RetroZilla/security/nss/lib/freebl/ecl/ecp_fp.h
2015-10-20 23:03:22 -04:00

407 lines
17 KiB
C

/*
* ***** BEGIN LICENSE BLOCK *****
* Version: MPL 1.1/GPL 2.0/LGPL 2.1
*
* The contents of this file are subject to the Mozilla Public License Version
* 1.1 (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* Software distributed under the License is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
* for the specific language governing rights and limitations under the
* License.
*
* The Original Code is the elliptic curve math library for prime field curves using floating point operations.
*
* The Initial Developer of the Original Code is
* Sun Microsystems, Inc.
* Portions created by the Initial Developer are Copyright (C) 2003
* the Initial Developer. All Rights Reserved.
*
* Contributor(s):
* Stephen Fung <fungstep@hotmail.com>, Sun Microsystems Laboratories
*
* Alternatively, the contents of this file may be used under the terms of
* either the GNU General Public License Version 2 or later (the "GPL"), or
* the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
* in which case the provisions of the GPL or the LGPL are applicable instead
* of those above. If you wish to allow use of your version of this file only
* under the terms of either the GPL or the LGPL, and not to allow others to
* use your version of this file under the terms of the MPL, indicate your
* decision by deleting the provisions above and replace them with the notice
* and other provisions required by the GPL or the LGPL. If you do not delete
* the provisions above, a recipient may use your version of this file under
* the terms of any one of the MPL, the GPL or the LGPL.
*
* ***** END LICENSE BLOCK ***** */
#ifndef __ecp_fp_h_
#define __ecp_fp_h_
#include "mpi.h"
#include "ecl.h"
#include "ecp.h"
#include <sys/types.h>
#include "mpi-priv.h"
#ifdef ECL_DEBUG
#include <assert.h>
#endif
/* Largest number of doubles to store one reduced number in floating
* point. Used for memory allocation on the stack. */
#define ECFP_MAXDOUBLES 10
/* For debugging purposes */
#ifndef ECL_DEBUG
#define ECFP_ASSERT(x)
#else
#define ECFP_ASSERT(x) assert(x)
#endif
/* ECFP_Ti = 2^(i*24) Define as preprocessor constants so we can use in
* multiple static constants */
#define ECFP_T0 1.0
#define ECFP_T1 16777216.0
#define ECFP_T2 281474976710656.0
#define ECFP_T3 4722366482869645213696.0
#define ECFP_T4 79228162514264337593543950336.0
#define ECFP_T5 1329227995784915872903807060280344576.0
#define ECFP_T6 22300745198530623141535718272648361505980416.0
#define ECFP_T7 374144419156711147060143317175368453031918731001856.0
#define ECFP_T8 6277101735386680763835789423207666416102355444464034512896.0
#define ECFP_T9 105312291668557186697918027683670432318895095400549111254310977536.0
#define ECFP_T10 1766847064778384329583297500742918515827483896875618958121606201292619776.0
#define ECFP_T11 29642774844752946028434172162224104410437116074403984394101141506025761187823616.0
#define ECFP_T12 497323236409786642155382248146820840100456150797347717440463976893159497012533375533056.0
#define ECFP_T13 8343699359066055009355553539724812947666814540455674882605631280555545803830627148527195652096.0
#define ECFP_T14 139984046386112763159840142535527767382602843577165595931249318810236991948760059086304843329475444736.0
