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密码学
OpenSSL椭圆曲线密码学
1. 列出所有椭圆曲线
# openssl ecparam -list_curves
secp112r1 : SECG/WTLS curve over a 112 bit prime field
secp112r2 : SECG curve over a 112 bit prime field
secp128r1 : SECG curve over a 128 bit prime field
secp128r2 : SECG curve over a 128 bit prime field
secp160k1 : SECG curve over a 160 bit prime field
secp160r1 : SECG curve over a 160 bit prime field
secp160r2 : SECG/WTLS curve over a 160 bit prime field
secp192k1 : SECG curve over a 192 bit prime field
secp224k1 : SECG curve over a 224 bit prime field
secp224r1 : NIST/SECG curve over a 224 bit prime field
secp256k1 : SECG curve over a 256 bit prime field
secp384r1 : NIST/SECG curve over a 384 bit prime field
secp521r1 : NIST/SECG curve over a 521 bit prime field
prime192v1: NIST/X9.62/SECG curve over a 192 bit prime field
prime192v2: X9.62 curve over a 192 bit prime field
prime192v3: X9.62 curve over a 192 bit prime field
prime239v1: X9.62 curve over a 239 bit prime field
prime239v2: X9.62 curve over a 239 bit prime field
prime239v3: X9.62 curve over a 239 bit prime field
prime256v1: X9.62/SECG curve over a 256 bit prime field
sect113r1 : SECG curve over a 113 bit binary field
sect113r2 : SECG curve over a 113 bit binary field
sect131r1 : SECG/WTLS curve over a 131 bit binary field
sect131r2 : SECG curve over a 131 bit binary field
sect163k1 : NIST/SECG/WTLS curve over a 163 bit binary field
sect163r1 : SECG curve over a 163 bit binary field
sect163r2 : NIST/SECG curve over a 163 bit binary field
sect193r1 : SECG curve over a 193 bit binary field
sect193r2 : SECG curve over a 193 bit binary field
sect233k1 : NIST/SECG/WTLS curve over a 233 bit binary field
sect233r1 : NIST/SECG/WTLS curve over a 233 bit binary field
sect239k1 : SECG curve over a 239 bit binary field
sect283k1 : NIST/SECG curve over a 283 bit binary field
sect283r1 : NIST/SECG curve over a 283 bit binary field
sect409k1 : NIST/SECG curve over a 409 bit binary field
sect409r1 : NIST/SECG curve over a 409 bit binary field
sect571k1 : NIST/SECG curve over a 571 bit binary field
sect571r1 : NIST/SECG curve over a 571 bit binary field
c2pnb163v1: X9.62 curve over a 163 bit binary field
c2pnb163v2: X9.62 curve over a 163 bit binary field
c2pnb163v3: X9.62 curve over a 163 bit binary field
c2pnb176v1: X9.62 curve over a 176 bit binary field
c2tnb191v1: X9.62 curve over a 191 bit binary field
c2tnb191v2: X9.62 curve over a 191 bit binary field
c2tnb191v3: X9.62 curve over a 191 bit binary field
c2pnb208w1: X9.62 curve over a 208 bit binary field
c2tnb239v1: X9.62 curve over a 239 bit binary field
c2tnb239v2: X9.62 curve over a 239 bit binary field
c2tnb239v3: X9.62 curve over a 239 bit binary field
c2pnb272w1: X9.62 curve over a 272 bit binary field
c2pnb304w1: X9.62 curve over a 304 bit binary field
c2tnb359v1: X9.62 curve over a 359 bit binary field
c2pnb368w1: X9.62 curve over a 368 bit binary field
c2tnb431r1: X9.62 curve over a 431 bit binary field
wap-wsg-idm-ecid-wtls1: WTLS curve over a 113 bit binary field
wap-wsg-idm-ecid-wtls3: NIST/SECG/WTLS curve over a 163 bit binary field
wap-wsg-idm-ecid-wtls4: SECG curve over a 113 bit binary field
wap-wsg-idm-ecid-wtls5: X9.62 curve over a 163 bit binary field
wap-wsg-idm-ecid-wtls6: SECG/WTLS curve over a 112 bit prime field
wap-wsg-idm-ecid-wtls7: SECG/WTLS curve over a 160 bit prime field
wap-wsg-idm-ecid-wtls8: WTLS curve over a 112 bit prime field
wap-wsg-idm-ecid-wtls9: WTLS curve over a 160 bit prime field
wap-wsg-idm-ecid-wtls10: NIST/SECG/WTLS curve over a 233 bit binary field
wap-wsg-idm-ecid-wtls11: NIST/SECG/WTLS curve over a 233 bit binary field
wap-wsg-idm-ecid-wtls12: WTLS curvs over a 224 bit prime field
Oakley-EC2N-3:
IPSec/IKE/Oakley curve #3 over a 155 bit binary field.
Not suitable for ECDSA.
Questionable extension field!
Oakley-EC2N-4:
IPSec/IKE/Oakley curve #4 over a 185 bit binary field.
Not suitable for ECDSA.
Questionable extension field!
brainpoolP160r1: RFC 5639 curve over a 160 bit prime field
brainpoolP160t1: RFC 5639 curve over a 160 bit prime field
brainpoolP192r1: RFC 5639 curve over a 192 bit prime field
brainpoolP192t1: RFC 5639 curve over a 192 bit prime field
brainpoolP224r1: RFC 5639 curve over a 224 bit prime field
brainpoolP224t1: RFC 5639 curve over a 224 bit prime field
brainpoolP256r1: RFC 5639 curve over a 256 bit prime field
brainpoolP256t1: RFC 5639 curve over a 256 bit prime field
brainpoolP320r1: RFC 5639 curve over a 320 bit prime field
brainpoolP320t1: RFC 5639 curve over a 320 bit prime field
brainpoolP384r1: RFC 5639 curve over a 384 bit prime field
brainpoolP384t1: RFC 5639 curve over a 384 bit prime field
brainpoolP512r1: RFC 5639 curve over a 512 bit prime field
brainpoolP512t1: RFC 5639 curve over a 512 bit prime field
2. 生成私钥参数
# openssl ecparam -name secp256k1 -genkey -out ec_private_key.pem
# cat ec_private_key.pem
-----BEGIN EC PARAMETERS-----
BgUrgQQACg==
-----END EC PARAMETERS-----
-----BEGIN EC PRIVATE KEY-----
MHQCAQEEIALxlDOugVRY/0nG84pmdM2e4p2T4N8lxw2IEAzKLdHeoAcGBSuBBAAK
oUQDQgAE5qsUg+aH9ecjRmqRol3fYncUf7f0HMluLpRi0LtxwKV9hVcG07uvASIt
glBMk9XnzxDlGpCKfH7WOUMCeVtXLQ==
-----END EC PRIVATE KEY-----
3. 生成公钥参数
# openssl ec -in ec_private_key.pem -pubout -out ec_public_key.pem
4. 显示秘钥信息
# openssl ec -in ec_private_key.pem -text
read EC key
Private-Key: (256 bit)
priv:
02:f1:94:33:ae:81:54:58:ff:49:c6:f3:8a:66:74:
cd:9e:e2:9d:93:e0:df:25:c7:0d:88:10:0c:ca:2d:
d1:de
pub:
04:e6:ab:14:83:e6:87:f5:e7:23:46:6a:91:a2:5d:
df:62:77:14:7f:b7:f4:1c:c9:6e:2e:94:62:d0:bb:
71:c0:a5:7d:85:57:06:d3:bb:af:01:22:2d:82:50:
4c:93:d5:e7:cf:10:e5:1a:90:8a:7c:7e:d6:39:43:
02:79:5b:57:2d
ASN1 OID: secp256k1
writing EC key
-----BEGIN EC PRIVATE KEY-----
MHQCAQEEIALxlDOugVRY/0nG84pmdM2e4p2T4N8lxw2IEAzKLdHeoAcGBSuBBAAK
oUQDQgAE5qsUg+aH9ecjRmqRol3fYncUf7f0HMluLpRi0LtxwKV9hVcG07uvASIt
glBMk9XnzxDlGpCKfH7WOUMCeVtXLQ==
-----END EC PRIVATE KEY-----
# openssl ec -in ec_public_key.pem -pubin -text
read EC key
Private-Key: (256 bit)
pub:
04:e6:ab:14:83:e6:87:f5:e7:23:46:6a:91:a2:5d:
df:62:77:14:7f:b7:f4:1c:c9:6e:2e:94:62:d0:bb:
71:c0:a5:7d:85:57:06:d3:bb:af:01:22:2d:82:50:
4c:93:d5:e7:cf:10:e5:1a:90:8a:7c:7e:d6:39:43:
02:79:5b:57:2d
ASN1 OID: secp256k1
writing EC key
-----BEGIN PUBLIC KEY-----
MFYwEAYHKoZIzj0CAQYFK4EEAAoDQgAE5qsUg+aH9ecjRmqRol3fYncUf7f0HMlu
LpRi0LtxwKV9hVcG07uvASItglBMk9XnzxDlGpCKfH7WOUMCeVtXLQ==
-----END PUBLIC KEY-----
- OpenSSL库对椭圆曲线加密算法编程
#include <openssl/ec.h> // for EC_GROUP_new_by_curve_name, EC_GROUP_free, EC_KEY_new, EC_KEY_set_group, EC_KEY_generate_key, EC_KEY_free
#include <openssl/ecdsa.h> // for ECDSA_do_sign, ECDSA_do_verify
#include <openssl/obj_mac.h> // for NID_secp256k1
#include <openssl/ssl.h>
#include <openssl/bio.h>
#include <stdio.h>
#include <string.h>
EC_KEY * generate_eckey()
{
EC_KEY *eckey=EC_KEY_new();
EC_GROUP *ecgroup= EC_GROUP_new_by_curve_name(NID_secp256k1);
EC_KEY_set_group(eckey, ecgroup);
EC_KEY_generate_key(eckey);
return eckey;
}
void write_private_key_to_pem(const char *priv_key_file_name, EC_KEY *eckey)
{
FILE *fp = fopen(priv_key_file_name, "w");
PEM_write_ECPrivateKey(fp, eckey, NULL, NULL, 0, NULL, NULL);
fclose(fp);
return;
}
