sss.c

/*
 * ShamirSecretSharing - A C language implementation of Shamir's secret sharing algorithm
 * Copyright (C) 2015-2023 G. David Butler <gdb@dbSystems.com>
 *
 * This file is part of ShamirSecretSharing
 *
 * ShamirSecretSharing is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Lesser General Public License as published
 * by the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * ShamirSecretSharing is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public License
 * along with this program.  If not, see <https://www.gnu.org/licenses/>.
 */

/*
 * David Madore's implementation recast as a thread safe library.
 * Edited comments follow: (Unedited comments can be found in test/main.c)
 *
 * shsecret.c - Secret sharing algorithm
 * Written by David Madore
 * 2000/06/19 - Public Domain
 * http://www.madore.org/~david/programs/#prog_shsecret
 * ftp://ftp.madore.org/pub/madore/misc/shsecret.c
 *
 * This program implements a secret sharing algorithm.  In other
 * words, given a buffer (secret), it can produce N buffers of the same
 * size ("shares") such that knowing any M shares among N will be
 * sufficient to recover the secret (using this very code again)
 * whereas knowing less than M shares will yield _absolutely no
 * information_ on the secret, even with infinite computing power.
 * This program does both the sharing and the unsharing.
 * N can be anywhere up to 255. M can be anywhere up to N.
 *
 * Features:
 * + Small is beautiful.
 * + Efficient (for small MN).
 * + No bignum arithmetic (only eight-bit calculations).
 * + Completely portable (only assumes input chars are eight-bit).
 * + No dynamic memory allocation whatsoever (roughly 70k static).
 *
 * This computes the so-called "Lagrange interpolating polynomial" on
 * the input buffers through the given input points and outputs its
 * values at the given output points in the given output buffers.  The
 * Lagrange interpolating polynomial, if defined by M input points, is
 * completely determined by its value at _any_ M points.
 * In particular, if shsecret is run with secret.txt as input buffer for
 * point 0 and M-1 sets of random data for points 1 to M-1, it will
 * create a Lagrange interpolating polynomial of degree M which is
 * random except that its value at 0 is given by secret.txt; its value
 * at any point other than 0 is random.  Given M such values, the
 * polynomial can be recovered, hence, in particular, its value at 0
 * (the secret).
 *
 * Concise mathematical details (you may skip this but read below):
 * We work in the Galois field F256 with 256 elements represented by
 * the integers from 0 to 255.  The two operations ("addition" and
 * "multiplication") of the field are the exclusive or and the Conway
 * multiplication.  Exclusive or can be defined (by induction) as
 *   a xor b = the smallest n not equal to a' xor b for a'<a
 *             nor to a xor b' for b'<b
 * Similarly, Conway multiplication can be defined as
 *   a conmul b = the smallest n not equal to
 *                (a' conmul b) xor (a' conmul b') xor (a conmul b')
 *                for some a'<a and b'<b
 * Note that 0 and 1 in the field are the true 0 and 1.
 * Note that the field has characteristic 2, so substraction is
 * precisely the same thing as addition (namely, exclusive or);
 * nevertheless I will write + and - as needed in what follows for
 * greater clarity.
 * Suppose zi are the output points and xj the input points (for
 * various values of i and j); suppose yj is the input data for input
 * point xj (i.e. one byte of the corresponding input buffer).  We wish
 * to compute the output data ti corresponding to zi.  The polynomial
 * (Conway) product of the (X-xk) for k not equal to j is equal to 0
 * at every xk except xj where it is not zero; we call Ic[j] its
 * value at xj.  If we (Conway) divide the product of the (X-xk) by
 * Ic[j] we get a polynomial which is 1 at xj and 0 at every
 * other xk: call it Pj.  The sum (i.e. XOR) of the yj Pj is the
 * Lagrange interpolating polynomial: it takes value yj at each xj.
 * So its value at zi is the sum of the yj Pj(zi).  Now Pj(zi) is the
 * product of the (zi-xk) for k not equal to j, divdided by
 * Ic[j].  Call Oc[i] the product of the (zi-xk) for
 * _every_ k.  Then Pj(zi) is Oc[i] divided by the product of
 * (zi-xj) by Ic[j].  This is expression is the horrible
 * Cmt[Oc[i]][Cit[Cmt[Ic[j]]
 *     [Op[i]^Ip[j]]]]
 * further down in this program (here Op[i] is zi,
 * Ip[j] is xj and ^ is the XOR operation; and Cmt is
 * the table giving the Conway multiplication and Cit is the
 * table giving the Conway inverse operation).
 *
 * Note: your secret sharing system will only be secure provided you
 * feed the program with _cryptographically secure random numbers_.
 *
 * Plea: although I put this file in the Public Domain, I would very
 * much appreciate getting credit if credit is due.  Thank you.
 */

