编辑：

Question

我使用以下命令

使用openssl生成了一个键

openssl genrsa 1024

我得到了以下结果

使用http://lapo.it/asn1js/我已在pem上方反编译并发现了

p = 12716592588957205057720227362856602359162165918588008158928004904780617816265357754968000322907349867949577092305558696339499022301055839537975977118688137

q = 10059832080410675679274931119486090017360564066559599189867309386706046720813347145402059918876964980032136051476889631968099168811652389989474036177869729

但是平均时间模数

n = 127931248913253271289716500205639992466284651287857358177145251825312810367993147780821624164062592337708505486275588028025122128928225266601591073331803580493341719724935049328478344297205955905466581637169109448199715137939448946445804542355907923908845024638480376219852266194827768486624319018352514599977

当它应该相等时：

N = 127926786079904340486324750015310657558743663036816604629670248604945247855865212421871439992814824964459404054462886419168595224468110358113599485755243718536935880977456835036272916419632947427885989469252242704342884476060911074859116149906854382812141105735147419775039435625802885168567201322191763704873

为什么地狱N不等于p * q？

编辑：

这是我的openssl生成的一堆密钥，我使用的是Mac OS X Mavericks，第一个密钥有正确的N，第二个密钥不正确，我没有检查过其他密钥，但无论如何这个问题似乎都在复制，我正在使用以下openssl版本“OpenSSL 0.9.8y 2013年2月5日”：

Answer 1

为什么地狱N不等于p * q？

用提供的密钥确认。但是，在使用openssl genrsa 1024生成自己的密钥时，我无法复制。

$ ./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 <stdio.h>
#include <stdlib.h>
#include <signal.h>

#include <openssl/bn.h>
#include <openssl/evp.h>
#include <openssl/rsa.h>
#include <openssl/pem.h>

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;
}

Answer 2

您好我使用此命令测试了您在编辑中提供的所有6个私钥

$ openssl rsa -check -in privkey

并且所有人都返回RSA key ok。除第一个外，它返回RSA key error: n does not equal p q。

我对你问题的回答

为什么地狱N不等于p * q？

是： N不等于p * q 。第一个密钥可能已被修改，或者在传输过程中已被更改，因此它未通过rsa检查测试。深入研究openssl源代码，我们可以看到openssl genrsa命令由

执行

int rsa_builtin_keygen(RSA *rsa, int bits, BIGNUM *e_value, BN_GENCB *cb)

/crypto/rsa/rsa_gen.c中的

。在ln：289，模数n用

计算

/* calculate n */
if (!BN_mul(rsa->n,rsa->p,rsa->q,ctx)) goto err;

表示n = p * q。您应该寻找导致问题的其他可能性，而不是对genrsa命令产生怀疑。

openssl生成的私钥不满足n = p * q

编辑：

2 个答案: