security/nss/lib/freebl/ecl/ecp_fp.h@b8a032363ba2
security/nss/lib/freebl/ecl/ecp_fp.h
Thu, 22 Jan 2015 13:21:57 +0100
- author
- Michael Schloh von Bennewitz <michael@schloh.com>
- date
- Thu, 22 Jan 2015 13:21:57 +0100
- branch
- TOR_BUG_9701
- changeset 15
- b8a032363ba2
- permissions
- -rw-r--r--
Incorporate requested changes from Mozilla in review:
https://bugzilla.mozilla.org/show_bug.cgi?id=1123480#c6
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/. */
5 #ifndef __ecp_fp_h_
6 #define __ecp_fp_h_
8 #include "mpi.h"
9 #include "ecl.h"
10 #include "ecp.h"
12 #include <sys/types.h>
13 #include "mpi-priv.h"
15 #ifdef ECL_DEBUG
16 #include <assert.h>
17 #endif
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
23 /* For debugging purposes */
24 #ifndef ECL_DEBUG
25 #define ECFP_ASSERT(x)
26 #else
27 #define ECFP_ASSERT(x) assert(x)
28 #endif
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
58 #define ECFP_TWO160 1461501637330902918203684832716283019655932542976.0
59 #define ECFP_TWO192 6277101735386680763835789423207666416102355444464034512896.0
60 #define ECFP_TWO224 26959946667150639794667015087019630673637144422540572481103610249216.0
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;
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 };
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
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 };
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 };
149 /* 0.011111111111111111111111 (binary) = 0.5 - 2^25 (24 ones) */
150 #define ECFP_BETABASE 0.4999999701976776123046875
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 };
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;
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;
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;
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;
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;
218 struct EC_group_fp_str;
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;
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);
288 };
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);
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);
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);
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);
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);
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);
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);
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);
354 /* Cleans up extra memory allocated in ECGroup for this implementation. */
355 void ec_GFp_extra_free_fp(ECGroup *group);
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);
362 /* Converts from an mpint into a floating point representation. */
363 void
364 ecfp_i2fp(double *out, const mp_int *x, const ECGroup *ecgroup);
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);
372 #endif
