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mbedtls_ecp_group Struct Reference

The ECP group structure. More...

Data Fields

mbedtls_ecp_group_id id
 
mbedtls_mpi P
 
mbedtls_mpi A
 
mbedtls_mpi B
 
mbedtls_ecp_point G
 
mbedtls_mpi N
 
size_t pbits
 
size_t nbits
 
unsigned int h
 
int(* modp )(mbedtls_mpi *)
 
int(* t_pre )(mbedtls_ecp_point *, void *)
 
int(* t_post )(mbedtls_ecp_point *, void *)
 
void * t_data
 
mbedtls_ecp_pointT
 
size_t T_size
 

Description

The ECP group structure.

We consider two types of curve equations:

  • Short Weierstrass: y^2 = x^3 + A x + B mod P (SEC1 + RFC-4492)
  • Montgomery: y^2 = x^3 + A x^2 + x mod P (Curve25519, Curve448)

In both cases, the generator (G) for a prime-order subgroup is fixed.

For Short Weierstrass, this subgroup is the whole curve, and its cardinality is denoted by N. Our code requires that N is an odd prime as mbedtls_ecp_mul() requires an odd number, and mbedtls_ecdsa_sign() requires that it is prime for blinding purposes.

For Montgomery curves, we do not store A, but (A + 2) / 4, which is the quantity used in the formulas. Additionally, 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. Otherwise, modp must point to a function that takes an mbedtls_mpi in the range of 0..2^(2*pbits)-1, and transforms it in-place to an integer which is congruent mod P to the given MPI, and is close enough to pbits in size, so that it may be efficiently brought in the 0..P-1 range by a few additions or subtractions. Therefore, it is only an approximative modular reduction. It must return 0 on success and non-zero on failure.

Note
Alternative implementations must keep the group IDs distinct. If two group structures have the same ID, then they must be identical.

Field Documentation

For Short Weierstrass: A in the equation. For Montgomery curves: (A + 2) / 4.

For Short Weierstrass: B in the equation. For Montgomery curves: unused.

The generator of the subgroup used.

An internal group identifier.

int(* modp)(mbedtls_mpi *)

The function for fast pseudo-reduction mod P (see above).

The order of G.

size_t nbits

For Short Weierstrass: The number of bits in P. For Montgomery curves: the number of bits in the private keys.

The prime modulus of the base field.

size_t pbits

The number of bits in P.

Pre-computed points for ecp_mul_comb().

void* t_data

Unused.

int(* t_post)(mbedtls_ecp_point *, void *)

Unused.

int(* t_pre)(mbedtls_ecp_point *, void *)

Unused.

size_t T_size

The number of pre-computed points.