json - 如何将私钥从JWK加载到openSSL？

Question

我有这个JWK(来自http://tools.ietf.org/html/draft-ietf-jose-json-web-signature-26#appendix-A.1):

 {"kty":"RSA",
       "n":"ofgWCuLjybRlzo0tZWJjNiuSfb4p4fAkd_wWJcyQoTbji9k0l8W26mPddx
            HmfHQp-Vaw-4qPCJrcS2mJPMEzP1Pt0Bm4d4QlL-yRT-SFd2lZS-pCgNMs
            D1W_YpRPEwOWvG6b32690r2jZ47soMZo9wGzjb_7OMg0LOL-bSf63kpaSH
            SXndS5z5rexMdbBYUsLA9e-KXBdQOS-UTo7WTBEMa2R2CapHg665xsmtdV
            MTBQY4uDZlxvb3qCo5ZwKh9kG4LT6_I5IhlJH7aGhyxXFvUK-DWNmoudF8
            NAco9_h9iaGNj8q2ethFkMLs91kzk2PAcDTW9gb54h4FRWyuXpoQ",
       "e":"AQAB",
       "d":"Eq5xpGnNCivDflJsRQBXHx1hdR1k6Ulwe2JZD50LpXyWPEAeP88vLNO97I
            jlA7_GQ5sLKMgvfTeXZx9SE-7YwVol2NXOoAJe46sui395IW_GO-pWJ1O0
            BkTGoVEn2bKVRUCgu-GjBVaYLU6f3l9kJfFNS3E0QbVdxzubSu3Mkqzjkn
            439X0M_V51gfpRLI9JYanrC4D4qAdGcopV_0ZHHzQlBjudU2QvXt4ehNYT
            CBr6XCLQUShb1juUO1ZdiYoFaFQT5Tw8bGUl_x_jTj3ccPDVZFD9pIuhLh
            BOneufuBiB4cS98l2SR_RQyGWSeWjnczT0QU91p1DhOVRuOopznQ"
      }

我需要将其加载到openSSL rsa结构中，以便可以将其输入到EVP_SignFinal调用中。 d是什么格式？ PEM？或二进制？如何将其加载到rsa结构中？

Answer 1

What format is "d"? PEM? or binary?

格式为 RFC 4648的Base64URL编码或“使用URL和文件名安全字母的Base 64编码”(请参阅​​第7页的第5节，表2)。

how do I load it into a rsa struct?

好的，所以OpenSSL很痛苦。要将其加载到 RSA结构中，无需将 n， e和 d从 Base64URL转换为 Base64。这是我在Crypto++中完成的方式(您可以在OpenSSL中完成，但会受到伤害):

string nz = "ofgWCuLjybRlzo0tZWJjNiuSfb4p4fAkd_wWJcyQoTbji9k0l8W26mPddx"
            "HmfHQp-Vaw-4qPCJrcS2mJPMEzP1Pt0Bm4d4QlL-yRT-SFd2lZS-pCgNMs"
            "D1W_YpRPEwOWvG6b32690r2jZ47soMZo9wGzjb_7OMg0LOL-bSf63kpaSH"
            "SXndS5z5rexMdbBYUsLA9e-KXBdQOS-UTo7WTBEMa2R2CapHg665xsmtdV"
            "MTBQY4uDZlxvb3qCo5ZwKh9kG4LT6_I5IhlJH7aGhyxXFvUK-DWNmoudF8"
            "NAco9_h9iaGNj8q2ethFkMLs91kzk2PAcDTW9gb54h4FRWyuXpoQ";

string ez = "AQAB";

string dz = "Eq5xpGnNCivDflJsRQBXHx1hdR1k6Ulwe2JZD50LpXyWPEAeP88vLNO97I"
            "jlA7_GQ5sLKMgvfTeXZx9SE-7YwVol2NXOoAJe46sui395IW_GO-pWJ1O0"
            "BkTGoVEn2bKVRUCgu-GjBVaYLU6f3l9kJfFNS3E0QbVdxzubSu3Mkqzjkn"
            "439X0M_V51gfpRLI9JYanrC4D4qAdGcopV_0ZHHzQlBjudU2QvXt4ehNYT"
            "CBr6XCLQUShb1juUO1ZdiYoFaFQT5Tw8bGUl_x_jTj3ccPDVZFD9pIuhLh"
            "BOneufuBiB4cS98l2SR_RQyGWSeWjnczT0QU91p1DhOVRuOopznQ";

string nn, ee, dd;