#define ECFP_T15 2348542582773833227889480596789337027375682548908319870707290971532209025114608443463698998384768703031934976.0
#define ECFP_T16 39402006196394479212279040100143613805079739270465446667948293404245\
721771497210611414266254884915640806627990306816.0
#define ECFP_T17 66105596879024859895191530803277103982840468296428121928464879527440\
5791236311345825189210439715284847591212025023358304256.0
#define ECFP_T18 11090678776483259438313656736572334813745748301503266300681918322458\
485231222502492159897624416558312389564843845614287315896631296.0
#define ECFP_T19 18607071341967536398062689481932916079453218833595342343206149099024\
36577570298683715049089827234727835552055312041415509848580169253519\
36.0
#define ECFP_TWO160 1461501637330902918203684832716283019655932542976.0
#define ECFP_TWO192 6277101735386680763835789423207666416102355444464034512896.0
#define ECFP_TWO224 26959946667150639794667015087019630673637144422540572481103610249216.0
/* Multiplicative constants */
static const double ecfp_two32 = 4294967296.0;
static const double ecfp_two64 = 18446744073709551616.0;
static const double ecfp_twom16 = .0000152587890625;
static const double ecfp_twom128 =
.00000000000000000000000000000000000000293873587705571876992184134305561419454666389193021880377187926569604314863681793212890625;
static const double ecfp_twom129 =
.000000000000000000000000000000000000001469367938527859384960920671527807097273331945965109401885939632848021574318408966064453125;
static const double ecfp_twom160 =
.0000000000000000000000000000000000000000000000006842277657836020854119773355907793609766904013068924666782559979930620520927053718196475529111921787261962890625;
static const double ecfp_twom192 =
.000000000000000000000000000000000000000000000000000000000159309191113245227702888039776771180559110455519261878607388585338616290151305816094308987472018268594098344692611135542392730712890625;
static const double ecfp_twom224 =
.00000000000000000000000000000000000000000000000000000000000000000003709206150687421385731735261547639513367564778757791002453039058917581340095629358997312082723208437536338919136001159027049567384892725385725498199462890625;
/* ecfp_exp[i] = 2^(i*ECFP_DSIZE) */
static const double ecfp_exp[2 * ECFP_MAXDOUBLES] = {
ECFP_T0, ECFP_T1, ECFP_T2, ECFP_T3, ECFP_T4, ECFP_T5,
ECFP_T6, ECFP_T7, ECFP_T8, ECFP_T9, ECFP_T10, ECFP_T11,
ECFP_T12, ECFP_T13, ECFP_T14, ECFP_T15, ECFP_T16, ECFP_T17, ECFP_T18,
ECFP_T19
};
/* 1.1 * 2^52 Uses 2^52 to truncate, the .1 is an extra 2^51 to protect
* the 2^52 bit, so that adding alphas to a negative number won't borrow
* and empty the important 2^52 bit */
#define ECFP_ALPHABASE_53 6755399441055744.0
/* Special case: On some platforms, notably x86 Linux, there is an
* extended-precision floating point representation with 64-bits of
* precision in the mantissa. These extra bits of precision require a
* larger value of alpha to truncate, i.e. 1.1 * 2^63. */
#define ECFP_ALPHABASE_64 13835058055282163712.0
/*
* ecfp_alpha[i] = 1.5 * 2^(52 + i*ECFP_DSIZE) we add and subtract alpha
* to truncate floating point numbers to a certain number of bits for
* tidying */
static const double ecfp_alpha_53[2 * ECFP_MAXDOUBLES] = {
ECFP_ALPHABASE_53 * ECFP_T0,
ECFP_ALPHABASE_53 * ECFP_T1,
ECFP_ALPHABASE_53 * ECFP_T2,
ECFP_ALPHABASE_53 * ECFP_T3,