#include "sss.h"

#define CON_TABLES 1 /* use generated tables */

/* The below tables were generated with:
 *
 * unsigned char Cmt[256][256];
 * unsigned char Cit[256];
 * unsigned int i;
 * unsigned int j;
 *
 * fillCmt(Cmt);
 * puts("static const unsigned char Cmt[256][256] = {{");
 * for (i = 0; i < 256; ++i) {
 *   if (i)
 *     puts("},{");
 *   for (j = 0; j < 256; ++j) {
 *     if (j)
 *       putchar(',');
 *     else
 *       putchar(' ');
 *     printf("%u", Cmt[i][j]);
 *     if (!((j + 1) % 16))
 *       putchar('\n');
 *   }
 * }
 * puts("}};");
 *
 * fillCit(Cmt, Cit);
 * puts("static const unsigned char Cit[256] = {");
 * for (i = 0; i < 256; ++i) {
 *  if (i)
 *    putchar(',');
 *  else
 *    putchar(' ');
 *  printf("%u", Cit[i]);
 *  if (!((i + 1) % 16))
 *    putchar('\n');
 * }
 * puts("};");
 */

#if CON_TABLES

/* Multiplication table for the Conway product up to 255 */
static const unsigned char Cmt[256][256] = {{
 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
},{
 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31
,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47
,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63
,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79
,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95
,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111
,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127
,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143
,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159
,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175
,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191
,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207
,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223
,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239
,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255
},{
 0,2,3,1,8,10,11,9,12,14,15,13,4,6,7,5
,32,34,35,33,40,42,43,41,44,46,47,45,36,38,39,37
,48,50,51,49,56,58,59,57,60,62,63,61,52,54,55,53
,16,18,19,17,24,26,27,25,28,30,31,29,20,22,23,21
,128,130,131,129,136,138,139,137,140,142,143,141,132,134,135,133
,160,162,163,161,168,170,171,169,172,174,175,173,164,166,167,165
,176,178,179,177,184,186,187,185,188,190,191,189,180,182,183,181
,144,146,147,145,152,154,155,153,156,158,159,157,148,150,151,149
,192,194,195,193,200,202,203,201,204,206,207,205,196,198,199,197
,224,226,227,225,232,234,235,233,236,238,239,237,228,230,231,229
,240,242,243,241,248,250,251,249,252,254,255,253,244,246,247,245
,208,210,211,209,216,218,219,217,220,222,223,221,212,214,215,213
,64,66,67,65,72,74,75,73,76,78,79,77,68,70,71,69
,96,98,99,97,104,106,107,105,108,110,111,109,100,102,103,101
,112,114,115,113,120,122,123,121,124,126,127,125,116,118,119,117
,80,82,83,81,88,90,91,89,92,94,95,93,84,86,87,85
},{
 0,3,1,2,12,15,13,14,4,7,5,6,8,11,9,10
,48,51,49,50,60,63,61,62,52,55,53,54,56,59,57,58
,16,19,17,18,28,31,29,30,20,23,21,22,24,27,25,26
,32,35,33,34,44,47,45,46,36,39,37,38,40,43,41,42
,192,195,193,194,204,207,205,206,196,199,197,198,200,203,201,202
,240,243,241,242,252,255,253,254,244,247,245,246,248,251,249,250
,208,211,209,210,220,223,221,222,212,215,213,214,216,219,217,218
,224,227,225,226,236,239,237,238,228,231,229,230,232,235,233,234
,64,67,65,66,76,79,77,78,68,71,69,70,72,75,73,74
,112,115,113,114,124,127,125,126,116,119,117,118,120,123,121,122
,80,83,81,82,92,95,93,94,84,87,85,86,88,91,89,90
