334 lines
15 KiB
Groff
334 lines
15 KiB
Groff
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.\" ========================================================================
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.\"
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.IX Title "ec 3"
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.TH ec 3 "2016-03-01" "1.0.2g" "OpenSSL"
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.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.\" way too many mistakes in technical documents.
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.if n .ad l
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.nh
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.SH "NAME"
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ec \- Elliptic Curve functions
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.SH "SYNOPSIS"
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.IX Header "SYNOPSIS"
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.Vb 2
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\& #include <openssl/ec.h>
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\& #include <openssl/bn.h>
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\&
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\& const EC_METHOD *EC_GFp_simple_method(void);
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\& const EC_METHOD *EC_GFp_mont_method(void);
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\& const EC_METHOD *EC_GFp_nist_method(void);
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\& const EC_METHOD *EC_GFp_nistp224_method(void);
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\& const EC_METHOD *EC_GFp_nistp256_method(void);
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\& const EC_METHOD *EC_GFp_nistp521_method(void);
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\&
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\& const EC_METHOD *EC_GF2m_simple_method(void);
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\&
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\& EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
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\& void EC_GROUP_free(EC_GROUP *group);
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\& void EC_GROUP_clear_free(EC_GROUP *group);
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\& int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
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\& EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
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\& const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
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\& int EC_METHOD_get_field_type(const EC_METHOD *meth);
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\& int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
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\& const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
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\& int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
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\& int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
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\& void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
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\& int EC_GROUP_get_curve_name(const EC_GROUP *group);
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\& void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
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\& int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
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\& void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
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\& point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
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\& unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
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\& size_t EC_GROUP_get_seed_len(const EC_GROUP *);
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\& size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
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\& int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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\& int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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\& int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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\& int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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\& int EC_GROUP_get_degree(const EC_GROUP *group);
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\& int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
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\& int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
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\& int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
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\& EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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\& EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
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\& EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
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\&
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\& size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
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\&
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\& EC_POINT *EC_POINT_new(const EC_GROUP *group);
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\& void EC_POINT_free(EC_POINT *point);
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\& void EC_POINT_clear_free(EC_POINT *point);
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\& int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
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\& EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
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\& const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
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\& int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
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\& int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
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\& const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx);
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\& int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
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\& const EC_POINT *p, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx);
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\& int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
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\& const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
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\& int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
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\& const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
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\& int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
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\& const BIGNUM *x, int y_bit, BN_CTX *ctx);
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\& int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
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\& const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
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\& int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
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\& const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
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\& int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
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\& const BIGNUM *x, int y_bit, BN_CTX *ctx);
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\& size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
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\& point_conversion_form_t form,
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\& unsigned char *buf, size_t len, BN_CTX *ctx);
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\& int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
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\& const unsigned char *buf, size_t len, BN_CTX *ctx);
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\& BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *,
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\& point_conversion_form_t form, BIGNUM *, BN_CTX *);
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\& EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *,
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\& EC_POINT *, BN_CTX *);
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\& char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *,
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\& point_conversion_form_t form, BN_CTX *);
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\& EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *,
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\& EC_POINT *, BN_CTX *);
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\&
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\& int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
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\& int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx);
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\& int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
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\& int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
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\& int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
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\& int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
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\& int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
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\& int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx);
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\& int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, size_t num, const EC_POINT *p[], const BIGNUM *m[], BN_CTX *ctx);
