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‎bn.pdf

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‎bn.tex

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\begin{document}
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\frontmatter
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\pagestyle{empty}
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\title{LibTomMath User Manual \\ v0.38}
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\title{LibTomMath User Manual \\ v0.39}
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\author{Tom St Denis \\ tomstdenis@iahu.ca}
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\maketitle
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This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been

‎bn_error.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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static const struct {

‎bn_fast_mp_invmod.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* computes the modular inverse via binary extended euclidean algorithm,

‎bn_fast_mp_montgomery_reduce.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* computes xR**-1 == x (mod N) via Montgomery Reduction

‎bn_fast_s_mp_mul_digs.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* Fast (comba) multiplier

‎bn_fast_s_mp_mul_high_digs.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* this is a modified version of fast_s_mul_digs that only produces

‎bn_fast_s_mp_sqr.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* the jist of squaring...

‎bn_mp_2expt.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* computes a = 2**b

‎bn_mp_abs.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* b = |a|

‎bn_mp_add.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* high level addition (handles signs) */

‎bn_mp_add_d.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* single digit addition */

‎bn_mp_addmod.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* d = a + b (mod c) */

‎bn_mp_and.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* AND two ints together */

‎bn_mp_clamp.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* trim unused digits

‎bn_mp_clear.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* clear one (frees) */

‎bn_mp_clear_multi.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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#include <stdarg.h>
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‎bn_mp_cmp.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* compare two ints (signed)*/

‎bn_mp_cmp_d.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* compare a digit */

‎bn_mp_cmp_mag.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* compare maginitude of two ints (unsigned) */

‎bn_mp_cnt_lsb.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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static const int lnz[16] = {

‎bn_mp_copy.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* copy, b = a */

‎bn_mp_count_bits.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* returns the number of bits in an int */

‎bn_mp_div.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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#ifdef BN_MP_DIV_SMALL

‎bn_mp_div_2.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* b = a/2 */

‎bn_mp_div_2d.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* shift right by a certain bit count (store quotient in c, optional remainder in d) */

‎bn_mp_div_3.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* divide by three (based on routine from MPI and the GMP manual) */

‎bn_mp_div_d.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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static int s_is_power_of_two(mp_digit b, int *p)

‎bn_mp_dr_is_modulus.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* determines if a number is a valid DR modulus */

‎bn_mp_dr_reduce.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.

‎bn_mp_dr_setup.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* determines the setup value */

‎bn_mp_exch.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* swap the elements of two integers, for cases where you can't simply swap the

‎bn_mp_expt_d.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* calculate c = a**b using a square-multiply algorithm */

‎bn_mp_exptmod.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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‎bn_mp_exptmod_fast.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85

‎bn_mp_exteuclid.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* Extended euclidean algorithm of (a, b) produces

‎bn_mp_fread.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* read a bigint from a file stream in ASCII */

‎bn_mp_fwrite.c

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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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int mp_fwrite(mp_int *a, int radix, FILE *stream)

‎bn_mp_gcd.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* Greatest Common Divisor using the binary method */
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int k, u_lsb, v_lsb, res;
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/* either zero than gcd is the largest */
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if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
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if (mp_iszero (a) == MP_YES) {
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return mp_abs (b, c);
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}
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if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
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if (mp_iszero (b) == MP_YES) {
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return mp_abs (a, c);
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}
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/* optimized. At this point if a == 0 then
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* b must equal zero too
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*/
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if (mp_iszero (a) == 1) {
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mp_zero(c);
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return MP_OKAY;
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}
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/* get copies of a and b we can modify */
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if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
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return res;

‎bn_mp_get_int.c

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* The library is free for all purposes without any express
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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* get the lower 32-bits of an mp_int */

‎bn_mp_grow.c

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* The library is free for all purposes without any express
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* guarantee it works.
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* grow as required */

‎bn_mp_init.c

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* guarantee it works.
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*
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* Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
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* Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
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*/
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/* init a new mp_int */

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