,96,99,97,98,108,111,109,110,100,103,101,102,104,107,105,106
,128,131,129,130,140,143,141,142,132,135,133,134,136,139,137,138
,176,179,177,178,188,191,189,190,180,183,181,182,184,187,185,186
,144,147,145,146,156,159,157,158,148,151,149,150,152,155,153,154
,160,163,161,162,172,175,173,174,164,167,165,166,168,171,169,170
},{
 0,4,8,12,6,2,14,10,11,15,3,7,13,9,5,1
,64,68,72,76,70,66,78,74,75,79,67,71,77,73,69,65
,128,132,136,140,134,130,142,138,139,143,131,135,141,137,133,129
,192,196,200,204,198,194,206,202,203,207,195,199,205,201,197,193
,96,100,104,108,102,98,110,106,107,111,99,103,109,105,101,97
,32,36,40,44,38,34,46,42,43,47,35,39,45,41,37,33
,224,228,232,236,230,226,238,234,235,239,227,231,237,233,229,225
,160,164,168,172,166,162,174,170,171,175,163,167,173,169,165,161
,176,180,184,188,182,178,190,186,187,191,179,183,189,185,181,177
,240,244,248,252,246,242,254,250,251,255,243,247,253,249,245,241
,48,52,56,60,54,50,62,58,59,63,51,55,61,57,53,49
,112,116,120,124,118,114,126,122,123,127,115,119,125,121,117,113
,208,212,216,220,214,210,222,218,219,223,211,215,221,217,213,209
,144,148,152,156,150,146,158,154,155,159,147,151,157,153,149,145
,80,84,88,92,86,82,94,90,91,95,83,87,93,89,85,81
,16,20,24,28,22,18,30,26,27,31,19,23,29,25,21,17
},{
 0,5,10,15,2,7,8,13,3,6,9,12,1,4,11,14
,80,85,90,95,82,87,88,93,83,86,89,92,81,84,91,94
,160,165,170,175,162,167,168,173,163,166,169,172,161,164,171,174
,240,245,250,255,242,247,248,253,243,246,249,252,241,244,251,254
,32,37,42,47,34,39,40,45,35,38,41,44,33,36,43,46
,112,117,122,127,114,119,120,125,115,118,121,124,113,116,123,126
,128,133,138,143,130,135,136,141,131,134,137,140,129,132,139,142
,208,213,218,223,210,215,216,221,211,214,217,220,209,212,219,222
,48,53,58,63,50,55,56,61,51,54,57,60,49,52,59,62
,96,101,106,111,98,103,104,109,99,102,105,108,97,100,107,110
,144,149,154,159,146,151,152,157,147,150,153,156,145,148,155,158
,192,197,202,207,194,199,200,205,195,198,201,204,193,196,203,206
,16,21,26,31,18,23,24,29,19,22,25,28,17,20,27,30
,64,69,74,79,66,71,72,77,67,70,73,76,65,68,75,78
,176,181,186,191,178,183,184,189,179,182,185,188,177,180,187,190
,224,229,234,239,226,231,232,237,227,230,233,236,225,228,235,238
},{
 0,6,11,13,14,8,5,3,7,1,12,10,9,15,2,4
,96,102,107,109,110,104,101,99,103,97,108,106,105,111,98,100
,176,182,187,189,190,184,181,179,183,177,188,186,185,191,178,180
,208,214,219,221,222,216,213,211,215,209,220,218,217,223,210,212
,224,230,235,237,238,232,229,227,231,225,236,234,233,239,226,228
,128,134,139,141,142,136,133,131,135,129,140,138,137,143,130,132
,80,86,91,93,94,88,85,83,87,81,92,90,89,95,82,84
,48,54,59,61,62,56,53,51,55,49,60,58,57,63,50,52
,112,118,123,125,126,120,117,115,119,113,124,122,121,127,114,116
,16,22,27,29,30,24,21,19,23,17,28,26,25,31,18,20
,192,198,203,205,206,200,197,195,199,193,204,202,201,207,194,196
,160,166,171,173,174,168,165,163,167,161,172,170,169,175,162,164
,144,150,155,157,158,152,149,147,151,145,156,154,153,159,146,148
,240,246,251,253,254,248,245,243,247,241,252,250,249,255,242,244
,32,38,43,45,46,40,37,35,39,33,44,42,41,47,34,36
,64,70,75,77,78,72,69,67,71,65,76,74,73,79,66,68
},{
 0,7,9,14,10,13,3,4,15,8,6,1,5,2,12,11
,112,119,121,126,122,125,115,116,127,120,118,113,117,114,124,123
,144,151,153,158,154,157,147,148,159,152,150,145,149,146,156,155
,224,231,233,238,234,237,227,228,239,232,230,225,229,226,236,235
