view libtommath/bn_s_mp_toom_mul.c @ 1885:5d8dbb6fdab7

Fix SSH_PUBKEYINFO, limit characters, add tests We fix a bad_bufptr() failure from a previous commit. We now limit the allowed characters to those that will definitely be safe in a shell. Some scripts/programs may use arbitrary environment variables without escaping correctly - that could be a problem in a restricted environment. The current allowed set is a-z A-Z 0-9 .,_-+@ This also adds a test for SSH_PUBKEYINFO, by default it only runs under github actions (or "act -j build").
author Matt Johnston <matt@ucc.asn.au>
date Wed, 16 Mar 2022 17:17:23 +0800
parents 1051e4eea25a
children
line wrap: on
line source

#include "tommath_private.h"
#ifdef BN_S_MP_TOOM_MUL_C
/* LibTomMath, multiple-precision integer library -- Tom St Denis */
/* SPDX-License-Identifier: Unlicense */

/* multiplication using the Toom-Cook 3-way algorithm
 *
 * Much more complicated than Karatsuba but has a lower
 * asymptotic running time of O(N**1.464).  This algorithm is
 * only particularly useful on VERY large inputs
 * (we're talking 1000s of digits here...).
*/

/*
   This file contains code from J. Arndt's book  "Matters Computational"
   and the accompanying FXT-library with permission of the author.
*/

/*
   Setup from

     Chung, Jaewook, and M. Anwar Hasan. "Asymmetric squaring formulae."
     18th IEEE Symposium on Computer Arithmetic (ARITH'07). IEEE, 2007.

   The interpolation from above needed one temporary variable more
   than the interpolation here:

     Bodrato, Marco, and Alberto Zanoni. "What about Toom-Cook matrices optimality."
     Centro Vito Volterra Universita di Roma Tor Vergata (2006)
*/

mp_err s_mp_toom_mul(const mp_int *a, const mp_int *b, mp_int *c)
{
   mp_int S1, S2, T1, a0, a1, a2, b0, b1, b2;
   int B, count;
   mp_err err;

   /* init temps */
   if ((err = mp_init_multi(&S1, &S2, &T1, NULL)) != MP_OKAY) {
      return err;
   }

   /* B */
   B = MP_MIN(a->used, b->used) / 3;

   /** a = a2 * x^2 + a1 * x + a0; */
   if ((err = mp_init_size(&a0, B)) != MP_OKAY)                   goto LBL_ERRa0;

   for (count = 0; count < B; count++) {
      a0.dp[count] = a->dp[count];
      a0.used++;
   }
   mp_clamp(&a0);
   if ((err = mp_init_size(&a1, B)) != MP_OKAY)                   goto LBL_ERRa1;
   for (; count < (2 * B); count++) {
      a1.dp[count - B] = a->dp[count];
      a1.used++;
   }
   mp_clamp(&a1);
   if ((err = mp_init_size(&a2, B + (a->used - (3 * B)))) != MP_OKAY) goto LBL_ERRa2;
   for (; count < a->used; count++) {
      a2.dp[count - (2 * B)] = a->dp[count];
      a2.used++;
   }
   mp_clamp(&a2);

   /** b = b2 * x^2 + b1 * x + b0; */
   if ((err = mp_init_size(&b0, B)) != MP_OKAY)                   goto LBL_ERRb0;
   for (count = 0; count < B; count++) {
      b0.dp[count] = b->dp[count];
      b0.used++;
   }
   mp_clamp(&b0);
   if ((err = mp_init_size(&b1, B)) != MP_OKAY)                   goto LBL_ERRb1;
   for (; count < (2 * B); count++) {
      b1.dp[count - B] = b->dp[count];
      b1.used++;
   }
   mp_clamp(&b1);
   if ((err = mp_init_size(&b2, B + (b->used - (3 * B)))) != MP_OKAY) goto LBL_ERRb2;
   for (; count < b->used; count++) {
      b2.dp[count - (2 * B)] = b->dp[count];
      b2.used++;
   }
   mp_clamp(&b2);

   /** \\ S1 = (a2+a1+a0) * (b2+b1+b0); */
   /** T1 = a2 + a1; */
   if ((err = mp_add(&a2, &a1, &T1)) != MP_OKAY)                  goto LBL_ERR;

   /** S2 = T1 + a0; */
   if ((err = mp_add(&T1, &a0, &S2)) != MP_OKAY)                  goto LBL_ERR;

   /** c = b2 + b1; */
   if ((err = mp_add(&b2, &b1, c)) != MP_OKAY)                    goto LBL_ERR;

   /** S1 = c + b0; */
   if ((err = mp_add(c, &b0, &S1)) != MP_OKAY)                    goto LBL_ERR;

   /** S1 = S1 * S2; */
   if ((err = mp_mul(&S1, &S2, &S1)) != MP_OKAY)                  goto LBL_ERR;

   /** \\S2 = (4*a2+2*a1+a0) * (4*b2+2*b1+b0); */
   /** T1 = T1 + a2; */
   if ((err = mp_add(&T1, &a2, &T1)) != MP_OKAY)                  goto LBL_ERR;

   /** T1 = T1 << 1; */
   if ((err = mp_mul_2(&T1, &T1)) != MP_OKAY)                     goto LBL_ERR;

