X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/b0ab12e6a6cb035df2b6312df7ad1736af0a6128..bc985cefafea2e1b02095a2ff2a9982c4c647d17:/ec.h diff --git a/ec.h b/ec.h index db5adfc..d398f4a 100644 --- a/ec.h +++ b/ec.h @@ -1,6 +1,6 @@ /* -*-c-*- * - * $Id: ec.h,v 1.1 2001/04/29 18:12:33 mdw Exp $ + * $Id: ec.h,v 1.7 2004/03/23 15:19:32 mdw Exp $ * * Elliptic curve definitions * @@ -30,6 +30,36 @@ /*----- Revision history --------------------------------------------------* * * $Log: ec.h,v $ + * Revision 1.7 2004/03/23 15:19:32 mdw + * Test elliptic curves more thoroughly. + * + * Revision 1.6 2004/03/22 02:19:10 mdw + * Rationalise the sliding-window threshold. Drop guarantee that right + * arguments to EC @add@ are canonical, and fix up projective implementations + * to cope. + * + * Revision 1.5 2004/03/21 22:52:06 mdw + * Merge and close elliptic curve branch. + * + * Revision 1.4.4.3 2004/03/21 22:39:46 mdw + * Elliptic curves on binary fields work. + * + * Revision 1.4.4.2 2004/03/20 00:13:31 mdw + * Projective coordinates for prime curves + * + * Revision 1.4.4.1 2003/06/10 13:43:53 mdw + * Simple (non-projective) curves over prime fields now seem to work. + * + * Revision 1.4 2003/05/15 23:25:59 mdw + * Make elliptic curve stuff build. + * + * Revision 1.3 2002/01/13 13:48:44 mdw + * Further progress. + * + * Revision 1.2 2001/05/07 17:29:44 mdw + * Treat projective coordinates as an internal representation. Various + * minor interface changes. + * * Revision 1.1 2001/04/29 18:12:33 mdw * Prototype version. * @@ -49,28 +79,61 @@ /*----- Data structures ---------------------------------------------------*/ +/* --- An elliptic curve representation --- */ + typedef struct ec_curve { const struct ec_ops *ops; /* Curve operations */ field *f; /* Underlying field structure */ } ec_curve; +/* --- An elliptic curve point --- */ + typedef struct ec { mp *x, *y; /* Point coordinates */ mp *z; /* Common denominator (or null) */ } ec; +/* --- A factor for simultaneous multiplication --- */ + +typedef struct ec_mulfactor { + ec base; /* The point */ + mp *exp; /* The exponent */ +} ec_mulfactor; + +/* --- Elliptic curve operations --- * + * + * All operations (apart from @destroy@ and @in@) are guaranteed to be + * performed on internal representations of points. + * + * (Historical note. We used to guarantee that the second to @add@ and @mul@ + * was the output of @in@ or @fix@, but this canonification turned out to + * make the precomputation in @ec_exp@ too slow. Projective implementations + * must therefore cope with a pair of arbitrary points.) + */ + typedef struct ec_ops { void (*destroy)(ec_curve */*c*/); - int (*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/); - void (*add)(ec_curve */*c*/, ec */*d*/, ec */*p*/, ec */*q*/); - void (*dbl)(ec_curve */*c*/, ec */*d*/, ec */*p*/); + ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + ec *(*out)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + ec *(*fix)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + ec *(*find)(ec_curve */*c*/, ec */*d*/, mp */*x*/); + ec *(*neg)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + ec *(*add)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); + ec *(*sub)(ec_curve */*c*/, ec */*d*/, const ec */*p*/, const ec */*q*/); + ec *(*dbl)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + int (*check)(ec_curve */*c*/, const ec */*p*/); } ec_ops; -#define EC_DESTROY(c) (c)->ops->destroy((c)) +#define EC_IN(c, d, p) (c)->ops->in((c), (d), (p)) +#define EC_OUT(c, d, p) (c)->ops->out((c), (d), (p)) +#define EC_FIX(c, d, p) (c)->ops->fix((c), (d), (p)) #define EC_FIND(c, d, x) (c)->ops->find((c), (d), (x)) +#define EC_NEG(c, d, x) (c)->ops->neg((c), (d), (x)) #define EC_ADD(c, d, p, q) (c)->ops->add((c), (d), (p), (q)) +#define EC_SUB(c, d, p, q) (c)->ops->sub((c), (d), (p), (q)) #define EC_DBL(c, d, p) (c)->ops->dbl((c), (d), (p)) +#define EC_CHECK(c, p) (c)->ops->check((c), (p)) /*----- Simple memory management things -----------------------------------*/ @@ -78,7 +141,7 @@ typedef struct ec_ops { * * Arguments: @ec *p@ = pointer to an elliptic-curve point * - * Returns: --- + * Returns: The argument @p@. * * Use: Initializes a new point. The initial value is the additive * identity (which is universal for all curves). @@ -91,7 +154,7 @@ typedef struct ec_ops { _p->x = _p->y = _p->z = MP_NEW; \ } while (0) -extern void ec_create(ec */*p*/); +extern ec *ec_create(ec */*p*/); /* --- @ec_destroy@ --- * * @@ -129,7 +192,7 @@ extern int ec_atinf(const