| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Reduction modulo sparse binary polynomials |
| 4 | * |
| 5 | * (c) 2004 Straylight/Edgeware |
| 6 | */ |
| 7 | |
| 8 | /*----- Licensing notice --------------------------------------------------* |
| 9 | * |
| 10 | * This file is part of Catacomb. |
| 11 | * |
| 12 | * Catacomb is free software; you can redistribute it and/or modify |
| 13 | * it under the terms of the GNU Library General Public License as |
| 14 | * published by the Free Software Foundation; either version 2 of the |
| 15 | * License, or (at your option) any later version. |
| 16 | * |
| 17 | * Catacomb is distributed in the hope that it will be useful, |
| 18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 20 | * GNU Library General Public License for more details. |
| 21 | * |
| 22 | * You should have received a copy of the GNU Library General Public |
| 23 | * License along with Catacomb; if not, write to the Free |
| 24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
| 25 | * MA 02111-1307, USA. |
| 26 | */ |
| 27 | |
| 28 | #ifndef CATACOMB_GFREDUCE_H |
| 29 | #define CATACOMB_GFREDUCE_H |
| 30 | |
| 31 | #ifdef __cplusplus |
| 32 | extern "C" { |
| 33 | #endif |
| 34 | |
| 35 | /*----- Header files ------------------------------------------------------*/ |
| 36 | |
| 37 | #include <stdio.h> |
| 38 | |
| 39 | #ifndef CATACOMB_GF_H |
| 40 | # include "gf.h" |
| 41 | #endif |
| 42 | |
| 43 | /*----- Data structures ---------------------------------------------------*/ |
| 44 | |
| 45 | typedef struct gfreduce_instr { |
| 46 | unsigned op; /* Instruction opcode */ |
| 47 | size_t arg; /* Immediate argument */ |
| 48 | } gfreduce_instr; |
| 49 | |
| 50 | enum { |
| 51 | GFRI_LOAD, /* Load @p[arg]@ */ |
| 52 | GFRI_LSL, /* XOR with @w << arg@ */ |
| 53 | GFRI_LSR, /* XOR with @w >> arg@ */ |
| 54 | GFRI_STORE, /* Store @p[arg]@ */ |
| 55 | GFRI_MAX |
| 56 | }; |
| 57 | |
| 58 | typedef struct gfreduce { |
| 59 | size_t lim; /* Word of degree bit */ |
| 60 | mpw mask; /* Mask for degree word */ |
| 61 | mp *p; /* Copy of the polynomial */ |
| 62 | size_t in; /* Number of instruction words */ |
| 63 | gfreduce_instr *iv; /* Vector of instructions */ |
| 64 | gfreduce_instr *fiv; /* Final-pass instruction suffix */ |
| 65 | } gfreduce; |
| 66 | |
| 67 | /*----- Functions provided ------------------------------------------------*/ |
| 68 | |
| 69 | /* --- @gfreduce_create@ --- * |
| 70 | * |
| 71 | * Arguments: @gfreduce *r@ = structure to fill in |
| 72 | * @mp *x@ = a (hopefully sparse) polynomial |
| 73 | * |
| 74 | * Returns: --- |
| 75 | * |
| 76 | * Use: Initializes a context structure for reduction. |
| 77 | */ |
| 78 | |
| 79 | extern void gfreduce_create(gfreduce */*r*/, mp */*p*/); |
| 80 | |
| 81 | /* --- @gfreduce_destroy@ --- * |
| 82 | * |
| 83 | * Arguments: @gfreduce *r@ = structure to free |
| 84 | * |
| 85 | * Returns: --- |
| 86 | * |
| 87 | * Use: Reclaims the resources from a reduction context. |
| 88 | */ |
| 89 | |
| 90 | extern void gfreduce_destroy(gfreduce */*r*/); |
| 91 | |
| 92 | /* --- @gfreduce_dump@ --- * |
| 93 | * |
| 94 | * Arguments: @const gfreduce *r@ = structure to dump |
| 95 | * @FILE *fp@ = file to dump on |
| 96 | * |
| 97 | * Returns: --- |
| 98 | * |
| 99 | * Use: Dumps a reduction context. |
| 100 | */ |
| 101 | |
| 102 | extern void gfreduce_dump(const gfreduce */*r*/, FILE */*fp*/); |
| 103 | |
| 104 | /* --- @gfreduce_do@ --- * |