,160,167,169,174,170,173,163,164,175,168,166,161,165,162,172,171
,208,215,217,222,218,221,211,212,223,216,214,209,213,210,220,219
,48,55,57,62,58,61,51,52,63,56,54,49,53,50,60,59
,64,71,73,78,74,77,67,68,79,72,70,65,69,66,76,75
,240,247,249,254,250,253,243,244,255,248,246,241,245,242,252,251
,128,135,137,142,138,141,131,132,143,136,134,129,133,130,140,139
,96,103,105,110,106,109,99,100,111,104,102,97,101,98,108,107
,16,23,25,30,26,29,19,20,31,24,22,17,21,18,28,27
,80,87,89,94,90,93,83,84,95,88,86,81,85,82,92,91
,32,39,41,46,42,45,35,36,47,40,38,33,37,34,44,43
,192,199,201,206,202,205,195,196,207,200,198,193,197,194,204,203
,176,183,185,190,186,189,179,180,191,184,182,177,181,178,188,187
},{
 0,8,12,4,11,3,7,15,13,5,1,9,6,14,10,2
,128,136,140,132,139,131,135,143,141,133,129,137,134,142,138,130
,192,200,204,196,203,195,199,207,205,197,193,201,198,206,202,194
,64,72,76,68,75,67,71,79,77,69,65,73,70,78,74,66
,176,184,188,180,187,179,183,191,189,181,177,185,182,190,186,178
,48,56,60,52,59,51,55,63,61,53,49,57,54,62,58,50
,112,120,124,116,123,115,119,127,125,117,113,121,118,126,122,114
,240,248,252,244,251,243,247,255,253,245,241,249,246,254,250,242
,208,216,220,212,219,211,215,223,221,213,209,217,214,222,218,210
,80,88,92,84,91,83,87,95,93,85,81,89,86,94,90,82
,16,24,28,20,27,19,23,31,29,21,17,25,22,30,26,18
,144,152,156,148,155,147,151,159,157,149,145,153,150,158,154,146
,96,104,108,100,107,99,103,111,109,101,97,105,102,110,106,98
,224,232,236,228,235,227,231,239,237,229,225,233,230,238,234,226
,160,168,172,164,171,163,167,175,173,165,161,169,166,174,170,162
,32,40,44,36,43,35,39,47,45,37,33,41,38,46,42,34
},{
 0,9,14,7,15,6,1,8,5,12,11,2,10,3,4,13
,144,153,158,151,159,150,145,152,149,156,155,146,154,147,148,157
,224,233,238,231,239,230,225,232,229,236,235,226,234,227,228,237
,112,121,126,119,127,118,113,120,117,124,123,114,122,115,116,125
,240,249,254,247,255,246,241,248,245,252,251,242,250,243,244,253
,96,105,110,103,111,102,97,104,101,108,107,98,106,99,100,109
,16,25,30,23,31,22,17,24,21,28,27,18,26,19,20,29
,128,137,142,135,143,134,129,136,133,140,139,130,138,131,132,141
,80,89,94,87,95,86,81,88,85,92,91,82,90,83,84,93
,192,201,206,199,207,198,193,200,197,204,203,194,202,195,196,205
,176,185,190,183,191,182,177,184,181,188,187,178,186,179,180,189
,32,41,46,39,47,38,33,40,37,44,43,34,42,35,36,45
,160,169,174,167,175,166,161,168,165,172,171,162,170,163,164,173
,48,57,62,55,63,54,49,56,53,60,59,50,58,51,52,61
,64,73,78,71,79,70,65,72,69,76,75,66,74,67,68,77
,208,217,222,215,223,214,209,216,213,220,219,210,218,211,212,221
},{
 0,10,15,5,3,9,12,6,1,11,14,4,2,8,13,7
,160,170,175,165,163,169,172,166,161,171,174,164,162,168,173,167
,240,250,255,245,243,249,252,246,241,251,254,244,242,248,253,247
,80,90,95,85,83,89,92,86,81,91,94,84,82,88,93,87
,48,58,63,53,51,57,60,54,49,59,62,52,50,56,61,55
,144,154,159,149,147,153,156,150,145,155,158,148,146,152,157,151
,192,202,207,197,195,201,204,198,193,203,206,196,194,200,205,199
,96,106,111,101,99,105,108,102,97,107,110,100,98,104,109,103
,16,26,31,21,19,25,28,22,17,27,30,20,18,24,29,23
,176,186,191,181,179,185,188,182,177,187,190,180,178,184,189,183
,224,234,239,229,227,233,236,230,225,235,238,228,226,232,237,231
,64,74,79,69,67,73,76,70,65,75,78,68,66,72,77,71
,32,42,47,37,35,41,44,38,33,43,46,36,34,40,45,39
,128,138,143,133,131,137,140,134,129,139,142,132,130,136,141,135
,208,218,223,213,211,217,220,214,209,219,222,212,210,216,221,215
