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Manuel Pégourié-Gonnard 2013-12-05 10:26:01 +01:00
parent d962273594
commit 7a949d3f5b
2 changed files with 21 additions and 17 deletions
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32
include/polarssl/ecp.h
View File

@ -108,10 +108,16 @@ ecp_point;
/** /**
* \brief ECP group structure * \brief ECP group structure
* *
* The curves we consider are defined by y^2 = x^3 + A x + B mod P, * We consider two types of curves equations:
* and a generator for a large subgroup of order N is fixed. * 1. Short Weierstrass y^2 = x^3 + A x + B mod P (SEC1 + RFC 4492)
* 2. Montgomery, y^2 = x^3 + A x^2 + x mod P (M255 + draft)
* In both cases, a generator G for a prime-order subgroup is fixed. In the
* short weierstrass, this subgroup is actually the whole curve, and its
* cardinal is denoted by N.
* *
* pbits and nbits must be the size of P and N in bits. * In the case of Montgomery curves, we don't store A but (A + 2) / 4 which is
* the quantity actualy used in the formulas. Also, nbits is not the size of N
* but the required size for private keys.
* *
* If modp is NULL, reduction modulo P is done using a generic algorithm. * If modp is NULL, reduction modulo P is done using a generic algorithm.
* Otherwise, it must point to a function that takes an mpi in the range * Otherwise, it must point to a function that takes an mpi in the range
@ -124,18 +130,18 @@ typedef struct
{ {
ecp_group_id id; /*!< internal group identifier */ ecp_group_id id; /*!< internal group identifier */
mpi P; /*!< prime modulus of the base field */ mpi P; /*!< prime modulus of the base field */
mpi A; /*!< linear term in the equation */ mpi A; /*!< 1. A in the equation, or 2. (A + 2) / 4 */
mpi B; /*!< constant term in the equation */ mpi B; /*!< 1. B in the equation, or 2. unused */
ecp_point G; /*!< generator of the subgroup used */ ecp_point G; /*!< generator of the (sub)group used */
mpi N; /*!< the order of G */ mpi N; /*!< 1. the order of G, or 2. unused */
size_t pbits; /*!< number of bits in P */ size_t pbits; /*!< number of bits in P */
size_t nbits; /*!< number of bits in N */ size_t nbits; /*!< number of bits in 1. P, or 2. private keys */
unsigned int h; /*!< cofactor (unused now: assume 1) */ unsigned int h; /*!< unused */
int (*modp)(mpi *); /*!< function for fast reduction mod P */ int (*modp)(mpi *); /*!< function for fast reduction mod P */
int (*t_pre)(ecp_point *, void *); /*!< currently unused */ int (*t_pre)(ecp_point *, void *); /*!< unused */
int (*t_post)(ecp_point *, void *); /*!< currently unused */ int (*t_post)(ecp_point *, void *); /*!< unused */
void *t_data; /*!< currently unused */ void *t_data; /*!< unused */
ecp_point *T; /*!< pre-computed points for ecp_mul() */ ecp_point *T; /*!< pre-computed points for ecp_mul_comb() */
size_t T_size; /*!< number for pre-computed points */ size_t T_size; /*!< number for pre-computed points */
} }
ecp_group; ecp_group;

6
library/ecp.c
View File

@ -731,7 +731,7 @@ cleanup:
* Theory", Algorithm 10.3.4.) * Theory", Algorithm 10.3.4.)
* *
* Warning: fails (returning an error) if one of the points is zero! * Warning: fails (returning an error) if one of the points is zero!
* This should never happen, see choice of w in ecp_mul(). * This should never happen, see choice of w in ecp_mul_comb().
* *
* Cost: 1N(t) := 1I + (6t - 3)M + 1S * Cost: 1N(t) := 1I + (6t - 3)M + 1S
*/ */
@ -896,7 +896,7 @@ cleanup:
* but those of P don't need to. R is not normalized. * but those of P don't need to. R is not normalized.
* *
* Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q. * Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
* None of these cases can happen as intermediate step in ecp_mul(): * None of these cases can happen as intermediate step in ecp_mul_comb():
* - at each step, P, Q and R are multiples of the base point, the factor * - at each step, P, Q and R are multiples of the base point, the factor
* being less than its order, so none of them is zero; * being less than its order, so none of them is zero;
* - Q is an odd multiple of the base point, P an even multiple, * - Q is an odd multiple of the base point, P an even multiple,
@ -982,7 +982,6 @@ cleanup:
/* /*
* Addition: R = P + Q, result's coordinates normalized * Addition: R = P + Q, result's coordinates normalized
* Cost: 1A + 1N = 1I + 11M + 4S
*/ */
int ecp_add( const ecp_group *grp, ecp_point *R, int ecp_add( const ecp_group *grp, ecp_point *R,
const ecp_point *P, const ecp_point *Q ) const ecp_point *P, const ecp_point *Q )
@ -1001,7 +1000,6 @@ cleanup:
/* /*
* Subtraction: R = P - Q, result's coordinates normalized * Subtraction: R = P - Q, result's coordinates normalized
* Cost: 1A + 1N = 1I + 11M + 4S
*/ */
int ecp_sub( const ecp_group *grp, ecp_point *R, int ecp_sub( const ecp_group *grp, ecp_point *R,
const ecp_point *P, const ecp_point *Q ) const ecp_point *P, const ecp_point *Q )