Topic: Using wc_ecc_mulmod() function in wolfssl produces some errors
When I use the wc_ecc_mulmod() function to perform calculations, some errors will occur. Ra1 and ra2 are two 32-bit random numbers, and G is the generator of the elliptic curve. The calculation (ra1ra2)G is not equal to ra1(ra2G). I noticed that when using wc_ecc_mulmod, the number cannot exceed the number of digits of the large prime number modulus, but I just need the product of two large prime numbers (ra1a2) , and then multiplied by the generator G. I did a test, ra3 = ra1ra2 mod prime, ra3G!=ra1(ra2G), is there any other way for wolfssl to achieve (ra1ra2)G= ra1(ra2*G) ? when ra1 and ra2 are relatively small numbers, there is no problem. For example, point A and point C in the following code are equal.thank you very much
#include <iostream>
#include <string>
#include <unistd.h>
#include <wolfssl/options.h>
#include <wolfssl/wolfcrypt/settings.h>
#include <wolfssl/ssl.h>
#include <wolfssl/wolfcrypt/types.h>
#include <wolfssl/wolfcrypt/random.h>
#include <wolfssl/wolfcrypt/ecc.h>
#include <wolfssl/wolfcrypt/sp_int.h>
#include <wolfssl/wolfcrypt/integer.h>
#include <wolfssl/wolfcrypt/wolfmath.h>
#include <wolfssl/wolfcrypt/sha.h>
#include <wolfssl/wolfcrypt/error-crypt.h>
#include <wolfssl/wolfcrypt/hash.h>
#include <wolfssl/wolfcrypt/asn.h>
#include <wolfssl/wolfcrypt/aes.h>
using namespace std;
int main(){
ecc_key key;
int ret;
WC_RNG rng;
wc_ecc_init(&key);
wc_InitRng(&rng);
int curveId = ECC_SECP256R1;
int keySize = wc_ecc_get_curve_size_from_id(curveId);
ret = wc_ecc_make_key_ex(&rng, keySize, &key, curveId);
//get param of ecc curve
mp_int a,b,prime,order,ra,s;
mp_init_multi(&a,&b,&prime,&order,&ra,&s);
ret = mp_read_radix(&a,key.dp->Af,16);
cout<<"get mp_int af: "<<ret<<endl;
ret = mp_read_radix(&b,key.dp->Bf,16);
cout<<"get mp_int bf: "<<ret<<endl;
ret = mp_read_radix(&prime,key.dp->prime,16);
cout<<"get mp_int prime: "<<ret<<endl;
ret = mp_read_radix(&order,key.dp->order,16);
cout<<"get mp_int order: "<<ret<<endl;
ret = wc_ecc_gen_k(&rng,32,&ra,&order);
cout<<"get mp_int ra: "<<ret<<endl;
ret = mp_copy(&key.k,&s);
cout<<"get mp_int s: "<<ret<<endl;
ecc_point* pointG = wc_ecc_new_point();
ret = wc_ecc_get_generator(pointG,wc_ecc_get_curve_idx(ECC_SECP256R1));
cout<<"get ecc_point pointG: "<<ret<<endl;
ret = wc_ecc_is_point(pointG,&a,&b,&prime);
cout<<"point is on curve: "<<ret<<endl;
//tes1:n1 = 10,n2 = 33,n3 = n1*n2, A = n3*G,B = n2*G,C = n1*B=> A == C
mp_int n1,n2,n3;
mp_init_multi(&n1,&n2,&n3,NULL,NULL,NULL);
mp_set_int(&n1,10);
mp_set_int(&n2,33);
ret = mp_mulmod(&n1,&n2,&prime,&n3);
ecc_point* A = wc_ecc_new_point();
ecc_point* B =wc_ecc_new_point();
ecc_point* C =wc_ecc_new_point();
ret = wc_ecc_mulmod(&n3,pointG,A,&a,&prime,1);
cout<<"n3*G: "<<ret<<endl;
ret = wc_ecc_mulmod(&n1,pointG,B,&a,&prime,1);
cout<<"n1*G: "<<ret<<endl;
ret = wc_ecc_mulmod(&n2,B,C,&a,&prime,1);
cout<<"n2*B: "<<ret<<endl;
ret = wc_ecc_cmp_point(A,C);
cout<<"A is equal to C: "<<ret<<endl;
//test2:ra1,ra2 are big number ra3 = ra1*ra2, D = ra3*G,E = ra2*G,F = ra1*E=> D != F
mp_int ra1,ra2,ra3;
mp_init_multi(&ra1,&ra2,&ra3,NULL,NULL,NULL);
ret = wc_ecc_gen_k(&rng,32,&ra1,&order);
cout<<"get mp_int ra1: "<<ret<<endl;
ret = wc_ecc_gen_k(&rng,32,&ra2,&order);
cout<<"get mp_int ra2: "<<ret<<endl;
ret = mp_mulmod(&ra1,&ra2,&prime,&ra3);
ecc_point* D = wc_ecc_new_point();
ecc_point* E =wc_ecc_new_point();
ecc_point* F =wc_ecc_new_point();
ret = wc_ecc_mulmod(&ra3,pointG,D,&a,&prime,1);
cout<<"ra3*G: "<<ret<<endl;
ret = wc_ecc_mulmod(&ra1,pointG,E,&a,&prime,1);
cout<<"ra1*G: "<<ret<<endl;
ret = wc_ecc_mulmod(&ra2,E,F,&a,&prime,1);
cout<<"ra2*E: "<<ret<<endl;
ret = wc_ecc_cmp_point(D,F);
cout<<"D is equal to F: "<<ret<<endl;
return 0;
}