,112,122,127,117,115,121,124,118,113,123,126,116,114,120,125,119
},{
 0,11,13,6,7,12,10,1,9,2,4,15,14,5,3,8
,176,187,189,182,183,188,186,177,185,178,180,191,190,181,179,184
,208,219,221,214,215,220,218,209,217,210,212,223,222,213,211,216
,96,107,109,102,103,108,106,97,105,98,100,111,110,101,99,104
,112,123,125,118,119,124,122,113,121,114,116,127,126,117,115,120
,192,203,205,198,199,204,202,193,201,194,196,207,206,197,195,200
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 0,22,43,61,78,88,101,115,135,145,172,186,201,223,226,244
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,91,162,5,252,68,189,26,227,126,135,32,217,97,152,63,198
,57,192,103,158,38,223,120,129,28,229,66,187,3,250,93,164
,124,133,34,219,99,154,61,196,89,160,7,254,70,191,24,225
,30,231,64,185,1,248,95,166,59,194,101,156,36,221,122,131
,207,54,145,104,208,41,142,119,234,19,180,77,245,12,171,82
,173,84,243,10,178,75,236,21,136,113,214,47,151,110,201,48
,148,109,202,51,139,114,213,44,177,72,239,22,174,87,240,9
,246,15,168,81,233,16,183,78,211,42,141,116,204,53,146,107
,39,222,121,128,56,193,102,159,2,251,92,165,29,228,67,186
,69,188,27,226,90,163,4,253,96,153,62,199,127,134,33,216
},{
 0,250,95,165,19,233,76,182,33,219,126,132,50,200,109,151
,82,168,13,247,65,187,30,228,115,137,44,214,96,154,63,197
,163,89,252,6,176,74,239,21,130,120,221,39,145,107,206,52
,241,11,174,84,226,24,189,71,208,42,143,117,195,57,156,102
,40,210,119,141,59,193,100,158,9,243,86,172,26,224,69,191
,122,128,37,223,105,147,54,204,91,161,4,254,72,178,23,237
,139,113,212,46,152,98,199,61,170,80,245,15,185,67,230,28
,217,35,134,124,202,48,149,111,248,2,167,93,235,17,180,78
,60,198,99,153,47,213,112,138,29,231,66,184,14,244,81,171
,110,148,49,203,125,135,34,216,79,181,16,234,92,166,3,249
,159,101,192,58,140,118,211,41,190,68,225,27,173,87,242,8
,205,55,146,104,222,36,129,123,236,22,179,73,255,5,160,90
,20,238,75,177,7,253,88,162,53,207,106,144,38,220,121,131
,70,188,25,227,85,175,10,240,103,157,56,194,116,142,43,209
,183,77,232,18,164,94,251,1,150,108,201,51,133,127,218,32
,229,31,186,64,246,12,169,83,196,62,155,97,215,45,136,114
},{
 0,251,93,166,23,236,74,177,41,210,116,143,62,197,99,152
,66,185,31,228,85,174,8,243,107,144,54,205,124,135,33,218
,131,120,222,37,148,111,201,50,170,81,247,12,189,70,224,27
,193,58,156,103,214,45,139,112,232,19,181,78,255,4,162,89
,104,147,53,206,127,132,34,217,65,186,28,231,86,173,11,240
,42,209,119,140,61,198,96,155,3,248,94,165,20,239,73,178
,235,16,182,77,252,7,161,90,194,57,159,100,213,46,136,115
,169,82,244,15,190,69,227,24,128,123,221,38,151,108,202,49
,188,71,225,26,171,80,246,13,149,110,200,51,130,121,223,36
,254,5,163,88,233,18,180,79,215,44,138,113,192,59,157,102
,63,196,98,153,40,211,117,142,22,237,75,176,1,250,92,167
,125,134,32,219,106,145,55,204,84,175,9,242,67,184,30,229
,212,47,137,114,195,56,158,101,253,6,160,91,234,17,183,76
,150,109,203,48,129,122,220,39,191,68,226,25,168,83,245,14
,87,172,10,241,64,187,29,230,126,133,35,216,105,146,52,207
,21,238,72,179,2,249,95,164,60,199,97,154,43,208,118,141
},{
 0,252,84,168,29,225,73,181,38,218,114,142,59,199,111,147
,50,206,102,154,47,211,123,135,20,232,64,188,9,245,93,161
,19,239,71,187,14,242,90,166,53,201,97,157,40,212,124,128
,33,221,117,137,60,192,104,148,7,251,83,175,26,230,78,178
,200,52,156,96,213,41,129,125,238,18,186,70,243,15,167,91
,250,6,174,82,231,27,179,79,220,32,136,116,193,61,149,105