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\& int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
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\& int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
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\& int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
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\&
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\& int EC_GROUP_get_basis_type(const EC_GROUP *);
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\& int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
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\& int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
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\& unsigned int *k2, unsigned int *k3);
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\& EC_GROUP *d2i_ECPKParameters(EC_GROUP **, const unsigned char **in, long len);
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\& int i2d_ECPKParameters(const EC_GROUP *, unsigned char **out);
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\& #define d2i_ECPKParameters_bio(bp,x) ASN1_d2i_bio_of(EC_GROUP,NULL,d2i_ECPKParameters,bp,x)
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\& #define i2d_ECPKParameters_bio(bp,x) ASN1_i2d_bio_of_const(EC_GROUP,i2d_ECPKParameters,bp,x)
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\& #define d2i_ECPKParameters_fp(fp,x) (EC_GROUP *)ASN1_d2i_fp(NULL, \e
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\& (char *(*)())d2i_ECPKParameters,(fp),(unsigned char **)(x))
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\& #define i2d_ECPKParameters_fp(fp,x) ASN1_i2d_fp(i2d_ECPKParameters,(fp), \e
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\& (unsigned char *)(x))
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\& int ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off);
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\& int ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off);
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\&
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\& EC_KEY *EC_KEY_new(void);
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\& int EC_KEY_get_flags(const EC_KEY *key);
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\& void EC_KEY_set_flags(EC_KEY *key, int flags);
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\& void EC_KEY_clear_flags(EC_KEY *key, int flags);
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\& EC_KEY *EC_KEY_new_by_curve_name(int nid);
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\& void EC_KEY_free(EC_KEY *key);
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\& EC_KEY *EC_KEY_copy(EC_KEY *dst, const EC_KEY *src);
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\& EC_KEY *EC_KEY_dup(const EC_KEY *src);
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\& int EC_KEY_up_ref(EC_KEY *key);
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\& const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key);
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\& int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group);
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\& const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key);
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\& int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *prv);
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\& const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key);
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\& int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub);
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\& unsigned EC_KEY_get_enc_flags(const EC_KEY *key);
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\& void EC_KEY_set_enc_flags(EC_KEY *eckey, unsigned int flags);
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\& point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key);
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\& void EC_KEY_set_conv_form(EC_KEY *eckey, point_conversion_form_t cform);
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\& void *EC_KEY_get_key_method_data(EC_KEY *key,
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\& void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
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\& void EC_KEY_insert_key_method_data(EC_KEY *key, void *data,
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\& void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
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\& void EC_KEY_set_asn1_flag(EC_KEY *eckey, int asn1_flag);
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\& int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx);
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\& int EC_KEY_generate_key(EC_KEY *key);
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\& int EC_KEY_check_key(const EC_KEY *key);
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\& int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y);
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\&
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\& EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len);
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\& int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out);
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\&
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\& EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len);
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\& int i2d_ECParameters(EC_KEY *key, unsigned char **out);
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\&
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\& EC_KEY *o2i_ECPublicKey(EC_KEY **key, const unsigned char **in, long len);
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\& int i2o_ECPublicKey(EC_KEY *key, unsigned char **out);
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\& int ECParameters_print(BIO *bp, const EC_KEY *key);
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\& int EC_KEY_print(BIO *bp, const EC_KEY *key, int off);
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\& int ECParameters_print_fp(FILE *fp, const EC_KEY *key);
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\& int EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off);
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\& #define ECParameters_dup(x) ASN1_dup_of(EC_KEY,i2d_ECParameters,d2i_ECParameters,x)
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\& #define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid) \e
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\& EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, EVP_PKEY_OP_PARAMGEN, \e
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\& EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL)
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.Ve
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.SH "DESCRIPTION"
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.IX Header "DESCRIPTION"
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This library provides an extensive set of functions for performing operations on elliptic curves over finite fields.
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In general an elliptic curve is one with an equation of the form:
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.PP
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y^2 = x^3 + ax + b
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.PP
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An \fB\s-1EC_GROUP\s0\fR structure is used to represent the definition of an elliptic curve. Points on a curve are stored using an
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\&\fB\s-1EC_POINT\s0\fR structure. An \fB\s-1EC_KEY\s0\fR is used to hold a private/public key pair, where a private key is simply a \s-1BIGNUM\s0 and a
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public key is a point on a curve (represented by an \fB\s-1EC_POINT\s0\fR).
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.PP
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The library contains a number of alternative implementations of the different functions. Each implementation is optimised
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for different scenarios. No matter which implementation is being used, the interface remains the same. The library
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handles calling the correct implementation when an interface function is invoked. An implementation is represented by
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an \fB\s-1EC_METHOD\s0\fR structure.
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.PP
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The creation and destruction of \fB\s-1EC_GROUP\s0\fR objects is described in \fIEC_GROUP_new\fR\|(3). Functions for
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manipulating \fB\s-1EC_GROUP\s0\fR objects are described in \fIEC_GROUP_copy\fR\|(3).
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.PP
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Functions for creating, destroying and manipulating \fB\s-1EC_POINT\s0\fR objects are explained in \fIEC_POINT_new\fR\|(3),
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whilst functions for performing mathematical operations and tests on \fBEC_POINTs\fR are coverd in \fIEC_POINT_add\fR\|(3).
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.PP
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For working with private and public keys refer to \fIEC_KEY_new\fR\|(3). Implementations are covered in
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\&\fIEC_GFp_simple_method\fR\|(3).
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.PP
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For information on encoding and decoding curve parameters to and from \s-1ASN1\s0 see \fId2i_ECPKParameters\fR\|(3).
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.SH "SEE ALSO"
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.IX Header "SEE ALSO"
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\&\fIcrypto\fR\|(3), \fIEC_GROUP_new\fR\|(3), \fIEC_GROUP_copy\fR\|(3),
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\&\fIEC_POINT_new\fR\|(3), \fIEC_POINT_add\fR\|(3), \fIEC_KEY_new\fR\|(3),
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\&\fIEC_GFp_simple_method\fR\|(3), \fId2i_ECPKParameters\fR\|(3)
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