ec */*p*/); * * Arguments: @ec *p@ = pointer to a point * - * Returns: --- + * Returns: The argument @p@. * * Use: Sets the given point to be the point %$O$% at infinity. */ @@ -146,14 +209,14 @@ extern int ec_atinf(const ec */*p*/); } \ } while (0) -extern void ec_setinf(ec */*p*/); +extern ec *ec_setinf(ec */*p*/); /* --- @ec_copy@ --- * * * Arguments: @ec *d@ = pointer to destination point * @const ec *p@ = pointer to source point * - * Returns: --- + * Returns: The destination @d@. * * Use: Creates a copy of an elliptic curve point. */ @@ -166,57 +229,74 @@ extern void ec_setinf(ec */*p*/); if (EC_ATINF(p)) \ _d->x = _d->y = _d->z = MP_NEW; \ else { \ - _d->x = _p->x; \ - _d->y = _p->y; \ - _d->z = _p->z; \ + _d->x = MP_COPY(_p->x); \ + _d->y = MP_COPY(_p->y); \ + _d->z = _p->z ? MP_COPY(_p->z) : MP_NEW; \ } \ } \ } while (0) -extern void ec_copy(ec */*d*/, const ec */*p*/); +extern ec *ec_copy(ec */*d*/, const ec */*p*/); + +/* --- @ec_eq@ --- * + * + * Arguments: @const ec *p, *q@ = two points + * + * Returns: Nonzero if the points are equal. Compares external-format + * points. + */ + +#define EC_EQ(p, q) \ + ((EC_ATINF(p) && EC_ATINF(q)) || \ + (!EC_ATINF(p) && !EC_ATINF(q) && \ + MP_EQ((p)->x, (q)->x) && \ + MP_EQ((p)->y, (q)->y))) + +extern int ec_eq(const ec *p, const ec *q); /*----- Interesting arithmetic --------------------------------------------*/ -/* --- @ec_denorm@ --- * +/* --- @ec_find@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point - * @const ec *p@ = pointer to the source point + * @mp *x@ = a possible x-coordinate * - * Returns: --- + * Returns: The destination if OK, or null if no point was found. * - * Use: Denormalizes the given point, converting to internal - * representations and setting the denominator to 1. + * Use: Finds a point on an elliptic curve with a given + * x-coordinate. If there is no point with the given + * %$x$%-coordinate, a null pointer is returned and the + * destination is left invalid. */ -extern void ec_denorm(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); -/* --- @ec_norm@ --- * +/* --- @ec_rand@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point - * @const ec *p@ = pointer to the source point + * @grand *r@ = random number source * - * Returns: --- + * Returns: The destination @d@. * - * Use: Normalizes the given point, by dividing through by the - * denominator and returning to external representation. + * Use: Finds a random point on the given curve. */ -extern void ec_norm(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_rand(ec_curve */*c*/, ec */*d*/, grand */*r*/); -/* --- @ec_find@ --- * +/* --- @ec_neg@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point - * @mp *x@ = a possible x-coordinate + * @const ec *p@ = pointer to the operand point * - * Returns: Zero if OK, nonzero if there isn't a point there. + * Returns: The destination point. * - * Use: Finds a point on an elliptic curve with a given x-coordinate. + * Use: Computes the negation of the given point. */ -extern void ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); +extern ec *ec_neg(ec_curve */*c*/, ec */*d*/, const ec */*p*/); /* --- @ec_add@ --- * * @@ -224,13 +304,27 @@ extern void ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); * @ec *d@ = pointer to the destination point * @const ec *p, *q@ = pointers to the operand points * - * Returns: --- + * Returns: The destination @d@. * * Use: Adds two points on an elliptic curve. */ -extern void ec_add(ec_curve */*c*/, ec */*d*/, - const ec */*p*/, const ec */*q*/); +extern ec *ec_add(ec_curve */*c*/, ec */*d*/, + const ec */*p*/, const ec */*q*/); + +/* --- @ec_sub@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @ec *d@ = pointer to the destination point + * @const ec *p, *q@ = pointers to the operand points + * + * Returns: The destination @d@. + * + * Use: Subtracts one point from another on an elliptic curve. + */ + +extern ec *ec_sub(ec_curve */*c*/, ec */*d*/, + const ec */*p*/, const ec */*q*/); /* --- @ec_dbl@ --- * * @@ -238,54 +332,153 @@ extern void ec_add(ec_curve */*c*/, ec */*d*/, * @ec *d@ = pointer to the destination point * @const ec *p@ = pointer to the operand point * - * Returns: --- + * Returns: The destination @d@. * * Use: Doubles a point on an elliptic curve. */ -extern void ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); -/* --- @ec_mul@ --- * +/* --- @ec_check@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @const ec *p@ = pointer to the point + * + * Returns: Zero if OK, nonzero if this is an