Generate private/public pair key using ECC : elliptic curves - cryptography

Question

I working on little ECC crypto problem.
The goal is to write a program in C or bash, which will take as input a hash composed of 128 characters in hexadecimal
(Example: 8A9A35145C4EA5260DF9972C804FE2D3F9F3D7A2AC01A6BEB21C82BB30957B3952273AC9166B90C1207347A925780F84A1D2359E7AA05201C674D2B9746FCA07)
and which will generate from the input hash a private key and a public key of type Elliptic Curve and display the key pair generated.
Can someone clarify for me the problem. I can't understand why we need a hash(or any string) to generate a pair key, as I found In many online solution like this one ther's no need to give a hash. Maybe is it a parphase ? Maybe It's the curve key or somthing similar.
I think all we need is to do something like this for the private key:
openssl ecparam -genkey -noout -out myprivatekey.pem
and for the public key generation:
openssl -ec -in myprivatekey.pem -pubout -out mypublickey.pem
The question is : why we need an input a hash composed of 128 to generate our pair keys? Is it a passphrase for security reason? how made the trick with openssl ?

Answer 1

You could use a hash if you've got some kind of input binary value which you need to convert to a key.
You can use a hash as input for a private key. To convert it you should first convert it to a number and then perform a calculation modulo n on it, where n is the order of the ECC domain parameters. The resulting value can be called s Then you can calculate the public key out of it by performing s * G, i.e. point multiplication with the base point.
OpenSSL is not a low level crypto library, so you'd have to program it, possibly using the OpenSSL API and the BN (big number) library that comes with it. It is not that tricky, but if you're still talking about 128 characters instead of 64 bytes then you may have a lot of learning to do.

Answer 2

In fact this is my own code, you can improve it and edit the solution bellow:
// 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;
start = BN_new();
ctx = BN_CTX_new(); // ctx is an optional buffer to save time from allocating and deallocating memory whenever required
res = start;
BN_hex2bn(&res,"8A9A35145C4EA5260DF9972C804FE2D3F9F3D7A2AC01A6BEB21C82BB30957B3952273AC9166B90C1207347A925780F84A1D2359E7AA05201C674D2B9746FCA07");
eckey = EC_KEY_new_by_curve_name(NID_secp256k1);
group = EC_KEY_get0_group(eckey);
pub_key = EC_POINT_new(group);
printf("private key : "); BN_print_fp(stdout, res); printf("\n");
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");
EC_KEY_set_public_key(eckey, pub_key);
char *cc = EC_POINT_point2hex(group, pub_key, 4, ctx);
char *c=cc;
int i;
printf("public key : ");
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;
}