| 1 | /* -*-c-*- |
| 2 | * |
| 3 | * Arithmetic in the Goldilocks field GF(2^448 - 2^224 - 1) |
| 4 | * |
| 5 | * (c) 2017 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_FGOLDI_H |
| 29 | #define CATACOMB_FGOLDI_H |
| 30 | |
| 31 | #ifdef __cplusplus |
| 32 | extern "C" { |
| 33 | #endif |
| 34 | |
| 35 | /*----- Header files ------------------------------------------------------*/ |
| 36 | |
| 37 | #include <mLib/bits.h> |
| 38 | |
| 39 | #ifndef CATACOMB_QFARITH_H |
| 40 | # include "qfarith.h" |
| 41 | #endif |
| 42 | |
| 43 | /*----- Data structures ---------------------------------------------------*/ |
| 44 | |
| 45 | typedef union { |
| 46 | int32 p28[16]; |
| 47 | int16 p12[40]; |
| 48 | } fgoldi; |
| 49 | |
| 50 | #if !defined(FGOLDI_IMPL) && defined(HAVE_INT64) |
| 51 | # define FGOLDI_IMPL 28 |
| 52 | #endif |
| 53 | |
| 54 | #ifndef FGOLDI_IMPL |
| 55 | # define FGOLDI_IMPL 12 |
| 56 | #endif |
| 57 | |
| 58 | #if FGOLDI_IMPL == 28 |
| 59 | typedef int32 fgoldi_piece; |
| 60 | #endif |
| 61 | #if FGOLDI_IMPL == 12 |
| 62 | typedef int16 fgoldi_piece; |
| 63 | #endif |
| 64 | |
| 65 | /*----- Functions provided ------------------------------------------------*/ |
| 66 | |
| 67 | /* --- @fgoldi_load@ --- * |
| 68 | * |
| 69 | * Arguments: @fgoldi *z@ = where to store the result |
| 70 | * @const octet xv[56]@ = source to read |
| 71 | * |
| 72 | * Returns: --- |
| 73 | * |
| 74 | * Use: Reads an element of %$\gf{2^{448} - 2^{224} - 19}$% in |
| 75 | * external representation from @xv@ and stores it in @z@. |
| 76 | * |
| 77 | * External representation is little-endian base-256. Some |
| 78 | * elements have multiple encodings, which are not produced by |
| 79 | * correct software; use of noncanonical encodings is not an |
| 80 | * error, and toleration of them is considered a performance |
| 81 | * feature. |
| 82 | */ |
| 83 | |
| 84 | extern void fgoldi_load(fgoldi */*z*/, const octet /*xv*/[56]); |
| 85 | |
| 86 | /* --- @fgoldi_store@ --- * |
| 87 | * |
| 88 | * Arguments: @octet zv[56]@ = where to write the result |
| 89 | * @const fgoldi *x@ = the field element to write |
| 90 | * |
| 91 | * Returns: --- |
| 92 | * |
| 93 | * Use: Stores a field element in the given octet vector in external |
| 94 | * representation. A canonical encoding is always stored. |
| 95 | */ |
| 96 | |
| 97 | extern void fgoldi_store(octet /*zv*/[56], const fgoldi */*x*/); |
| 98 | |
| 99 | /* --- @fgoldi_set@ --- * |
| 100 | * |
| 101 | * Arguments: @fgoldi *z@ = where to write the result |
| 102 | * @int a@ = a small-ish constant |
| 103 | * |
| 104 | * Returns: --- |
| 105 | * |
| 106 | * Use: Sets @z@ to equal @a@. |
| 107 | */ |
| 108 | |
| 109 | extern void fgoldi_set(fgoldi */*x*/, int /*a*/); |
| 110 | |
| 111 | /* --- @fgoldi_add@ --- * |
| 112 | * |
| 113 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) |
| 114 | * @const fgoldi *x, *y@ = two operands |
| 115 | * |
| 116 | * Returns: --- |
| 117 | * |
| 118 | * Use: Set @z@ to the sum %$x + y$%. |
| 119 | */ |
| 120 | |
| 121 | extern void fgoldi_add(fgoldi */*z*/, |
| 122 | const fgoldi */*x*/, const fgoldi */*y*/); |
| 123 | |
| 124 | /* --- @fgoldi_sub@ --- * |
| 125 | * |
| 126 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) |
| 127 | * @const fgoldi *x, *y@ = two operands |
| 128 | * |
| 129 | * Returns: --- |
| 130 | * |
| 131 | * Use: Set @z@ to the difference %$x - y$%. |
| 132 | */ |
| 133 | |
| 134 | extern void fgoldi_sub(fgoldi */*z*/, |
| 135 | const fgoldi */*x*/, const fgoldi */*y*/); |
| 136 | |
| 137 | /* --- @fgoldi_neg@ --- * |
| 138 | * |
| 139 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@) |
| 140 | * @const fgoldi *x@ = an operand |
| 141 | * |
| 142 | * Returns: --- |
| 143 | * |
| 144 | * Use: Set @z = -x@. |
| 145 | */ |
| 146 | |
| 147 | extern void fgoldi_neg(fgoldi */*z*/, const fgoldi */*x*/); |
| 148 | |
| 149 | /* --- @fgoldi_pick2@ --- * |
| 150 | * |
| 151 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) |
| 152 | * @const fgoldi *x, *y@ = two operands |
| 153 | * @uint32 m@ = a mask |
| 154 | * |
| 155 | * Returns: --- |
| 156 | * |
| 157 | * Use: If @m@ is zero, set @z = y@; if @m@ is all-bits-set, then set |
| 158 | * @z = x@. If @m@ has some other value, then scramble @z@ in |
| 159 | * an unhelpful way. |
| 160 | */ |