   /** T1 = T1 + a0; */
   if ((err = mp_add(&T1, &a0, &T1)) != MP_OKAY)                  goto LBL_ERR;

   /** c = c + b2; */
   if ((err = mp_add(c, &b2, c)) != MP_OKAY)                      goto LBL_ERR;

   /** c = c << 1; */
   if ((err = mp_mul_2(c, c)) != MP_OKAY)                         goto LBL_ERR;

   /** c = c + b0; */
   if ((err = mp_add(c, &b0, c)) != MP_OKAY)                      goto LBL_ERR;

   /** S2 = T1 * c; */
   if ((err = mp_mul(&T1, c, &S2)) != MP_OKAY)                    goto LBL_ERR;

   /** \\S3 = (a2-a1+a0) * (b2-b1+b0); */
   /** a1 = a2 - a1; */
   if ((err = mp_sub(&a2, &a1, &a1)) != MP_OKAY)                  goto LBL_ERR;

   /** a1 = a1 + a0; */
   if ((err = mp_add(&a1, &a0, &a1)) != MP_OKAY)                  goto LBL_ERR;

   /** b1 = b2 - b1; */
   if ((err = mp_sub(&b2, &b1, &b1)) != MP_OKAY)                  goto LBL_ERR;

   /** b1 = b1 + b0; */
   if ((err = mp_add(&b1, &b0, &b1)) != MP_OKAY)                  goto LBL_ERR;

   /** a1 = a1 * b1; */
   if ((err = mp_mul(&a1, &b1, &a1)) != MP_OKAY)                  goto LBL_ERR;

   /** b1 = a2 * b2; */
   if ((err = mp_mul(&a2, &b2, &b1)) != MP_OKAY)                  goto LBL_ERR;

   /** \\S2 = (S2 - S3)/3; */
   /** S2 = S2 - a1; */
   if ((err = mp_sub(&S2, &a1, &S2)) != MP_OKAY)                  goto LBL_ERR;

   /** S2 = S2 / 3; \\ this is an exact division  */
   if ((err = mp_div_3(&S2, &S2, NULL)) != MP_OKAY)               goto LBL_ERR;

   /** a1 = S1 - a1; */
   if ((err = mp_sub(&S1, &a1, &a1)) != MP_OKAY)                  goto LBL_ERR;

   /** a1 = a1 >> 1; */
   if ((err = mp_div_2(&a1, &a1)) != MP_OKAY)                     goto LBL_ERR;

   /** a0 = a0 * b0; */
   if ((err = mp_mul(&a0, &b0, &a0)) != MP_OKAY)                  goto LBL_ERR;

   /** S1 = S1 - a0; */
   if ((err = mp_sub(&S1, &a0, &S1)) != MP_OKAY)                  goto LBL_ERR;

   /** S2 = S2 - S1; */
   if ((err = mp_sub(&S2, &S1, &S2)) != MP_OKAY)                  goto LBL_ERR;

   /** S2 = S2 >> 1; */
   if ((err = mp_div_2(&S2, &S2)) != MP_OKAY)                     goto LBL_ERR;

   /** S1 = S1 - a1; */
   if ((err = mp_sub(&S1, &a1, &S1)) != MP_OKAY)                  goto LBL_ERR;

   /** S1 = S1 - b1; */
   if ((err = mp_sub(&S1, &b1, &S1)) != MP_OKAY)                  goto LBL_ERR;

   /** T1 = b1 << 1; */
   if ((err = mp_mul_2(&b1, &T1)) != MP_OKAY)                     goto LBL_ERR;

   /** S2 = S2 - T1; */
   if ((err = mp_sub(&S2, &T1, &S2)) != MP_OKAY)                  goto LBL_ERR;

   /** a1 = a1 - S2; */
   if ((err = mp_sub(&a1, &S2, &a1)) != MP_OKAY)                  goto LBL_ERR;


   /** P = b1*x^4+ S2*x^3+ S1*x^2+ a1*x + a0; */
   if ((err = mp_lshd(&b1, 4 * B)) != MP_OKAY)                    goto LBL_ERR;
   if ((err = mp_lshd(&S2, 3 * B)) != MP_OKAY)                    goto LBL_ERR;
   if ((err = mp_add(&b1, &S2, &b1)) != MP_OKAY)                  goto LBL_ERR;
   if ((err = mp_lshd(&S1, 2 * B)) != MP_OKAY)                    goto LBL_ERR;
   if ((err = mp_add(&b1, &S1, &b1)) != MP_OKAY)                  goto LBL_ERR;
   if ((err = mp_lshd(&a1, 1 * B)) != MP_OKAY)                    goto LBL_ERR;
   if ((err = mp_add(&b1, &a1, &b1)) != MP_OKAY)                  goto LBL_ERR;
   if ((err = mp_add(&b1, &a0, c)) != MP_OKAY)                    goto LBL_ERR;

   /** a * b - P */


LBL_ERR:
   mp_clear(&b2);
LBL_ERRb2:
   mp_clear(&b1);
LBL_ERRb1:
   mp_clear(&b0);
LBL_ERRb0:
   mp_clear(&a2);
LBL_ERRa2:
   mp_clear(&a1);
LBL_ERRa1:
   mp_clear(&a0);
LBL_ERRa0:
   mp_clear_multi(&S1, &S2, &T1, NULL);
   return err;
}

#endif