ECFP_ALPHABASE_53 * ECFP_T4,
ECFP_ALPHABASE_53 * ECFP_T5,
ECFP_ALPHABASE_53 * ECFP_T6,
ECFP_ALPHABASE_53 * ECFP_T7,
ECFP_ALPHABASE_53 * ECFP_T8,
ECFP_ALPHABASE_53 * ECFP_T9,
ECFP_ALPHABASE_53 * ECFP_T10,
ECFP_ALPHABASE_53 * ECFP_T11,
ECFP_ALPHABASE_53 * ECFP_T12,
ECFP_ALPHABASE_53 * ECFP_T13,
ECFP_ALPHABASE_53 * ECFP_T14,
ECFP_ALPHABASE_53 * ECFP_T15,
ECFP_ALPHABASE_53 * ECFP_T16,
ECFP_ALPHABASE_53 * ECFP_T17,
ECFP_ALPHABASE_53 * ECFP_T18,
ECFP_ALPHABASE_53 * ECFP_T19
};
/*
* ecfp_alpha[i] = 1.5 * 2^(63 + i*ECFP_DSIZE) we add and subtract alpha
* to truncate floating point numbers to a certain number of bits for
* tidying */
static const double ecfp_alpha_64[2 * ECFP_MAXDOUBLES] = {
ECFP_ALPHABASE_64 * ECFP_T0,
ECFP_ALPHABASE_64 * ECFP_T1,
ECFP_ALPHABASE_64 * ECFP_T2,
ECFP_ALPHABASE_64 * ECFP_T3,
ECFP_ALPHABASE_64 * ECFP_T4,
ECFP_ALPHABASE_64 * ECFP_T5,
ECFP_ALPHABASE_64 * ECFP_T6,
ECFP_ALPHABASE_64 * ECFP_T7,
ECFP_ALPHABASE_64 * ECFP_T8,
ECFP_ALPHABASE_64 * ECFP_T9,
ECFP_ALPHABASE_64 * ECFP_T10,
ECFP_ALPHABASE_64 * ECFP_T11,
ECFP_ALPHABASE_64 * ECFP_T12,
ECFP_ALPHABASE_64 * ECFP_T13,
ECFP_ALPHABASE_64 * ECFP_T14,
ECFP_ALPHABASE_64 * ECFP_T15,
ECFP_ALPHABASE_64 * ECFP_T16,
ECFP_ALPHABASE_64 * ECFP_T17,
ECFP_ALPHABASE_64 * ECFP_T18,
ECFP_ALPHABASE_64 * ECFP_T19
};
/* 0.011111111111111111111111 (binary) = 0.5 - 2^25 (24 ones) */
#define ECFP_BETABASE 0.4999999701976776123046875
/*
* We subtract beta prior to using alpha to simulate rounding down. We
* make this close to 0.5 to round almost everything down, but exactly 0.5
* would cause some incorrect rounding. */
static const double ecfp_beta[2 * ECFP_MAXDOUBLES] = {
ECFP_BETABASE * ECFP_T0,
ECFP_BETABASE * ECFP_T1,
ECFP_BETABASE * ECFP_T2,
ECFP_BETABASE * ECFP_T3,
ECFP_BETABASE * ECFP_T4,
ECFP_BETABASE * ECFP_T5,
ECFP_BETABASE * ECFP_T6,
ECFP_BETABASE * ECFP_T7,
ECFP_BETABASE * ECFP_T8,
ECFP_BETABASE * ECFP_T9,
ECFP_BETABASE * ECFP_T10,
ECFP_BETABASE * ECFP_T11,
ECFP_BETABASE * ECFP_T12,
ECFP_BETABASE * ECFP_T13,
ECFP_BETABASE * ECFP_T14,
ECFP_BETABASE * ECFP_T15,
ECFP_BETABASE * ECFP_T16,
ECFP_BETABASE * ECFP_T17,
ECFP_BETABASE * ECFP_T18,
ECFP_BETABASE * ECFP_T19
};
static const double ecfp_beta_160 = ECFP_BETABASE * ECFP_TWO160;
static const double ecfp_beta_192 = ECFP_BETABASE * ECFP_TWO192;
static const double ecfp_beta_224 = ECFP_BETABASE * ECFP_TWO224;
/* Affine EC Point. This is the basic representation (x, y) of an elliptic
* curve point. */
typedef struct {
double x[ECFP_MAXDOUBLES];
double y[ECFP_MAXDOUBLES];
} ecfp_aff_pt;
/* Jacobian EC Point. This coordinate system uses X = x/z^2, Y = y/z^3,
* which enables calculations with fewer inversions than affine
* coordinates. */
typedef struct {
double x[ECFP_MAXDOUBLES];
double y[ECFP_MAXDOUBLES];
double z[ECFP_MAXDOUBLES];
} ecfp_jac_pt;
/* Chudnovsky Jacobian EC Point. This coordinate system is the same as
* Jacobian, except it keeps z^2, z^3 for faster additions. */
typedef struct {
double x[ECFP_MAXDOUBLES];
double y[ECFP_MAXDOUBLES];
double z[ECFP_MAXDOUBLES];
double z2[ECFP_MAXDOUBLES];
double z3[ECFP_MAXDOUBLES];
} ecfp_chud_pt;
/* Modified Jacobian EC Point. This coordinate system is the same as
* Jacobian, except it keeps a*z^4 for faster doublings. */
typedef struct {
double x[ECFP_MAXDOUBLES];
double y[ECFP_MAXDOUBLES];
double z[ECFP_MAXDOUBLES];
double az4[ECFP_MAXDOUBLES];
