Generate EC Diffie-Hellman public and private key

问题:

I need to generate an EC Diffie Hellman key pair. I am using the secp256r1 named curve, and OpenSSL. This is what I have with me so far:

unsigned char *ecdh(size_t *secret_len)
{
    EVP_PKEY_CTX *pctx, *kctx;
    EVP_PKEY_CTX *ctx;
    unsigned char *secret;
    EVP_PKEY *pkey = NULL, *peerkey, *params = NULL;
    /* NB: assumes pkey, peerkey have been already set up */

    /* Create the context for parameter generation */
    if(NULL == (pctx = EVP_PKEY_CTX_new_id(EVP_PKEY_EC, NULL))) 
        printf("Error in EC key generation\n");

    /* Initialise the parameter generation */
    if(1 != EVP_PKEY_paramgen_init(pctx)) 
        printf("Error in EC key generation\n");

    /* We're going to use the ANSI X9.62 Prime 256v1 curve */
    if(1 != EVP_PKEY_CTX_set_ec_paramgen_curve_nid(pctx, NID_X9_62_prime256v1)) 
        printf("Error in EC key generation\n");

    /* Create the parameter object params */
    if (!EVP_PKEY_paramgen(pctx, &params)) 
        printf("Error in EC key generation\n");

    /* Create the context for the key generation */
    if(NULL == (kctx = EVP_PKEY_CTX_new(params, NULL))) 
        printf("Error in EC key generation\n");

    /* Generate the key */
    if(1 != EVP_PKEY_keygen_init(kctx)) 
        printf("Error in EC key generation\n");

    if (1 != EVP_PKEY_keygen(kctx, &pkey)) 
        printf("Error in EC key generation\n");

    /* Get the peer's public key, and provide the peer with our public key -
     * how this is done will be specific to your circumstances */
    peerkey = get_peerkey(pkey);

    /* Create the context for the shared secret derivation */
    if(NULL == (ctx = EVP_PKEY_CTX_new(pkey, NULL))) 
        printf("Error in EC key generation\n");

    /* Initialise */
    if(1 != EVP_PKEY_derive_init(ctx)) 
        printf("Error in EC key generation\n");

    /* Provide the peer public key */
    if(1 != EVP_PKEY_derive_set_peer(ctx, peerkey)) 
        printf("Error in EC key generation\n");

    /* Determine buffer length for shared secret */
    if(1 != EVP_PKEY_derive(ctx, NULL, secret_len)) 
        printf("Error in EC key generation\n");

    /* Create the buffer */
    if(NULL == (secret = OPENSSL_malloc(*secret_len))) 
        printf("Error in EC key generation\n");

    /* Derive the shared secret */
    if(1 != (EVP_PKEY_derive(ctx, secret, secret_len))) 
        printf("Error in EC key generation\n");

    EVP_PKEY_CTX_free(ctx);
    EVP_PKEY_free(peerkey);
    EVP_PKEY_free(pkey);
    EVP_PKEY_CTX_free(kctx);
    EVP_PKEY_free(params);
    EVP_PKEY_CTX_free(pctx);

    /* Never use a derived secret directly. Typically it is passed
     * through some hash function to produce a key */
    return secret;
} 

I figured out that for this function to work, i need a EVP_KEY object with the second party's public key. I have this public key in a byte array, and also its length. How do I convert it to the required type? And also I could not find the secp256r1 curve in OpenSSL, but I used the one in the code after doing some research. Is it correct?

Thanks !

回答1:

The peer's public key is a point on the curve. From crypto\ec\ec_lcl.h:

struct ec_key_st {
    int version;

    EC_GROUP *group;

    EC_POINT *pub_key;
    BIGNUM   *priv_key;

    unsigned int enc_flag;
    point_conversion_form_t conv_form;

    int     references;
    int flags;

    EC_EXTRA_DATA *method_data;
} /* EC_KEY */;

I believe you need to call EC_POINT_new (c_lcl.h is a private header, so you won't have access to the structure).

Luckily, there's a lot of functions to manipulate them. From the EC_POINT_new(3) docs:

EC_POINTs can be converted to and from various external representations. Supported representations are octet strings, BIGNUMs and hexadecimal. The format of the external representation is described by the point_conversion_form. See EC_GROUP_copy(3) for a description of point_conversion_form. Octet strings are stored in a buffer along with an associated buffer length. A point held in a BIGNUM is calculated by converting the point to an octet string and then converting that octet string into a BIGNUM integer. Points in hexadecimal format are stored in a NULL terminated character string where each character is one of the printable values 0-9 or A-F (or a-f).

Also see EC_POINT_set_affine_coordinates_GFp, EC_POINT_set_affine_coordinates_GF2m and EC_KEY_set_public_key:

$ grep -R EC_KEY_set_public_key *
crypto/ec/ec.h:int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub);
...

You can see an example of how to set the point on the OpenSSL wiki at Elliptic Curve Cryptography.