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comparison: security/nss/lib/freebl/ecl/ecp_fp.h
security/nss/lib/freebl/ecl/ecp_fp.h
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| 1 /* This Source Code Form is subject to the terms of the Mozilla Public | |
| 2 * License, v. 2.0. If a copy of the MPL was not distributed with this | |
| 3 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ | |
| 4 | |
| 5 #ifndef __ecp_fp_h_ | |
| 6 #define __ecp_fp_h_ | |
| 7 | |
| 8 #include "mpi.h" | |
| 9 #include "ecl.h" | |
| 10 #include "ecp.h" | |
| 11 | |
| 12 #include <sys/types.h> | |
| 13 #include "mpi-priv.h" | |
| 14 | |
| 15 #ifdef ECL_DEBUG | |
| 16 #include <assert.h> | |
| 17 #endif | |
| 18 | |
| 19 /* Largest number of doubles to store one reduced number in floating | |
| 20 * point. Used for memory allocation on the stack. */ | |
| 21 #define ECFP_MAXDOUBLES 10 | |
| 22 | |
| 23 /* For debugging purposes */ | |
| 24 #ifndef ECL_DEBUG | |
| 25 #define ECFP_ASSERT(x) | |
| 26 #else | |
| 27 #define ECFP_ASSERT(x) assert(x) | |
| 28 #endif | |
| 29 | |
| 30 /* ECFP_Ti = 2^(i*24) Define as preprocessor constants so we can use in | |
| 31 * multiple static constants */ | |
| 32 #define ECFP_T0 1.0 | |
| 33 #define ECFP_T1 16777216.0 | |
| 34 #define ECFP_T2 281474976710656.0 | |
| 35 #define ECFP_T3 4722366482869645213696.0 | |
| 36 #define ECFP_T4 79228162514264337593543950336.0 | |
| 37 #define ECFP_T5 1329227995784915872903807060280344576.0 | |
| 38 #define ECFP_T6 22300745198530623141535718272648361505980416.0 | |
| 39 #define ECFP_T7 374144419156711147060143317175368453031918731001856.0 | |
| 40 #define ECFP_T8 6277101735386680763835789423207666416102355444464034512896.0 | |
| 41 #define ECFP_T9 105312291668557186697918027683670432318895095400549111254310977536.0 | |
| 42 #define ECFP_T10 1766847064778384329583297500742918515827483896875618958121606201292619776.0 | |
| 43 #define ECFP_T11 29642774844752946028434172162224104410437116074403984394101141506025761187823616.0 | |
| 44 #define ECFP_T12 497323236409786642155382248146820840100456150797347717440463976893159497012533375533056.0 | |
| 45 #define ECFP_T13 8343699359066055009355553539724812947666814540455674882605631280555545803830627148527195652096.0 | |
| 46 #define ECFP_T14 139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736.0 | |
| 47 #define ECFP_T15 2348542582773833227889480596789337027375682548908319870707290971532209025114608443463698998384768703031934976.0 | |
| 48 #define ECFP_T16 39402006196394479212279040100143613805079739270465446667948293404245\ | |
| 49 721771497210611414266254884915640806627990306816.0 | |
| 50 #define ECFP_T17 66105596879024859895191530803277103982840468296428121928464879527440\ | |
| 51 5791236311345825189210439715284847591212025023358304256.0 | |
| 52 #define ECFP_T18 11090678776483259438313656736572334813745748301503266300681918322458\ | |
| 53 485231222502492159897624416558312389564843845614287315896631296.0 | |
| 54 #define ECFP_T19 18607071341967536398062689481932916079453218833595342343206149099024\ | |
| 55 36577570298683715049089827234727835552055312041415509848580169253519\ | |
| 56 36.0 | |
| 57 | |
| 58 #define ECFP_TWO160 1461501637330902918203684832716283019655932542976.0 | |
