Private key generated by openssl does not satisfy n = p * q

Question

I\'ve generated a key with openssl by using the following command

openssl genrsa 1024

I\'ve got the following result

-----BEGI         


        

Answer 1

Why the hell N is not equal to p * q ?

Confirmed with the key provided. However, I could not duplicate when generating my own key with openssl genrsa 1024.

$ ./test-rsa.exe

***** P *****
12716592588957205057720227362856602359162165918588008158928004904780617816265357
754968000322907349867949577092305558696339499022301055839537975977118688137

***** Q *****
10059832080410675679274931119486090017360564066559599189867309386706046720813347
145402059918876964980032136051476889631968099168811652389989474036177869729

***** N *****
12793124891325327128971650020563999246628465128785735817714525182531281036799314
77808216241640625923377085054862755880280251221289282252666015910733318035804933
41719724935049328478344297205955905466581637169109448199715137939448946445804542
355907923908845024638480376219852266194827768486624319018352514599977

*** Calc N ***
12792678607990434048632475001531065755874366303681660462967024860494524785586521
24218714399928148249644594040544628864191685952244681103581135994857552437185369
35880977456835036272916419632947427885989469252242704342884476060911074859116149
906854382812141105735147419775039435625802885168567201322191763704873

---

$ cat test-rsa.c

#include 
#include 
#include 

#include 
#include 
#include 
#include 

const char s_key[] = "-----BEGIN RSA PRIVATE KEY-----\n"
"MIICXAIBAAKBgQC2Lh4HLcCR76Wv3oXl6sZ7pv8l9b/66H+I6Bb86tz8RhWCmTCG\n"
"xPVgtZ+w9WutU/rqBHHZOpotX4QDksRD8dRFh6a3HwkIFQdTcDoiD39yNP8F02Gd\n"
"dAl8p/URC5jNCLMSfUK38wMocmoI1I5vqdMNrzUnOup18rl4089Z+faMKQIDAQAB\n"
"AoGBAJrL4z5iWiengxqV8yETBeU8WcJft+n0dapXzHDNAUo8Izr+AIYEBp1Ot4se\n"
"f4igu6zuae80JJ45c2u14p/5dWzN9/URmhTP8xLGjGCjltOJLLyhBPP+ZsLjqu6l\n"
"57MNV6jDqDLdRC66w4NMRCN3FACxcldIC5L6B9OA7UvO1ugBAkEA8s1o6BvufTeD\n"
"ktyOMfW0ZeLGk/6EXp8nf7BIzYhAAPtSt8DegnfYFx2XDgKnYSB15dTDIDMe/KaA\n"
"GcuUb/ZjiQJBAMATb1fFdl7PGccVPgeTaupJayHPySc9PSsACV6VIAnpcU/3NZzd\n"
"MkdIL/JsOsD+1M9uQJqvRZO4qQdjcR5Om6ECQEJGgYlB/pJdcePHomTOvcRF55CE\n"
"G9u8M8rt8qFvvJDICWcxFUulrO16XT4syUWA1825it2iNqYeSL9By63YIokCQBnm\n"
"RPw71xM/r8UleyDAYwlGbxi3EPOmkUnsDldfmltby/ixZ9xIA1CTTkvNBjsh4YY6\n"
"4qE5AxPBMaGaahVhGiECQHyQvXUNE2IUco+ZwmmLnb2ey1s5tBg7i0lEZG47G7GV\n"
"o+yKdJHpToJD8eRJA/2D+pMhQIZm8X/XDIoi1AQ/TRY=\n"
"-----END RSA PRIVATE KEY-----\n";

int main(int argc, char* argv[])
{
    UNUSED(argc), UNUSED(argv);

    int rc;
    FILE* fd = NULL;
    EVP_PKEY* pkey = NULL;
    RSA* rsa = NULL;
    BIGNUM* n = NULL;
    BN_CTX* ctx = NULL;

    fd = fopen("./key.pem", "w+");
    if(fd == NULL) exit(1);

    rc = fwrite(s_key, 1, sizeof(s_key), fd);
    if(rc != sizeof(s_key)) exit(2);

    rc = fseek(fd, 0, SEEK_SET);
    if(rc != 0) exit(3);

    pkey = PEM_read_PrivateKey(fd, NULL, NULL, NULL);
    if(pkey == NULL) exit(4);

    rsa = EVP_PKEY_get1_RSA(pkey);
    if(rsa == NULL) exit(5);

#if 0
    fprintf(stdout, "\n***** RSA *****\n");
    RSA_print_fp(stdout, rsa, 0);
#endif

    fprintf(stdout, "\n***** P *****\n");
    fprintf(stdout, "%s\n", BN_bn2dec(rsa->p));

    fprintf(stdout, "\n***** Q *****\n");
    fprintf(stdout, "%s\n", BN_bn2dec(rsa->q));

    fprintf(stdout, "\n***** N *****\n");
    fprintf(stdout, "%s\n", BN_bn2dec(rsa->n));

    n = BN_new();
    if(!n) exit(6);

    ctx = BN_CTX_new();
    if(ctx == NULL) exit(7);

    rc = BN_mul(n, rsa->p, rsa->q, ctx);
    if(rc != 1) exit(8);

    fprintf(stdout, "\n*** Calc N ***\n");
    fprintf(stdout, "%s\n", BN_bn2dec(n));

    BN_CTX_free(ctx);
    BN_free(n);
    RSA_free(rsa);
    EVP_PKEY_free(pkey);
    fclose(fd);

    return 0;
}