,219,39,143,115,198,58,146,110,253,1,169,85,224,28,180,72
,233,21,189,65,244,8,160,92,207,51,155,103,210,46,134,122
,76,176,24,228,81,173,5,249,106,150,62,194,119,139,35,223
,126,130,42,214,99,159,55,203,88,164,12,240,69,185,17,237
,95,163,11,247,66,190,22,234,121,133,45,209,100,152,48,204
,109,145,57,197,112,140,36,216,75,183,31,227,86,170,2,254
,132,120,208,44,153,101,205,49,162,94,246,10,191,67,235,23
,182,74,226,30,171,87,255,3,144,108,196,56,141,113,217,37
,151,107,195,63,138,118,222,34,177,77,229,25,172,80,248,4
,165,89,241,13,184,68,236,16,131,127,215,43,158,98,202,54
},{
 0,253,86,171,25,228,79,178,46,211,120,133,55,202,97,156
,34,223,116,137,59,198,109,144,12,241,90,167,21,232,67,190
,51,206,101,152,42,215,124,129,29,224,75,182,4,249,82,175
,17,236,71,186,8,245,94,163,63,194,105,148,38,219,112,141
,136,117,222,35,145,108,199,58,166,91,240,13,191,66,233,20
,170,87,252,1,179,78,229,24,132,121,210,47,157,96,203,54
,187,70,237,16,162,95,244,9,149,104,195,62,140,113,218,39
,153,100,207,50,128,125,214,43,183,74,225,28,174,83,248,5
,204,49,154,103,213,40,131,126,226,31,180,73,251,6,173,80
,238,19,184,69,247,10,161,92,192,61,150,107,217,36,143,114
,255,2,169,84,230,27,176,77,209,44,135,122,200,53,158,99
,221,32,139,118,196,57,146,111,243,14,165,88,234,23,188,65
,68,185,18,239,93,160,11,246,106,151,60,193,115,142,37,216
,102,155,48,205,127,130,41,212,72,181,30,227,81,172,7,250
,119,138,33,220,110,147,56,197,89,164,15,242,64,189,22,235
,85,168,3,254,76,177,26,231,123,134,45,208,98,159,52,201
},{
 0,254,87,169,21,235,66,188,42,212,125,131,63,193,104,150
,18,236,69,187,7,249,80,174,56,198,111,145,45,211,122,132
,35,221,116,138,54,200,97,159,9,247,94,160,28,226,75,181
,49,207,102,152,36,218,115,141,27,229,76,178,14,240,89,167
,72,182,31,225,93,163,10,244,98,156,53,203,119,137,32,222
,90,164,13,243,79,177,24,230,112,142,39,217,101,155,50,204
,107,149,60,194,126,128,41,215,65,191,22,232,84,170,3,253
,121,135,46,208,108,146,59,197,83,173,4,250,70,184,17,239
,140,114,219,37,153,103,206,48,166,88,241,15,179,77,228,26
,158,96,201,55,139,117,220,34,180,74,227,29,161,95,246,8
,175,81,248,6,186,68,237,19,133,123,210,44,144,110,199,57
,189,67,234,20,168,86,255,1,151,105,192,62,130,124,213,43
,196,58,147,109,209,47,134,120,238,16,185,71,251,5,172,82
,214,40,129,127,195,61,148,106,252,2,171,85,233,23,190,64
,231,25,176,78,242,12,165,91,205,51,154,100,216,38,143,113
,245,11,162,92,224,30,183,73,223,33,136,118,202,52,157,99
},{
 0,255,85,170,17,238,68,187,34,221,119,136,51,204,102,153
,2,253,87,168,19,236,70,185,32,223,117,138,49,206,100,155
,3,252,86,169,18,237,71,184,33,222,116,139,48,207,101,154
,1,254,84,171,16,239,69,186,35,220,118,137,50,205,103,152
,8,247,93,162,25,230,76,179,42,213,127,128,59,196,110,145
,10,245,95,160,27,228,78,177,40,215,125,130,57,198,108,147
,11,244,94,161,26,229,79,176,41,214,124,131,56,199,109,146
,9,246,92,163,24,231,77,178,43,212,126,129,58,197,111,144
,12,243,89,166,29,226,72,183,46,209,123,132,63,192,106,149
,14,241,91,164,31,224,74,181,44,211,121,134,61,194,104,151
,15,240,90,165,30,225,75,180,45,210,120,135,60,195,105,150
,13,242,88,167,28,227,73,182,47,208,122,133,62,193,107,148
,4,251,81,174,21,234,64,191,38,217,115,140,55,200,98,157
,6,249,83,172,23,232,66,189,36,219,113,142,53,202,96,159
,7,248,82,173,22,233,67,188,37,218,112,143,52,203,97,158
,5,250,80,175,20,235,65,190,39,216,114,141,54,201,99,156
}};