| 59 #define ECFP_TWO192 6277101735386680763835789423207666416102355444464034512896.0 | |
| 60 #define ECFP_TWO224 26959946667150639794667015087019630673637144422540572481103610249216.0 | |
| 61 | |
| 62 /* Multiplicative constants */ | |
| 63 static const double ecfp_two32 = 4294967296.0; | |
| 64 static const double ecfp_two64 = 18446744073709551616.0; | |
| 65 static const double ecfp_twom16 = .0000152587890625; | |
| 66 static const double ecfp_twom128 = | |
| 67 .00000000000000000000000000000000000000293873587705571876992184134305561419454666389193021880377187926569604314863681793212890625; | |
| 68 static const double ecfp_twom129 = | |
| 69 .000000000000000000000000000000000000001469367938527859384960920671527807097273331945965109401885939632848021574318408966064453125; | |
| 70 static const double ecfp_twom160 = | |
| 71 .0000000000000000000000000000000000000000000000006842277657836020854119773355907793609766904013068924666782559979930620520927053718196475529111921787261962890625; | |
| 72 static const double ecfp_twom192 = | |
| 73 .000000000000000000000000000000000000000000000000000000000159309191113245227702888039776771180559110455519261878607388585338616290151305816094308987472018268594098344692611135542392730712890625; | |
| 74 static const double ecfp_twom224 = | |
| 75 .00000000000000000000000000000000000000000000000000000000000000000003709206150687421385731735261547639513367564778757791002453039058917581340095629358997312082723208437536338919136001159027049567384892725385725498199462890625; | |
| 76 | |
| 77 /* ecfp_exp[i] = 2^(i*ECFP_DSIZE) */ | |
| 78 static const double ecfp_exp[2 * ECFP_MAXDOUBLES] = { | |
| 79 ECFP_T0, ECFP_T1, ECFP_T2, ECFP_T3, ECFP_T4, ECFP_T5, | |
| 80 ECFP_T6, ECFP_T7, ECFP_T8, ECFP_T9, ECFP_T10, ECFP_T11, | |
| 81 ECFP_T12, ECFP_T13, ECFP_T14, ECFP_T15, ECFP_T16, ECFP_T17, ECFP_T18, | |
| 82 ECFP_T19 | |
| 83 }; | |
| 84 | |
| 85 /* 1.1 * 2^52 Uses 2^52 to truncate, the .1 is an extra 2^51 to protect | |
| 86 * the 2^52 bit, so that adding alphas to a negative number won't borrow | |
| 87 * and empty the important 2^52 bit */ | |
| 88 #define ECFP_ALPHABASE_53 6755399441055744.0 | |
| 89 /* Special case: On some platforms, notably x86 Linux, there is an | |
| 90 * extended-precision floating point representation with 64-bits of | |
| 91 * precision in the mantissa. These extra bits of precision require a | |
| 92 * larger value of alpha to truncate, i.e. 1.1 * 2^63. */ | |
| 93 #define ECFP_ALPHABASE_64 13835058055282163712.0 | |
| 94 | |
| 95 /* | |
| 96 * ecfp_alpha[i] = 1.5 * 2^(52 + i*ECFP_DSIZE) we add and subtract alpha | |
| 97 * to truncate floating point numbers to a certain number of bits for | |
| 98 * tidying */ | |
| 99 static const double ecfp_alpha_53[2 * ECFP_MAXDOUBLES] = { | |
| 100 ECFP_ALPHABASE_53 * ECFP_T0, | |
| 101 ECFP_ALPHABASE_53 * ECFP_T1, | |
| 102 ECFP_ALPHABASE_53 * ECFP_T2, | |
| 103 ECFP_ALPHABASE_53 * ECFP_T3, | |
| 104 ECFP_ALPHABASE_53 * ECFP_T4, | |
| 105 ECFP_ALPHABASE_53 * ECFP_T5, | |
| 106 ECFP_ALPHABASE_53 * ECFP_T6, | |
| 107 ECFP_ALPHABASE_53 * ECFP_T7, | |
| 108 ECFP_ALPHABASE_53 * ECFP_T8, | |
| 109 ECFP_ALPHABASE_53 * ECFP_T9, | |
| 110 ECFP_ALPHABASE_53 * ECFP_T10, | |
| 111 ECFP_ALPHABASE_53 * ECFP_T11, | |