} ecfp_jm_pt;
struct EC_group_fp_str;
typedef struct EC_group_fp_str EC_group_fp;
struct EC_group_fp_str {
int fpPrecision; /* Set to number of bits in mantissa, 53
* or 64 */
int numDoubles;
int primeBitSize;
int orderBitSize;
int doubleBitSize;
int numInts;
int aIsM3; /* True if curvea == -3 (mod p), then we
* can optimize doubling */
double curvea[ECFP_MAXDOUBLES];
/* Used to truncate a double to the number of bits in the curve */
double bitSize_alpha;
/* Pointer to either ecfp_alpha_53 or ecfp_alpha_64 */
const double *alpha;
void (*ecfp_singleReduce) (double *r, const EC_group_fp * group);
void (*ecfp_reduce) (double *r, double *x, const EC_group_fp * group);
/* Performs a "tidy" operation, which performs carrying, moving excess
* bits from one double to the next double, so that the precision of
* the doubles is reduced to the regular precision ECFP_DSIZE. This
* might result in some float digits being negative. */
void (*ecfp_tidy) (double *t, const double *alpha,
const EC_group_fp * group);
/* Perform a point addition using coordinate system Jacobian + Affine
* -> Jacobian. Input and output should be multi-precision floating
* point integers. */
void (*pt_add_jac_aff) (const ecfp_jac_pt * p, const ecfp_aff_pt * q,
ecfp_jac_pt * r, const EC_group_fp * group);
/* Perform a point doubling in Jacobian coordinates. Input and output
* should be multi-precision floating point integers. */
void (*pt_dbl_jac) (const ecfp_jac_pt * dp, ecfp_jac_pt * dr,
const EC_group_fp * group);
/* Perform a point addition using Jacobian coordinate system. Input
* and output should be multi-precision floating point integers. */
void (*pt_add_jac) (const ecfp_jac_pt * p, const ecfp_jac_pt * q,
ecfp_jac_pt * r, const EC_group_fp * group);
/* Perform a point doubling in Modified Jacobian coordinates. Input
* and output should be multi-precision floating point integers. */
void (*pt_dbl_jm) (const ecfp_jm_pt * p, ecfp_jm_pt * r,
const EC_group_fp * group);
/* Perform a point doubling using coordinates Affine -> Chudnovsky
* Jacobian. Input and output should be multi-precision floating point
* integers. */
void (*pt_dbl_aff2chud) (const ecfp_aff_pt * p, ecfp_chud_pt * r,
const EC_group_fp * group);
/* Perform a point addition using coordinates: Modified Jacobian +
* Chudnovsky Jacobian -> Modified Jacobian. Input and output should
* be multi-precision floating point integers. */
void (*pt_add_jm_chud) (ecfp_jm_pt * p, ecfp_chud_pt * q,
ecfp_jm_pt * r, const EC_group_fp * group);
/* Perform a point addition using Chudnovsky Jacobian coordinates.
* Input and output should be multi-precision floating point integers.
*/
void (*pt_add_chud) (const ecfp_chud_pt * p, const ecfp_chud_pt * q,
ecfp_chud_pt * r, const EC_group_fp * group);
/* Expects out to be an array of size 16 of Chudnovsky Jacobian
* points. Fills in Chudnovsky Jacobian form (x, y, z, z^2, z^3), for
* -15P, -13P, -11P, -9P, -7P, -5P, -3P, -P, P, 3P, 5P, 7P, 9P, 11P,
* 13P, 15P */
void (*precompute_chud) (ecfp_chud_pt * out, const ecfp_aff_pt * p,
const EC_group_fp * group);
/* Expects out to be an array of size 16 of Jacobian points. Fills in
* Chudnovsky Jacobian form (x, y, z), for O, P, 2P, ... 15P */
void (*precompute_jac) (ecfp_jac_pt * out, const ecfp_aff_pt * p,
const EC_group_fp * group);
};
/* Computes r = x*y.