/* Inversion table for the Conway multiplication */
static const unsigned char Cit[256] = {
 0,1,3,2,15,12,9,11,10,6,8,7,5,14,13,4
,170,160,109,107,131,139,116,115,228,234,92,89,73,77,220,209
,85,214,80,219,199,179,203,184,66,226,70,236,156,247,149,248
,255,182,189,240,120,164,174,127,142,100,98,134,193,152,145,205
,119,207,40,227,112,195,42,237,76,28,186,97,72,29,177,103
,34,218,104,253,215,32,242,110,93,27,151,123,26,88,124,158
,187,75,58,135,57,143,176,79,82,252,108,19,106,18,87,243
,68,194,117,23,22,114,206,64,52,165,150,91,94,159,175,55
,238,146,138,20,196,222,59,99,224,155,130,21,200,211,56,101
,204,62,129,239,249,46,122,90,61,192,225,137,44,246,95,125
,17,171,181,212,53,121,244,232,190,217,16,161,251,230,54,126
,102,78,198,37,213,162,49,254,39,202,74,96,241,50,168,216
,153,60,113,69,132,223,178,36,140,210,185,38,144,63,118,65
,221,31,201,141,163,180,33,84,191,169,81,35,30,208,133,197
,136,154,41,67,24,235,173,250,167,245,25,229,43,71,128,147
,51,188,86,111,166,233,157,45,47,148,231,172,105,83,183,48
};