| 105 | * |
| 106 | * Arguments: @const gfreduce *r@ = reduction context |
| 107 | * @mp *d@ = destination |
| 108 | * @mp *x@ = source |
| 109 | * |
| 110 | * Returns: Destination, @x@ reduced modulo the reduction poly. |
| 111 | */ |
| 112 | |
| 113 | extern mp *gfreduce_do(const gfreduce */*r*/, mp */*d*/, mp */*x*/); |
| 114 | |
| 115 | /* --- @gfreduce_sqrt@ --- * |
| 116 | * |
| 117 | * Arguments: @const gfreduce *r@ = pointer to reduction context |
| 118 | * @mp *d@ = destination |
| 119 | * @mp *x@ = some polynomial |
| 120 | * |
| 121 | * Returns: The square root of @x@ modulo @r->p@, or null. |
| 122 | */ |
| 123 | |
| 124 | extern mp *gfreduce_sqrt(const gfreduce */*r*/, mp */*d*/, mp */*x*/); |
| 125 | |
| 126 | /* --- @gfreduce_trace@ --- * |
| 127 | * |
| 128 | * Arguments: @const gfreduce *r@ = pointer to reduction context |
| 129 | * @mp *x@ = some polynomial |
| 130 | * |
| 131 | * Returns: The trace of @x@. (%$\Tr(x)=x + x^2 + \cdots + x^{2^{m-1}}$% |
| 132 | * if %$x \in \gf{2^m}$%). Since the trace is invariant under |
| 133 | * the Frobenius automorphism (i.e., %$\Tr(x)^2 = \Tr(x)$%), it |
| 134 | * must be an element of the base field, i.e., %$\gf{2}$%, and |
| 135 | * we only need a single bit to represent it. |
| 136 | */ |
| 137 | |
| 138 | extern int gfreduce_trace(const gfreduce */*r*/, mp */*x*/); |
| 139 | |
| 140 | /* --- @gfreduce_halftrace@ --- * |
| 141 | * |
| 142 | * Arguments: @const gfreduce *r@ = pointer to reduction context |
| 143 | * @mp *d@ = destination |
| 144 | * @mp *x@ = some polynomial |
| 145 | * |
| 146 | * Returns: The half-trace of @x@. |
| 147 | * (%$\HfTr(x)= x + x^{2^2} + \cdots + x^{2^{m-1}}$% |
| 148 | * if %$x \in \gf{2^m}$% with %$m$% odd). |
| 149 | */ |
| 150 | |
| 151 | extern mp *gfreduce_halftrace(const gfreduce */*r*/, mp */*d*/, mp */*x*/); |
| 152 | |
| 153 | /* --- @gfreduce_quadsolve@ --- * |
| 154 | * |
| 155 | * Arguments: @const gfreduce *r@ = pointer to reduction context |
| 156 | * @mp *d@ = destination |
| 157 | * @mp *x@ = some polynomial |
| 158 | * |
| 159 | * Returns: A polynomial @y@ such that %$y^2 + y = x$%, or null. |
| 160 | * |
| 161 | * Use: Solves quadratic equations in a field with characteristic 2. |
| 162 | * Suppose we have an equation %$y^2 + A y + B = 0$% where |
| 163 | * %$A \ne 0$%. (If %$A = 0$% then %$y = \sqrt{B}$% and you |
| 164 | * want @gfreduce_sqrt@ instead.) Use this function to solve |
| 165 | * %$z^2 + z = B/A^2$%; then set %$y = A z$%, since |
| 166 | * %$y^2 + y = A^2 z^2 + A^2 z = A^2 (z^2 + z) = B$% as |
| 167 | * required. |
| 168 | * |
| 169 | * The two roots are %$z$% and %$z + 1$%; this function always |
| 170 | * returns the one with zero scalar coefficient. |
| 171 | */ |
| 172 | |
| 173 | extern mp *gfreduce_quadsolve(const gfreduce */*r*/, mp */*d*/, mp */*x*/); |
| 174 | |
| 175 | /* --- @gfreduce_exp@ --- * |
| 176 | * |
| 177 | * Arguments: @const gfreduce *gr@ = pointer to reduction context |
| 178 | * @mp *d@ = fake destination |
| 179 | * @mp *a@ = base |
| 180 | * @mp *e@ = exponent |
| 181 | * |
| 182 | * Returns: Result, %$a^e \bmod m$%. |
| 183 | */ |
| 184 | |
| 185 | extern mp *gfreduce_exp(const gfreduce */*gr*/, mp */*d*/, |
| 186 | mp */*a*/, mp */*e*/); |
| 187 | |
| 188 | /*----- That's all, folks -------------------------------------------------*/ |
| 189 | |
| 190 | #ifdef __cplusplus |
| 191 | } |
| 192 | #endif |
| 193 | |
| 194 | #endif |