| 112 ECFP_ALPHABASE_53 * ECFP_T12, | |
| 113 ECFP_ALPHABASE_53 * ECFP_T13, | |
| 114 ECFP_ALPHABASE_53 * ECFP_T14, | |
| 115 ECFP_ALPHABASE_53 * ECFP_T15, | |
| 116 ECFP_ALPHABASE_53 * ECFP_T16, | |
| 117 ECFP_ALPHABASE_53 * ECFP_T17, | |
| 118 ECFP_ALPHABASE_53 * ECFP_T18, | |
| 119 ECFP_ALPHABASE_53 * ECFP_T19 | |
| 120 }; | |
| 121 | |
| 122 /* | |
| 123 * ecfp_alpha[i] = 1.5 * 2^(63 + i*ECFP_DSIZE) we add and subtract alpha | |
| 124 * to truncate floating point numbers to a certain number of bits for | |
| 125 * tidying */ | |
| 126 static const double ecfp_alpha_64[2 * ECFP_MAXDOUBLES] = { | |
| 127 ECFP_ALPHABASE_64 * ECFP_T0, | |
| 128 ECFP_ALPHABASE_64 * ECFP_T1, | |
| 129 ECFP_ALPHABASE_64 * ECFP_T2, | |
| 130 ECFP_ALPHABASE_64 * ECFP_T3, | |
| 131 ECFP_ALPHABASE_64 * ECFP_T4, | |
| 132 ECFP_ALPHABASE_64 * ECFP_T5, | |
| 133 ECFP_ALPHABASE_64 * ECFP_T6, | |
| 134 ECFP_ALPHABASE_64 * ECFP_T7, | |
| 135 ECFP_ALPHABASE_64 * ECFP_T8, | |
| 136 ECFP_ALPHABASE_64 * ECFP_T9, | |
| 137 ECFP_ALPHABASE_64 * ECFP_T10, | |
| 138 ECFP_ALPHABASE_64 * ECFP_T11, | |
| 139 ECFP_ALPHABASE_64 * ECFP_T12, | |
| 140 ECFP_ALPHABASE_64 * ECFP_T13, | |
| 141 ECFP_ALPHABASE_64 * ECFP_T14, | |
| 142 ECFP_ALPHABASE_64 * ECFP_T15, | |
| 143 ECFP_ALPHABASE_64 * ECFP_T16, | |
| 144 ECFP_ALPHABASE_64 * ECFP_T17, | |
| 145 ECFP_ALPHABASE_64 * ECFP_T18, | |
| 146 ECFP_ALPHABASE_64 * ECFP_T19 | |
| 147 }; | |
| 148 | |
| 149 /* 0.011111111111111111111111 (binary) = 0.5 - 2^25 (24 ones) */ | |
| 150 #define ECFP_BETABASE 0.4999999701976776123046875 | |
| 151 | |
| 152 /* | |
| 153 * We subtract beta prior to using alpha to simulate rounding down. We | |
| 154 * make this close to 0.5 to round almost everything down, but exactly 0.5 | |
| 155 * would cause some incorrect rounding. */ | |
| 156 static const double ecfp_beta[2 * ECFP_MAXDOUBLES] = { | |
| 157 ECFP_BETABASE * ECFP_T0, | |
| 158 ECFP_BETABASE * ECFP_T1, | |
| 159 ECFP_BETABASE * ECFP_T2, | |
| 160 ECFP_BETABASE * ECFP_T3, | |
| 161 ECFP_BETABASE * ECFP_T4, | |
| 162 ECFP_BETABASE * ECFP_T5, | |
| 163 ECFP_BETABASE * ECFP_T6, | |
| 164 ECFP_BETABASE * ECFP_T7, | |
| 165 ECFP_BETABASE * ECFP_T8, | |
| 166 ECFP_BETABASE * ECFP_T9, | |
| 167 ECFP_BETABASE * ECFP_T10, | |
| 168 ECFP_BETABASE * ECFP_T11, | |
| 169 ECFP_BETABASE * ECFP_T12, | |
| 170 ECFP_BETABASE * ECFP_T13, | |
| 171 ECFP_BETABASE * ECFP_T14, | |
| 172 ECFP_BETABASE * ECFP_T15, | |
| 173 ECFP_BETABASE * ECFP_T16, | |
| 174 ECFP_BETABASE * ECFP_T17, | |
| 175 ECFP_BETABASE * ECFP_T18, | |
| 176 ECFP_BETABASE * ECFP_T19 | |
| 177 }; | |
| 178 | |
| 179 static const double ecfp_beta_160 = ECFP_BETABASE * ECFP_TWO160; | |
| 180 static const double ecfp_beta_192 = ECFP_BETABASE * ECFP_TWO192; | |
| 181 static const double ecfp_beta_224 = ECFP_BETABASE * ECFP_TWO224; | |
| 182 | |
| 183 /* Affine EC Point. This is the basic representation (x, y) of an elliptic | |
| 184 * curve point. */ | |
| 185 typedef struct { | |
| 186 double x[ECFP_MAXDOUBLES]; | |
| 187 double y[ECFP_MAXDOUBLES]; | |
| 188 } ecfp_aff_pt; | |
| 189 | |
| 190 /* Jacobian EC Point. This coordinate system uses X = x/z^2, Y = y/z^3, | |
| 191 * which enables calculations with fewer inversions than affine | |
| 192 * coordinates. */ | |