* r must be different (point to different memory) than x and y.
* Does not tidy or reduce. */
void ecfp_multiply(double *r, const double *x, const double *y);
/* Performs a "tidy" operation, which performs carrying, moving excess
* bits from one double to the next double, so that the precision of the
* doubles is reduced to the regular precision group->doubleBitSize. This
* might result in some float digits being negative. */
void ecfp_tidy(double *t, const double *alpha, const EC_group_fp * group);
/* Performs tidying on only the upper float digits of a multi-precision
* floating point integer, i.e. the digits beyond the regular length which
* are removed in the reduction step. */
void ecfp_tidyUpper(double *t, const EC_group_fp * group);
/* Performs tidying on a short multi-precision floating point integer (the
* lower group->numDoubles floats). */
void ecfp_tidyShort(double *t, const EC_group_fp * group);
/* Performs a more mathematically precise "tidying" so that each term is
* positive. This is slower than the regular tidying, and is used for
* conversion from floating point to integer. */
void ecfp_positiveTidy(double *t, const EC_group_fp * group);
/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
* a, b and p are the elliptic curve coefficients and the prime that
* determines the field GFp. Elliptic curve points P and R can be
* identical. Uses mixed Jacobian-affine coordinates. Uses 4-bit window
* method. */
mp_err
ec_GFp_point_mul_jac_4w_fp(const mp_int *n, const mp_int *px,
const mp_int *py, mp_int *rx, mp_int *ry,
const ECGroup *ecgroup);
/* Computes R = nP where R is (rx, ry) and P is the base point. The
* parameters a, b and p are the elliptic curve coefficients and the prime
* that determines the field GFp. Elliptic curve points P and R can be
* identical. Uses mixed Jacobian-affine coordinates (Jacobian
* coordinates for doubles and affine coordinates for additions; based on
* recommendation from Brown et al.). Uses window NAF method (algorithm
* 11) for scalar-point multiplication from Brown, Hankerson, Lopez,
* Menezes. Software Implementation of the NIST Elliptic Curves Over Prime
* Fields. */
mp_err ec_GFp_point_mul_wNAF_fp(const mp_int *n, const mp_int *px,
const mp_int *py, mp_int *rx, mp_int *ry,
const ECGroup *ecgroup);
/* Uses mixed Jacobian-affine coordinates to perform a point
* multiplication: R = n * P, n scalar. Uses mixed Jacobian-affine
* coordinates (Jacobian coordinates for doubles and affine coordinates
* for additions; based on recommendation from Brown et al.). Not very
* time efficient but quite space efficient, no precomputation needed.
* group contains the elliptic curve coefficients and the prime that
* determines the field GFp. Elliptic curve points P and R can be
* identical. Performs calculations in floating point number format, since
* this is faster than the integer operations on the ULTRASPARC III.
* Uses left-to-right binary method (double & add) (algorithm 9) for
* scalar-point multiplication from Brown, Hankerson, Lopez, Menezes.
* Software Implementation of the NIST Elliptic Curves Over Prime Fields. */
mp_err
ec_GFp_pt_mul_jac_fp(const mp_int *n, const mp_int *px, const mp_int *py,
mp_int *rx, mp_int *ry, const ECGroup *ecgroup);
/* Cleans up extra memory allocated in ECGroup for this implementation. */
void ec_GFp_extra_free_fp(ECGroup *group);
/* Converts from a floating point representation into an mp_int. Expects
* that d is already reduced. */
void
ecfp_fp2i(mp_int *mpout, double *d, const ECGroup *ecgroup);
/* Converts from an mpint into a floating point representation. */
void
ecfp_i2fp(double *out, const mp_int *x, const ECGroup *ecgroup);
/* Tests what precision floating point arithmetic is set to. This should
* be either a 53-bit mantissa (IEEE standard) or a 64-bit mantissa
* (extended precision on x86) and sets it into the EC_group_fp. Returns
* either 53 or 64 accordingly. */
int ec_set_fp_precision(EC_group_fp * group);
#endif