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mbedtls_ecp_group Struct Reference
The ECP group structure. More...
#include <ecp.h>
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 |
int(* | modp )(mbedtls_mpi *) |
int(* | t_pre )(mbedtls_ecp_point *, void *) |
int(* | t_post )(mbedtls_ecp_point *, void *) |
void * | t_data |
mbedtls_ecp_point * | T |
size_t | T_size |
Detailed 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.
Definition at line 159 of file mbedtls/inc/mbedtls/ecp.h.
Field Documentation
For Short Weierstrass: A
in the equation. For Montgomery curves: (A + 2) / 4
.
Definition at line 163 of file mbedtls/inc/mbedtls/ecp.h.
For Short Weierstrass: B
in the equation. For Montgomery curves: unused.
Definition at line 165 of file mbedtls/inc/mbedtls/ecp.h.
The generator of the subgroup used.
Definition at line 167 of file mbedtls/inc/mbedtls/ecp.h.
mbedtls_ecp_group_id id |
An internal group identifier.
Definition at line 161 of file mbedtls/inc/mbedtls/ecp.h.
int(* modp)(mbedtls_mpi *) |
The function for fast pseudo-reduction mod P
(see above).
Definition at line 174 of file mbedtls/inc/mbedtls/ecp.h.
The order of G
.
Definition at line 168 of file mbedtls/inc/mbedtls/ecp.h.
size_t nbits |
For Short Weierstrass: The number of bits in P
. For Montgomery curves: the number of bits in the private keys.
Definition at line 170 of file mbedtls/inc/mbedtls/ecp.h.
The prime modulus of the base field.
Definition at line 162 of file mbedtls/inc/mbedtls/ecp.h.
size_t pbits |
The number of bits in P
.
Definition at line 169 of file mbedtls/inc/mbedtls/ecp.h.
Pre-computed points for ecp_mul_comb().
Definition at line 179 of file mbedtls/inc/mbedtls/ecp.h.
void* t_data |
Unused.
Definition at line 178 of file mbedtls/inc/mbedtls/ecp.h.
int(* t_post)(mbedtls_ecp_point *, void *) |
Unused.
Definition at line 177 of file mbedtls/inc/mbedtls/ecp.h.
int(* t_pre)(mbedtls_ecp_point *, void *) |
Unused.
Definition at line 176 of file mbedtls/inc/mbedtls/ecp.h.
size_t T_size |
The number of pre-computed points.
Definition at line 180 of file mbedtls/inc/mbedtls/ecp.h.
Generated on Tue Jul 12 2022 12:47:06 by