| 193 typedef struct { | |
| 194 double x[ECFP_MAXDOUBLES]; | |
| 195 double y[ECFP_MAXDOUBLES]; | |
| 196 double z[ECFP_MAXDOUBLES]; | |
| 197 } ecfp_jac_pt; | |
| 198 | |
| 199 /* Chudnovsky Jacobian EC Point. This coordinate system is the same as | |
| 200 * Jacobian, except it keeps z^2, z^3 for faster additions. */ | |
| 201 typedef struct { | |
| 202 double x[ECFP_MAXDOUBLES]; | |
| 203 double y[ECFP_MAXDOUBLES]; | |
| 204 double z[ECFP_MAXDOUBLES]; | |
| 205 double z2[ECFP_MAXDOUBLES]; | |
| 206 double z3[ECFP_MAXDOUBLES]; | |
| 207 } ecfp_chud_pt; | |
| 208 | |
| 209 /* Modified Jacobian EC Point. This coordinate system is the same as | |
| 210 * Jacobian, except it keeps a*z^4 for faster doublings. */ | |
| 211 typedef struct { | |
| 212 double x[ECFP_MAXDOUBLES]; | |
| 213 double y[ECFP_MAXDOUBLES]; | |
| 214 double z[ECFP_MAXDOUBLES]; | |
| 215 double az4[ECFP_MAXDOUBLES]; | |
| 216 } ecfp_jm_pt; | |
| 217 | |
| 218 struct EC_group_fp_str; | |
| 219 | |
| 220 typedef struct EC_group_fp_str EC_group_fp; | |
| 221 struct EC_group_fp_str { | |
| 222 int fpPrecision; /* Set to number of bits in mantissa, 53 | |
| 223 * or 64 */ | |
| 224 int numDoubles; | |
| 225 int primeBitSize; | |
| 226 int orderBitSize; | |
| 227 int doubleBitSize; | |
| 228 int numInts; | |
| 229 int aIsM3; /* True if curvea == -3 (mod p), then we | |
| 230 * can optimize doubling */ | |
| 231 double curvea[ECFP_MAXDOUBLES]; | |
| 232 /* Used to truncate a double to the number of bits in the curve */ | |
| 233 double bitSize_alpha; | |
| 234 /* Pointer to either ecfp_alpha_53 or ecfp_alpha_64 */ | |
| 235 const double *alpha; | |
| 236 | |
| 237 void (*ecfp_singleReduce) (double *r, const EC_group_fp * group); | |
| 238 void (*ecfp_reduce) (double *r, double *x, const EC_group_fp * group); | |
| 239 /* Performs a "tidy" operation, which performs carrying, moving excess | |
| 240 * bits from one double to the next double, so that the precision of | |
| 241 * the doubles is reduced to the regular precision ECFP_DSIZE. This | |
| 242 * might result in some float digits being negative. */ | |
| 243 void (*ecfp_tidy) (double *t, const double *alpha, | |
| 244 const EC_group_fp * group); | |
| 245 /* Perform a point addition using coordinate system Jacobian + Affine | |
| 246 * -> Jacobian. Input and output should be multi-precision floating | |
| 247 * point integers. */ | |
| 248 void (*pt_add_jac_aff) (const ecfp_jac_pt * p, const ecfp_aff_pt * q, | |
| 249 ecfp_jac_pt * r, const EC_group_fp * group); | |
| 250 /* Perform a point doubling in Jacobian coordinates. Input and output | |
| 251 * should be multi-precision floating point integers. */ | |
| 252 void (*pt_dbl_jac) (const ecfp_jac_pt * dp, ecfp_jac_pt * dr, | |
| 253 const EC_group_fp * group); | |
| 254 /* Perform a point addition using Jacobian coordinate system. Input | |
| 255 * and output should be multi-precision floating point integers. */ | |
| 256 void (*pt_add_jac) (const ecfp_jac_pt * p, const ecfp_jac_pt * q, | |
| 257 ecfp_jac_pt * r, const EC_group_fp * group); | |
| 258 /* Perform a point doubling in Modified Jacobian coordinates. Input | |
| 259 * and output should be multi-precision floating point integers. */ | |
