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@ -108,10 +108,16 @@ ecp_point;
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/**
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* \brief ECP group structure
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*
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* The curves we consider are defined by y^2 = x^3 + A x + B mod P,
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* and a generator for a large subgroup of order N is fixed.
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* We consider two types of curves equations:
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* 1. Short Weierstrass y^2 = x^3 + A x + B mod P (SEC1 + RFC 4492)
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* 2. Montgomery, y^2 = x^3 + A x^2 + x mod P (M255 + draft)
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* In both cases, a generator G for a prime-order subgroup is fixed. In the
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* short weierstrass, this subgroup is actually the whole curve, and its
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* cardinal is denoted by N.
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*
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* pbits and nbits must be the size of P and N in bits.
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* In the case of Montgomery curves, we don't store A but (A + 2) / 4 which is
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* the quantity actualy used in the formulas. Also, nbits is not the size of N
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* but the required size for private keys.
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*
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* If modp is NULL, reduction modulo P is done using a generic algorithm.
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* Otherwise, it must point to a function that takes an mpi in the range
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@ -124,18 +130,18 @@ typedef struct
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{
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ecp_group_id id; /*!< internal group identifier */
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mpi P; /*!< prime modulus of the base field */
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mpi A; /*!< linear term in the equation */
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mpi B; /*!< constant term in the equation */
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ecp_point G; /*!< generator of the subgroup used */
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mpi N; /*!< the order of G */
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mpi A; /*!< 1. A in the equation, or 2. (A + 2) / 4 */
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mpi B; /*!< 1. B in the equation, or 2. unused */
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ecp_point G; /*!< generator of the (sub)group used */
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mpi N; /*!< 1. the order of G, or 2. unused */
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size_t pbits; /*!< number of bits in P */
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size_t nbits; /*!< number of bits in N */
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unsigned int h; /*!< cofactor (unused now: assume 1) */
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size_t nbits; /*!< number of bits in 1. P, or 2. private keys */
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unsigned int h; /*!< unused */
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int (*modp)(mpi *); /*!< function for fast reduction mod P */
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int (*t_pre)(ecp_point *, void *); /*!< currently unused */
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int (*t_post)(ecp_point *, void *); /*!< currently unused */
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void *t_data; /*!< currently unused */
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ecp_point *T; /*!< pre-computed points for ecp_mul() */
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int (*t_pre)(ecp_point *, void *); /*!< unused */
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int (*t_post)(ecp_point *, void *); /*!< unused */
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void *t_data; /*!< unused */
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ecp_point *T; /*!< pre-computed points for ecp_mul_comb() */
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size_t T_size; /*!< number for pre-computed points */
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}
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ecp_group;
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@ -731,7 +731,7 @@ cleanup:
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* Theory", Algorithm 10.3.4.)
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*
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* Warning: fails (returning an error) if one of the points is zero!
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* This should never happen, see choice of w in ecp_mul().
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* This should never happen, see choice of w in ecp_mul_comb().
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*
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* Cost: 1N(t) := 1I + (6t - 3)M + 1S
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*/
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@ -896,7 +896,7 @@ cleanup:
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* but those of P don't need to. R is not normalized.
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*
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* Special cases: (1) P or Q is zero, (2) R is zero, (3) P == Q.
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* None of these cases can happen as intermediate step in ecp_mul():
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* None of these cases can happen as intermediate step in ecp_mul_comb():
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* - at each step, P, Q and R are multiples of the base point, the factor
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* being less than its order, so none of them is zero;
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* - Q is an odd multiple of the base point, P an even multiple,
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@ -982,7 +982,6 @@ cleanup:
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/*
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* Addition: R = P + Q, result's coordinates normalized
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* Cost: 1A + 1N = 1I + 11M + 4S
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*/
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int ecp_add( const ecp_group *grp, ecp_point *R,
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const ecp_point *P, const ecp_point *Q )
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@ -1001,7 +1000,6 @@ cleanup:
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/*
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* Subtraction: R = P - Q, result's coordinates normalized
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* Cost: 1A + 1N = 1I + 11M + 4S
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*/
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int ecp_sub( const ecp_group *grp, ecp_point *R,
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const ecp_point *P, const ecp_point *Q )
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