#else /* CON_TABLES */

static void
fillCmt(
  unsigned char cmt[][256]
){
  /* Multiplication table for the first 8 powers of two under Conway
   * multiplication.  DO NOT CHANGE THIS UNDER ANY CIRCUMSTANCES. */
  static const unsigned char cmp[8][8] = {
   {   1,   2,   4,   8,  16,  32,  64, 128, }
  ,{   2,   3,   8,  12,  32,  48, 128, 192, }
  ,{   4,   8,   6,  11,  64, 128,  96, 176, }
  ,{   8,  12,  11,  13, 128, 192, 176, 208, }
  ,{  16,  32,  64, 128,  24,  44,  75, 141, }
  ,{  32,  48, 128, 192,  44,  52, 141, 198, }
  ,{  64, 128,  96, 176,  75, 141, 103, 185, }
  ,{ 128, 192, 176, 208, 141, 198, 185, 222, }
  };
  unsigned int i;
  unsigned int j;
  unsigned int k;
  unsigned int l;
  unsigned char n;

  for (i = 0; i < 256; ++i)
    for (j = 0; j < 256; ++j) {
      n = 0;
      for (k = 0; i >> k; ++k)
        for (l = 0; j >> l; ++l)
          if (((i >> k) & 1) && ((j >> l) & 1))
            n ^= cmp[k][l];
      cmt[i][j] = n;
    }
}

static void
fillCit(
  unsigned char cmt[][256]
 ,unsigned char cit[]
){
  unsigned int i;
  unsigned int j;

  cit[0] = 0;
  for (i = 1; i < 256; ++i) {
    for (j = 1; cmt[i][j] != 1; ++j);
    cit[i] = j;
  }
}

#endif /* CON_TABLES */

void
sss(
  unsigned char *ip
 ,unsigned char *op
 ,unsigned char **iv
 ,unsigned char **ov
 ,unsigned int in
 ,unsigned int on
 ,unsigned int ln
){
#if !CON_TABLES
  unsigned char Cmt[256][256];
  unsigned char Cit[256];
#endif
  unsigned char ic[256]; /* cross product of points in-in (xi-xj) */
  unsigned char oc[256]; /* cross product of points out-in (zi-xj) */
  unsigned int i;
  unsigned int j;
  unsigned int k;
  unsigned char n;

#if !CON_TABLES
  fillCmt(Cmt);
  fillCit(Cmt, Cit);
#endif
  if (!ip || !op || !iv || !ov)
    return;
  /* do crosses */
  for (i = 0; i < in; ++i) {
    n = 1;
    for (j = 0; j < in; ++j)
      if (j != i)
        n = Cmt[n][*(ip + i) ^ *(ip + j)];
    ic[i] = n;
  }
  for (i = 0; i < on; ++i) {
    n = 1;
    for (j = 0; j < in; ++j)
      n = Cmt[n][*(op + i) ^ *(ip + j)];
    oc[i] = n;
  }
  /* do outputs */
  for (k = 0; k < ln; ++k) {
    for (i = 0; i < on; ++i) {
      n = 0;
      if (!oc[i]) {
        for (j = 0; j < in; ++j)
          if (*(op + i) == *(ip + j))
            n = *(*(iv + j) + k);
      } else
        for (j = 0; j < in; ++j)
          n ^= Cmt[*(*(iv + j) + k)][Cmt[oc[i]][Cit[Cmt[ic[j]][*(op + i) ^ *(ip + j)]]]];
      *(*(ov + i) + k) = n;
    }
  }
}