| 260 void (*pt_dbl_jm) (const ecfp_jm_pt * p, ecfp_jm_pt * r, | |
| 261 const EC_group_fp * group); | |
| 262 /* Perform a point doubling using coordinates Affine -> Chudnovsky | |
| 263 * Jacobian. Input and output should be multi-precision floating point | |
| 264 * integers. */ | |
| 265 void (*pt_dbl_aff2chud) (const ecfp_aff_pt * p, ecfp_chud_pt * r, | |
| 266 const EC_group_fp * group); | |
| 267 /* Perform a point addition using coordinates: Modified Jacobian + | |
| 268 * Chudnovsky Jacobian -> Modified Jacobian. Input and output should | |
| 269 * be multi-precision floating point integers. */ | |
| 270 void (*pt_add_jm_chud) (ecfp_jm_pt * p, ecfp_chud_pt * q, | |
| 271 ecfp_jm_pt * r, const EC_group_fp * group); | |
| 272 /* Perform a point addition using Chudnovsky Jacobian coordinates. | |
| 273 * Input and output should be multi-precision floating point integers. | |
| 274 */ | |
| 275 void (*pt_add_chud) (const ecfp_chud_pt * p, const ecfp_chud_pt * q, | |
| 276 ecfp_chud_pt * r, const EC_group_fp * group); | |
| 277 /* Expects out to be an array of size 16 of Chudnovsky Jacobian | |
| 278 * points. Fills in Chudnovsky Jacobian form (x, y, z, z^2, z^3), for | |
| 279 * -15P, -13P, -11P, -9P, -7P, -5P, -3P, -P, P, 3P, 5P, 7P, 9P, 11P, | |
| 280 * 13P, 15P */ | |
| 281 void (*precompute_chud) (ecfp_chud_pt * out, const ecfp_aff_pt * p, | |
| 282 const EC_group_fp * group); | |
| 283 /* Expects out to be an array of size 16 of Jacobian points. Fills in | |
| 284 * Chudnovsky Jacobian form (x, y, z), for O, P, 2P, ... 15P */ | |
| 285 void (*precompute_jac) (ecfp_jac_pt * out, const ecfp_aff_pt * p, | |
| 286 const EC_group_fp * group); | |
| 287 | |
| 288 }; | |
| 289 | |
| 290 /* Computes r = x*y. | |
| 291 * r must be different (point to different memory) than x and y. | |
| 292 * Does not tidy or reduce. */ | |
| 293 void ecfp_multiply(double *r, const double *x, const double *y); | |
| 294 | |
| 295 /* Performs a "tidy" operation, which performs carrying, moving excess | |
| 296 * bits from one double to the next double, so that the precision of the | |
| 297 * doubles is reduced to the regular precision group->doubleBitSize. This | |
| 298 * might result in some float digits being negative. */ | |
| 299 void ecfp_tidy(double *t, const double *alpha, const EC_group_fp * group); | |
| 300 | |
| 301 /* Performs tidying on only the upper float digits of a multi-precision | |
| 302 * floating point integer, i.e. the digits beyond the regular length which | |
| 303 * are removed in the reduction step. */ | |
| 304 void ecfp_tidyUpper(double *t, const EC_group_fp * group); | |
| 305 | |
| 306 /* Performs tidying on a short multi-precision floating point integer (the | |
| 307 * lower group->numDoubles floats). */ | |
| 308 void ecfp_tidyShort(double *t, const EC_group_fp * group); | |
| 309 | |
| 310 /* Performs a more mathematically precise "tidying" so that each term is | |
| 311 * positive. This is slower than the regular tidying, and is used for | |
| 312 * conversion from floating point to integer. */ | |
| 313 void ecfp_positiveTidy(double *t, const EC_group_fp * group); | |
| 314 | |
| 315 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters | |
| 316 * a, b and p are the elliptic curve coefficients and the prime that | |