invalid point. + * + * Use: Checks that a point is actually on an elliptic curve. + */ + +extern int ec_check(ec_curve */*c*/, const ec */*p*/); + +/* --- @ec_mul@, @ec_imul@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point * @const ec *p@ = pointer to the generator point * @mp *n@ = integer multiplier * - * Returns: --- + * Returns: The destination @d@. * - * Use: Multiplies a point by a scalar, returning %$n p$%. + * Use: Multiplies a point by a scalar, returning %$n p$%. The + * @imul@ variant uses internal representations for argument + * and result. */ -extern void ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); +extern ec *ec_mul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); +extern ec *ec_imul(ec_curve */*c*/, ec */*d*/, const ec */*p*/, mp */*n*/); + +/* --- @ec_mmul@, @ec_immul@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @ec *d@ = pointer to the destination point + * @const ec_mulfactor *f@ = pointer to vector of factors + * @size_t n@ = number of factors + * + * Returns: The destination @d@. + * + * Use: Does simultaneous point multiplication. The @immul@ variant + * uses internal representations for arguments and result. + */ + +extern ec *ec_mmul(ec_curve */*c*/, ec */*d*/, + const ec_mulfactor */*f*/, size_t /*n*/); +extern ec *ec_immul(ec_curve */*c*/, ec */*d*/, + const ec_mulfactor */*f*/, size_t /*n*/); + +/*----- Standard curve operations -----------------------------------------*/ + +/* --- @ec_idin@, @ec_idout@, @ec_idfix@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @ec *d@ = pointer to the destination + * @const ec *p@ = pointer to a source point + * + * Returns: The destination @d@. + * + * Use: An identity operation if your curve has no internal + * representation. (The field internal representation is still + * used.) + */ + +extern ec *ec_idin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_idfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + +/* --- @ec_projin@, @ec_projout@, @ec_projfix@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @ec *d@ = pointer to the destination + * @const ec *p@ = pointer to a source point + * + * Returns: The destination @d@. + * + * Use: Conversion functions if your curve operations use a + * projective representation. + */ + +extern ec *ec_projin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_projout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_projfix(ec_curve */*c*/, ec */*d*/, const ec */*p*/); + +/* --- @ec_stdsub@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @ec *d@ = pointer to the destination + * @const ec *p, *q@ = the operand points + * + * Returns: The destination @d@. + * + * Use: Standard point subtraction operation, in terms of negation + * and addition. This isn't as efficient as a ready-made + * subtraction operator. + */ + +extern ec *ec_stdsub(ec_curve */*c*/, ec */*d*/, + const ec */*p*/, const ec */*q*/); /*----- Creating curves ---------------------------------------------------*/ -/* --- @ec_prime@ --- * +/* --- @ec_destroycurve@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an ellptic curve * - * Arguments: @field *f@ = the underyling field for this elliptic curve + * Returns: --- + * + * Use: Destroys a description of an elliptic curve. + */ + +extern void ec_destroycurve(ec_curve */*c*/); + +/* --- @ec_prime@, @ec_primeproj@ --- * + * + * Arguments: @field *f@ = the underlying field for this elliptic curve * @mp *a, *b@ = the coefficients for this curve * * Returns: A pointer to the curve. * * Use: Creates a curve structure for an elliptic curve defined over - * a prime field. + * a prime field. The @primeproj@ variant uses projective + * coordinates, which can be a win. */ extern ec_curve *ec_prime(field */*f*/, mp */*a*/, mp */*b*/); +extern ec_curve *ec_primeproj(field */*f*/, mp */*a*/, mp */*b*/); -/* --- @ec_bin@ --- * +/* --- @ec_bin@, @ec_binproj@ --- * * * Arguments: @field *f@ = the underlying field for this elliptic curve * @mp *a, *b@ = the coefficients for this curve * * Returns: A pointer to the curve. * - * Use: Creates a curve structure for a non-supersingular elliptic - * curve defined over a binary field. + * Use: Creates a curve structure for an elliptic curve defined over + * a binary field. The @binproj@ variant uses projective + * coordinates, which can be a win. */ extern ec_curve *ec_bin(field */*f*/, mp */*a*/, mp */*b*/); +extern ec_curve *ec_binproj(field */*f*/, mp */*a*/, mp */*b*/); /*----- That's all, folks -------------------------------------------------*/