EC_KEY *read_private_key_from_pem(const char *priv_key_file_name)
{
FILE *fp = fopen(priv_key_file_name, "r");
EC_KEY *eckey = PEM_read_ECPrivateKey(fp, NULL, NULL, NULL);
fclose(fp);
return eckey;
}
void write_public_key_to_pem(const char *pubkey_file_name, EC_KEY *eckey)
{
BIO *out = BIO_new_file(pubkey_file_name, "w");
if(out == NULL)
{
printf("write public key to pem file failed! (%s:%d)\n", __FILE__,__LINE__);
}
PEM_write_bio_EC_PUBKEY(out, eckey);
BIO_free(out);
return ;
}
EC_KEY *read_public_key_from_pem(const char *pubkey_file_name)
{
//BIO *in = BIO_new(BIO_s_file());
//BIO_read_filename(in, pubkey_file_name);
BIO *in = BIO_new_file(pubkey_file_name, "r");
EC_KEY *eckey = EC_KEY_new();
eckey = PEM_read_bio_EC_PUBKEY(in, &eckey, NULL, NULL);
//EC_KEY *eckey = d2i_EC_PUBKEY_bio(in, NULL);
//FILE *fp = fopen(pubkey_file_name, "r");
//eckey = PEM_read_EC_PUBKEY(fp, &eckey, NULL, NULL);
if (eckey == NULL)
{
printf("read public key pem failed! (%s:%d)\n", __FILE__, __LINE__);
}
BIO_free(in);
return eckey;
}
int main()
{
//read private or public key from pem file
EC_KEY *privkey = read_private_key_from_pem("ec_private_key.pem");
EC_KEY *pubkey = read_public_key_from_pem("ec_public_key.pem");
//print key to stdout
BIO *bio_stdout = BIO_new_fp(stdout, BIO_NOCLOSE);
EC_KEY_print(bio_stdout, privkey, 0);
printf("================================================================\n");
EC_KEY_print(bio_stdout, pubkey, 0);
printf("================================================================\n");
//print g point
EC_GROUP *ec_group = EC_KEY_get0_group(pubkey);
EC_POINT *ec_point = EC_GROUP_get0_generator(ec_group);
char *G = EC_POINT_point2hex(ec_group, ec_point,POINT_CONVERSION_UNCOMPRESSED, NULL);
printf("G = %s\n", G);
//print private key bignum
BIGNUM *ec_privkey = EC_KEY_get0_private_key(privkey);
//BN_print_fp(stdout, ec_privkey);
char *k = BN_bn2hex(ec_privkey);
printf("k = %s\n", k);
//print public key point
EC_POINT *ec_pubkey = EC_KEY_get0_public_key(privkey);
char *K = EC_POINT_point2hex(ec_group, ec_pubkey,POINT_CONVERSION_UNCOMPRESSED, NULL);
printf("K = %s\n", K);
//print K = kG
BN_CTX *ctx = BN_CTX_new();
EC_POINT *r = EC_POINT_new(ec_group);
EC_POINT_mul(ec_group, r, NULL, ec_point, ec_privkey, ctx);
char *PK = EC_POINT_point2hex(ec_group, r,POINT_CONVERSION_UNCOMPRESSED, NULL);
printf("kG = %s\n", PK);
//print cofactor
BIGNUM *cofactor = EC_GROUP_get0_cofactor(ec_group);
char *p = BN_bn2hex(cofactor);
printf("p = %s\n", p);
//conversion string to bignum
printf("================================================================\n");
char *msg = "hello world";
BIGNUM *m = BN_new();
BN_bin2bn((unsigned char *)msg, strlen(msg),m);
char *str_m = BN_bn2hex(m);
printf("(string)m = %s, (hex)m = %s\n", msg, str_m);
//extract the message digest
printf("================================================================\n");
int md_len;
unsigned char md_value[EVP_MAX_MD_SIZE];
EVP_MD_CTX *md = EVP_MD_CTX_new();
EVP_DigestInit_ex(md, EVP_sha256(), NULL);
EVP_DigestUpdate(md, msg, sizeof(msg));
EVP_DigestFinal_ex(md, md_value, &md_len);
BIGNUM *hash = BN_new();
BN_bin2bn(md_value, md_len, hash);
char *str_hash = BN_bn2hex(hash);
printf("hash = %s\n ", str_hash);
printf("================================================================\n");
return 0;
}
编译：
# gcc main.c -g -o exam -lcrypto