| 317 * determines the field GFp. Elliptic curve points P and R can be | |
| 318 * identical. Uses mixed Jacobian-affine coordinates. Uses 4-bit window | |
| 319 * method. */ | |
| 320 mp_err | |
| 321 ec_GFp_point_mul_jac_4w_fp(const mp_int *n, const mp_int *px, | |
| 322 const mp_int *py, mp_int *rx, mp_int *ry, | |
| 323 const ECGroup *ecgroup); | |
| 324 | |
| 325 /* Computes R = nP where R is (rx, ry) and P is the base point. The | |
| 326 * parameters a, b and p are the elliptic curve coefficients and the prime | |
| 327 * that determines the field GFp. Elliptic curve points P and R can be | |
| 328 * identical. Uses mixed Jacobian-affine coordinates (Jacobian | |
| 329 * coordinates for doubles and affine coordinates for additions; based on | |
| 330 * recommendation from Brown et al.). Uses window NAF method (algorithm | |
| 331 * 11) for scalar-point multiplication from Brown, Hankerson, Lopez, | |
| 332 * Menezes. Software Implementation of the NIST Elliptic Curves Over Prime | |
| 333 * Fields. */ | |
| 334 mp_err ec_GFp_point_mul_wNAF_fp(const mp_int *n, const mp_int *px, | |
| 335 const mp_int *py, mp_int *rx, mp_int *ry, | |
| 336 const ECGroup *ecgroup); | |
| 337 | |
| 338 /* Uses mixed Jacobian-affine coordinates to perform a point | |
| 339 * multiplication: R = n * P, n scalar. Uses mixed Jacobian-affine | |
| 340 * coordinates (Jacobian coordinates for doubles and affine coordinates | |
| 341 * for additions; based on recommendation from Brown et al.). Not very | |
| 342 * time efficient but quite space efficient, no precomputation needed. | |
| 343 * group contains the elliptic curve coefficients and the prime that | |
| 344 * determines the field GFp. Elliptic curve points P and R can be | |
| 345 * identical. Performs calculations in floating point number format, since | |
| 346 * this is faster than the integer operations on the ULTRASPARC III. | |
| 347 * Uses left-to-right binary method (double & add) (algorithm 9) for | |
| 348 * scalar-point multiplication from Brown, Hankerson, Lopez, Menezes. | |
| 349 * Software Implementation of the NIST Elliptic Curves Over Prime Fields. */ | |
| 350 mp_err | |
| 351 ec_GFp_pt_mul_jac_fp(const mp_int *n, const mp_int *px, const mp_int *py, | |
| 352 mp_int *rx, mp_int *ry, const ECGroup *ecgroup); | |
| 353 | |
| 354 /* Cleans up extra memory allocated in ECGroup for this implementation. */ | |
| 355 void ec_GFp_extra_free_fp(ECGroup *group); | |
| 356 | |
| 357 /* Converts from a floating point representation into an mp_int. Expects | |
| 358 * that d is already reduced. */ | |
| 359 void | |
| 360 ecfp_fp2i(mp_int *mpout, double *d, const ECGroup *ecgroup); | |
| 361 | |
| 362 /* Converts from an mpint into a floating point representation. */ | |
| 363 void | |
| 364 ecfp_i2fp(double *out, const mp_int *x, const ECGroup *ecgroup); | |
| 365 | |
| 366 /* Tests what precision floating point arithmetic is set to. This should | |
| 367 * be either a 53-bit mantissa (IEEE standard) or a 64-bit mantissa | |
| 368 * (extended precision on x86) and sets it into the EC_group_fp. Returns | |
| 369 * either 53 or 64 accordingly. */ | |
| 370 int ec_set_fp_precision(EC_group_fp * group); | |
| 371 | |
| 372 #endif |
