incorrect value to be produced just less efficient (fixed)
-- Fixed similar bug in the Montgomery reduction code.
-- Added tons of (mp_digit) casts so the 7/15/28/31 bit digit code will work flawlessly out of the box.
Also added limited support for 64-bit machines with a 60-bit digit. Both thanks to Tom Wu (
-- Added new comments here and there, cleaned up some code [style stuff]
-- Fixed a lingering typo in mp_exptmod* that would set bitcnt to zero then one. Very silly stuff :-)
-- Fixed up mp_exptmod_fast so it would set "redux" to the comba Montgomery reduction if allowed. This
saves quite a few calls and if statements.
-- Added etc/mont.c a test of the Montgomery reduction [assuming all else works :-| ]
-- Fixed up etc/tune.c to use a wider test range [more appropriate] also added a x86 based addition which
uses RDTSC for high precision timing.
-- Updated demo/demo.c to remove MPI stuff [won't work anyways], made the tests run for 2 seconds each so its
not so insanely slow. Also made the output space delimited [and fixed up various errors]
-- Added logs directory, logs/graph.dem which will use gnuplot to make a series of PNG files
that go with the pre-made index.html. You have to build [via make timing] and run ltmtest first in the
root of the package.
-- Fixed a bug in mp_sub and mp_add where "-a - -a" or "-a + a" would produce -0 as the result [obviously invalid].
-- Fixed a bug in mp_rshd. If the count == a.used it should zero/return [instead of shifting]
-- Fixed a "off-by-one" bug in mp_mul2d. The initial size check on alloc would be off by one if the residue
shifting caused a carry.
-- Fixed a bug where s_mp_mul_digs() would not call the Comba based routine if allowed. This made Barrett reduction
slower than it had to be.
Mar 29th, 2003
v0.16 -- Sped up mp_div by making normalization one shift call
-- Sped up mp_mul_2d/mp_div_2d by aliasing pointers :-)
-- Cleaned up mp_gcd to use the macros for odd/even detection
-- Added comments here and there, mostly there but occasionally here too.
Mar 22nd, 2003
v0.15 -- Added series of prime testing routines to lib
-- Fixed up etc/tune.c
-- Added DR reduction algorithm
-- Beefed up the manual more.
-- Fixed up demo/demo.c so it doesn't have so many warnings and it does the full series of
-- Added "pre-gen" directory which will hold a ""'ed copy of the entire lib [done at
zipup time so its always the latest]
-- Added conditional casts for C++ users [boo!]
Mar 15th, 2003
v0.14 -- Tons of manual updates
-- cleaned up the directory
-- added MSVC makefiles
-- source changes [that I don't recall]
-- Fixed up the lshd/rshd code to use pointer aliasing
-- Fixed up the mul_2d and div_2d to not call rshd/lshd unless needed
-- Fixed up etc/tune.c a tad
-- fixed up demo/demo.c to output comma-delimited results of timing
also fixed up timing demo to use a finer granularity for various functions
-- fixed up demo/demo.c testing to pause during testing so my Duron won't catch on fire
[stays around 31-35C during testing :-)]
Feb 13th, 2003
v0.13 -- tons of minor speed-ups in low level add, sub, mul_2 and div_2 which propagate
to other functions like mp_invmod, mp_div, etc...
-- Sped up mp_exptmod_fast by using new code to find R mod m [e.g. B^n mod m]
-- minor fixes
Jan 17th, 2003
v0.12 -- re-wrote the majority of the makefile so its more portable and will
install via "make install" on most *nix platforms
-- Re-packaged all the source as seperate files. Means the library a single
file packagage any more. Instead of just adding "bn.c" you have to add
-- Renamed "bn.h" to "tommath.h"
-- Changes to the manual to reflect all of this
-- Used GNU Indent to clean up the source
Jan 15th, 2003
v0.11 -- More subtle fixes
-- Moved to gentoo linux [hurrah!] so made *nix specific fixes to the make process
-- Sped up the montgomery reduction code quite a bit
-- fixed up demo so when building timing for the x86 it assumes ELF format now
Jan 9th, 2003
v0.10 -- Pekka Riikonen suggested fixes to the radix conversion code.
-- Added baseline montgomery and comba montgomery reductions, sped up exptmods
[to a point, see bn.h for MONTGOMERY_EXPT_CUTOFF]
Jan 6th, 2003
v0.09 -- Updated the manual to reflect recent changes. :-)
-- Added Jacobi function (mp_jacobi) to supplement the number theory side of the lib
-- Added a Mersenne prime finder demo in ./etc/mersenne.c
Jan 2nd, 2003
v0.08 -- Sped up the multipliers by moving the inner loop variables into a smaller scope
-- Corrected a bunch of small "warnings"
-- Added more comments
-- Made "mtest" be able to use /dev/random, /dev/urandom or stdin for RNG data
-- Corrected some bugs where error messages were potentially ignored
-- add etc/pprime.c program which makes numbers which are provably prime.
Jan 1st, 2003
v0.07 -- Removed alot of heap operations from core functions to speed them up
-- Added a root finding function [and mp_sqrt macro like from MPI]
-- Added more to manual
Dec 31st, 2002
v0.06 -- Sped up the s_mp_add, s_mp_sub which inturn sped up mp_invmod, mp_exptmod, etc...
-- Cleaned up the header a bit more
Dec 30th, 2002
v0.05 -- Builds with MSVC out of the box
-- Fixed a bug in mp_invmod w.r.t. even moduli
-- Made mp_toradix and mp_read_radix use char instead of unsigned char arrays
-- Fixed up exptmod to use fewer multiplications
-- Fixed up mp_init_size to use only one heap operation
-- Note there is a slight "off-by-one" bug in the library somewhere
without the padding (see the source for comment) the library
crashes in libtomcrypt. Anyways a reasonable workaround is to pad the
numbers which will always correct it since as the numbers grow the padding
will still be beyond the end of the number
-- Added more to the manual
Dec 29th, 2002
v0.04 -- Fixed a memory leak in mp_to_unsigned_bin
-- optimized invmod code
-- Fixed bug in mp_div
-- use exchange instead of copy for results
-- added a bit more to the manual
Dec 27th, 2002
v0.03 -- Sped up s_mp_mul_high_digs by not computing the carries of the lower digits
-- Fixed a bug where mp_set_int wouldn't zero the value first and set the used member.
-- fixed a bug in s_mp_mul_high_digs where the limit placed on the result digits was not calculated properly
-- fixed bugs in add/sub/mul/sqr_mod functions where if the modulus and dest were the same it wouldn't work
-- fixed a bug in mp_mod and mp_mod_d concerning negative inputs
-- mp_mul_d didn't preserve sign
-- Many many many many fixes
-- Works in LibTomCrypt now :-)
-- Added iterations to the timing demos... more accurate.
-- Tom needs a job.
Dec 26th, 2002
v0.02 -- Fixed a few "slips" in the manual. This is "LibTomMath" afterall :-)
-- Added mp_cmp_mag, mp_neg, mp_abs and mp_radix_size that were missing.
-- Sped up the fast [comba] multipliers more [yahoo!]
Dec 25th,2002
v0.01 -- Initial release. Gimme a break.
-- Todo list,
add details to manual [e.g. algorithms]
more comments in code
example programs
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