How do I obtain the public key from an ECDSA priva

Question

I am providing this sample application to show my problem

#include <stdio.h>
#include <stdlib.h>
#include <openssl/ec.h>
#include <openssl/bn.h>

int main()
{
     EC_KEY *pkey = NULL;
     EC_POINT *pub_key = NULL;
     const EC_GROUP *group = NULL;
     BIGNUM start;
     BIGNUM *res;
     BN_CTX *ctx;

     BN_init(&start);
     ctx = BN_CTX_new();

     res = &start;
     BN_hex2bn(&res,"3D79F601620A6D05DB7FED883AB8BCD08A9101B166BC60166869DA5FC08D936E");
     pkey = EC_KEY_new_by_curve_name(NID_secp256k1);
     group = EC_KEY_get0_group(pkey);
     pub_key = EC_POINT_new(group);

     EC_KEY_set_private_key(pkey, res);

     assert(EC_POINT_bn2point(group,res, pub_key, ctx)); // Null here

     EC_KEY_set_public_key(pkey, pub_key);


    return 0;
}

What I am trying to do, is to display the Public key from a private key(should an elliptic private key). I did not know how to do it until I encountered a similar problem

How do I feed OpenSSL random data for use in ECDSA signing?

Which is from where I pointed myself how to get the public key and to use EC_POINT_bn2point instead of hex2point which internally does BN_hex2bn according to the OpenSSL source.

So, why is EC_POINT_bn2point returning NULL? I am seriously considering recompiling OpenSSL and putting some debug routines to figure out why it fails.

Answer 1

Working example:

// using figures on: https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses
// gcc -Wall ecdsapubkey.c -o ecdsapubkey -lcrypto
#include <stdio.h>
#include <stdlib.h>
#include <openssl/ec.h>
#include <openssl/obj_mac.h>
#include <openssl/bn.h>

int main()
{
     EC_KEY *eckey = NULL;
     EC_POINT *pub_key = NULL;
     const EC_GROUP *group = NULL;
     BIGNUM start;
     BIGNUM *res;
     BN_CTX *ctx;

     BN_init(&start);
     ctx = BN_CTX_new(); // ctx is an optional buffer to save time from allocating and deallocating memory whenever required

     res = &start;
//     BN_hex2bn(&res,"3D79F601620A6D05DB7FED883AB8BCD08A9101B166BC60166869DA5FC08D936E");
     BN_hex2bn(&res,"18E14A7B6A307F426A94F8114701E7C8E774E7F9A47E2C2035DB29A206321725");
     eckey = EC_KEY_new_by_curve_name(NID_secp256k1);
     group = EC_KEY_get0_group(eckey);
     pub_key = EC_POINT_new(group);

     EC_KEY_set_private_key(eckey, res);

     /* pub_key is a new uninitialized `EC_POINT*`.  priv_key res is a `BIGNUM*`. */
     if (!EC_POINT_mul(group, pub_key, res, NULL, NULL, ctx))
       printf("Error at EC_POINT_mul.\n");

//     assert(EC_POINT_bn2point(group, &res, pub_key, ctx)); // Null here

     EC_KEY_set_public_key(eckey, pub_key);

     char *cc = EC_POINT_point2hex(group, pub_key, 4, ctx);

     char *c=cc;

     int i;

     for (i=0; i<130; i++) // 1 byte 0x42, 32 bytes for X coordinate, 32 bytes for Y coordinate
     {
       printf("%c", *c++);
     }

     printf("\n");

     BN_CTX_free(ctx);

     free(cc);

     return 0;
}

See also http://wiki.openssl.org/index.php/Elliptic_Curve_Cryptography - for library

http://www.nsa.gov/ia/_files/ecdsa.pdf - for algorithm

http://cs.ucsb.edu/~koc/ccs130h/notes/ecdsa-cert.pdf - for math

Answer 2

An ECDSA private key d (an integer) and public key Q (a point) is computed by Q = dG, where G is a non-secret domain parameter. Suite B Implementer’s Guide to FIPS 186-3 (ECDSA) describes ECDSA in detail.

OpenSSL uses ECDSA_generate_key to generate a key pair. What it does is generate a private key randomly, and then it does the Q = dG multiplication to compute the public key:

/* pub_key is a new uninitialized `EC_POINT*`.  priv_key is a `BIGNUM*`. */
if (!EC_POINT_mul(ecdsa->group, pub_key, priv_key, NULL, NULL, ctx)) goto err;

So you can do the same thing. If I had the private key, I'd set it as the private key in an EC_KEY or ECDSA struct. Then I'd configure the domain parameters on it. And finally I'd do the EC_POINT_mul to get the public key point.