X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/41a324a748544b0fb9b0acfc65b1a39b7611550c..41cb1beba35c8a69ee7ae1298f51711995011b5c:/ec.h diff --git a/ec.h b/ec.h index 12ff823..105838c 100644 --- a/ec.h +++ b/ec.h @@ -1,6 +1,6 @@ /* -*-c-*- * - * $Id: ec.h,v 1.2 2001/05/07 17:29:44 mdw Exp $ + * $Id: ec.h,v 1.4 2003/05/15 23:25:59 mdw Exp $ * * Elliptic curve definitions * @@ -30,6 +30,12 @@ /*----- Revision history --------------------------------------------------* * * $Log: ec.h,v $ + * 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. @@ -53,32 +59,47 @@ /*----- 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 --- */ + typedef struct ec_ops { void (*destroy)(ec_curve */*c*/); ec *(*in)(ec_curve */*c*/, ec */*d*/, const ec */*p*/); ec *(*out)(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*/); } 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->in((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)) /*----- Simple memory management things -----------------------------------*/ @@ -175,9 +196,9 @@ extern ec *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) @@ -186,33 +207,31 @@ extern ec *ec_copy(ec */*d*/, const ec */*p*/); /*----- Interesting arithmetic --------------------------------------------*/ -/* --- @ec_denorm@ --- * +/* --- @ec_in@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point * @const ec *p@ = pointer to the source point * - * Returns: --- + * Returns: The destination point. * - * Use: Denormalizes the given point, converting to internal - * representations and setting the denominator to 1. + * Use: Converts a point to internal representation. */ -extern void ec_denorm(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_in(ec_curve */*c*/, ec */*d*/, const ec */*p*/); -/* --- @ec_norm@ --- * +/* --- @ec_out@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point * @const ec *p@ = pointer to the source point * - * Returns: --- + * Returns: The destination point. * - * Use: Normalizes the given point, by dividing through by the - * denominator and returning to external representation. + * Use: Converts a point to external representation. */ -extern void ec_norm(ec_curve */*c*/, ec */*d*/, const ec */*p*/); +extern ec *ec_out(ec_curve */*c*/, ec */*d*/, const ec */*p*/); /* --- @ec_find@ --- * * @@ -220,12 +239,28 @@ extern void ec_norm(ec_curve */*c*/, ec */*d*/, const ec */*p*/); * @ec *d@ = pointer to the destination point * @mp *x@ = a possible x-coordinate * - * Returns: Zero if OK, nonzero if there isn't a point there. + * Returns: The destination if OK, or null if no point was found. + * + * 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 ec *ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); + +/* --- @ec_neg@ --- * + * + * Arguments: @ec_curve *c@ = pointer to an elliptic curve + * @ec *d@ = pointer to the destination point + * @const ec *p@ = pointer to the operand point * - * Use: Finds a point on an elliptic curve with a given x-coordinate. + * Returns: The destination point. + * + * 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@ --- * * @@ -241,6 +276,20 @@ extern void ec_find(ec_curve */*c*/, ec */*d*/, mp */*x*/); 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@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve @@ -254,7 +303,7 @@ extern ec *ec_add(ec_curve */*c*/, ec */*d*/, extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); -/* --- @ec_mul@ --- * +/* --- @ec_mul@, @ec_imul@ --- * * * Arguments: @ec_curve *c@ = pointer to an elliptic curve * @ec *d@ = pointer to the destination point @@ -263,10 +312,31 @@ extern ec *ec_dbl(ec_curve */*c*/, ec */*d*/, const ec */*p*/); * * 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 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 -----------------------------------------*/ @@ -301,9 +371,36 @@ extern ec *ec_idout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); extern ec *ec_projin(ec_curve */*c*/, ec */*d*/, const ec */*p*/); extern ec *ec_projout(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 + * + * Returns: --- + * + * Use: Destroys a description of an elliptic curve. + */ + +extern void ec_destroycurve(ec_curve */*c*/); + +/* --- @ec_prime@, @ec_primeproj@ --- * * * Arguments: @field *f@ = the underyling field for this elliptic curve * @mp *a, *b@ = the coefficients for this curve @@ -311,10 +408,12 @@ extern ec *ec_projout(ec_curve */*c*/, ec */*d*/, const ec */*p*/); * 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@ --- * *