| 161 | |
| 162 | extern void fgoldi_pick2(fgoldi */*z*/, |
| 163 | const fgoldi */*x*/, const fgoldi */*y*/, |
| 164 | uint32 /*m*/); |
| 165 | |
| 166 | /* --- @fgoldi_pickn@ --- * |
| 167 | * |
| 168 | * Arguments: @fgoldi *z@ = where to put the result |
| 169 | * @const fgoldi *v@ = a table of entries |
| 170 | * @size_t n@ = the number of entries in @v@ |
| 171 | * @size_t i@ = an index |
| 172 | * |
| 173 | * Returns: --- |
| 174 | * |
| 175 | * Use: If @0 <= i < n < 32@ then set @z = v[i]@. If @n >= 32@ then |
| 176 | * do something unhelpful; otherwise, if @i >= n@ then set @z@ |
| 177 | * to zero. |
| 178 | */ |
| 179 | |
| 180 | extern void fgoldi_pickn(fgoldi */*z*/, |
| 181 | const fgoldi */*v*/, size_t /*n*/, size_t /*i*/); |
| 182 | |
| 183 | /* --- @fgoldi_condswap@ --- * |
| 184 | * |
| 185 | * Arguments: @fgoldi *x, *y@ = two operands |
| 186 | * @uint32 m@ = a mask |
| 187 | * |
| 188 | * Returns: --- |
| 189 | * |
| 190 | * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then |
| 191 | * exchange @x@ and @y@. If @m@ has some other value, then |
| 192 | * scramble @x@ and @y@ in an unhelpful way. |
| 193 | */ |
| 194 | |
| 195 | extern void fgoldi_condswap(fgoldi */*x*/, fgoldi */*y*/, uint32 /*m*/); |
| 196 | |
| 197 | /* --- @fgoldi_condneg@ --- * |
| 198 | * |
| 199 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@) |
| 200 | * @const fgoldi *x@ = an operand |
| 201 | * @uint32 m@ = a mask |
| 202 | * |
| 203 | * Returns: --- |
| 204 | * |
| 205 | * Use: If @m@ is zero, set @z = x@; if @m@ is all-bits-set, then set |
| 206 | * @z = -x@. If @m@ has some other value then scramble @z@ in |
| 207 | * an unhelpful way. |
| 208 | */ |
| 209 | |
| 210 | extern void fgoldi_condneg(fgoldi */*z*/, const fgoldi */*x*/, uint32 /*m*/); |
| 211 | |
| 212 | /* --- @fgoldi_mulconst@ --- * |
| 213 | * |
| 214 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@) |
| 215 | * @const fgoldi *x@ = an operand |
| 216 | * @long a@ = a small-ish constant; %$|a| < 2^{20}$%. |
| 217 | * |
| 218 | * Returns: --- |
| 219 | * |
| 220 | * Use: Set @z@ to the product %$a x$%. |
| 221 | */ |
| 222 | |
| 223 | extern void fgoldi_mulconst(fgoldi */*z*/, const fgoldi */*x*/, long /*a*/); |
| 224 | |
| 225 | /* --- @fgoldi_mul@ --- * |
| 226 | * |
| 227 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) |
| 228 | * @const fgoldi *x, *y@ = two operands |
| 229 | * |
| 230 | * Returns: --- |
| 231 | * |
| 232 | * Use: Set @z@ to the product %$x y$%. |
| 233 | */ |
| 234 | |
| 235 | extern void fgoldi_mul(fgoldi */*z*/, |
| 236 | const fgoldi */*x*/, const fgoldi */*y*/); |
| 237 | |
| 238 | /* --- @fgoldi_sqr@ --- * |
| 239 | * |
| 240 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) |
| 241 | * @const fgoldi *x@ = an operand |
| 242 | * |
| 243 | * Returns: --- |
| 244 | * |
| 245 | * Use: Set @z@ to the square %$x^2$%. |
| 246 | */ |
| 247 | |
| 248 | extern void fgoldi_sqr(fgoldi */*z*/, const fgoldi */*x*/); |
| 249 | |
| 250 | /* --- @fgoldi_inv@ --- * |
| 251 | * |
| 252 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@) |
| 253 | * @const fgoldi *x@ = an operand |
| 254 | * |
| 255 | * Returns: --- |
| 256 | * |
| 257 | * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If |
| 258 | * %$x = 0$% then @z@ is set to zero. This is considered a |
| 259 | * feature. |
| 260 | */ |
| 261 | |
| 262 | extern void fgoldi_inv(fgoldi */*z*/, const fgoldi */*x*/); |
| 263 | |
| 264 | /* --- @fgoldi_quosqrt@ --- * |
| 265 | * |
| 266 | * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@) |
| 267 | * @const fgoldi *x, *y@ = two operands |
| 268 | * |
| 269 | * Returns: Zero if successful, @-1@ if %$x/y$% is not a square. |
| 270 | * |
| 271 | * Use: Stores in @z@ the one of the square roots %$\pm\sqrt{x/y}$%. |
| 272 | * If %$x = y = 0% then the result is zero; if %$y = 0$% but %$x |
| 273 | * \ne 0$% then the operation fails. If you wanted a specific |
| 274 | * square root then you'll have to pick it yourself. |
| 275 | */ |
| 276 | |
| 277 | extern int fgoldi_quosqrt(fgoldi */*z*/, |
| 278 | const fgoldi */*x*/, const fgoldi */*y*/); |
| 279 | |
| 280 | /*----- That's all, folks -------------------------------------------------*/ |
| 281 | |
| 282 | #ifdef __cplusplus |
| 283 | } |
| 284 | #endif |
| 285 | |
| 286 | #endif |