// First, convert Base64URL encoding to Base64
std::replace(nz.begin(), nz.end(), '-', '+');
std::replace(ez.begin(), ez.end(), '-', '+');
std::replace(dz.begin(), dz.end(), '-', '+');
std::replace(nz.begin(), nz.end(), '_', '/');
std::replace(ez.begin(), ez.end(), '_', '/');
std::replace(dz.begin(), dz.end(), '_', '/');

// Now, Base64 decode
StringSource ss1(nz, true, new Base64Decoder(new StringSink(nn)));
StringSource ss2(ez, true, new Base64Decoder(new StringSink(ee)));
StringSource ss3(dz, true, new Base64Decoder(new StringSink(dd)));

编辑:Crypto++现在具有 Base64URLEncoder和 Base64URLDecoder类，因此您不需要查找/替换操作。

上面的代码运行之后， nn， ee和 dd是二进制字符串(即非ASCII字符)。从那里，您可以将它们加载到 Integer，并使用以下命令获取Base 10字符串:

Integer n((byte*)nn.data(), nn.size());
Integer e((byte*)ee.data(), ee.size());
Integer d((byte*)dd.data(), dd.size());

cout << "N: " << endl << n << endl << endl;
cout << "E: " << endl << e << endl << endl;
cout << "D: " << endl << d << endl << endl;

$ ./cryptopp-test.exe

N: 
20446702916744654562596343388758805860065209639960173505037453331270270518732245
08977372301204320323609709562340204469011575537734525469644875960570778896584888
95017468362112062706438336639499925362469853626937363871851454247879222415857219
92924045675229348655595626434390043002821512765630397723028023792577935108185822
75369257422156693093780503115582009714681996492027000881132703628678639279359312
17624250488602118597634417704467037220158572506211078553986931332640811506974231
88751482418465308470313958250757758547155699749157985955379381294962058862159085
915015369381046959790476428631998204940879604226680285601.

E: 
65537.

D:
23583109899396195101799862623499368829246520235662137651186064319555667005065389
11356936879137503597382515919515633242482643314423192704128296593672966061810149
31632061789402182278402640746140338406535182197235078430096761014345948432406842
76746396884059179774424728049430754391920261073195321175575450790865379829879825
22396626690057355718157403493216553255260857777965627529169195827622139772389760
13057175483467867984218114225248961766503010944557397801270779301059273764049922
00150833924259148778478404572782464027609558833769999511998277062853834711506435
61410605789710883438795588594095047409018233862167884701.

OpenSSL需要 n， e， d， p和 q进行私钥操作。 d mod p-1， d mod q-1和 inv q mod p是可选的。仅使用 n， e和 d，您需要解决缺少的参数(至少 p和 q)。艰难的两个是 p和 q。这是为它们解决的Crypto++代码(可以随意转换为OpenSSL):

Integer p, q;

RSA_solve(n, e, d, p, q);

cout << "P: " << endl << p << endl << endl;
cout << "Q: " << endl << q << endl << endl;

和:

void RSA_solve(const Integer& n, const Integer& e, const Integer& d, Integer& p, Integer& q)
{
    AutoSeededRandomPool prng;
    Integer g = 1;
    unsigned int SAFETY = 0;

STEP_1:
    const Integer k = e * d - 1;
    if(!k.IsEven())
        throw runtime_error("e * d - 1 is not even");

STEP_2:
    // g = 3, 5, 7, ...
    g += 2; while(!VerifyPrime(prng, g)) g += 2;
    Integer t = k;

STEP_3:
    if(SAFETY++ > 128)
        throw runtime_error("could not factor n");

    if(!t.IsEven())
        goto STEP_2;

    t /= 2;
    Integer x = a_exp_b_mod_c(g, t, n);

STEP_4:
    if(!(x > 1))
        goto STEP_3;

    Integer y = GCD(x-1, n);
    if(!(y > 1))
        goto STEP_3;

    p = std::max(y, n/y);
    q = std::min(y, n/y);

    Integer check = p * q;
    if(n != check)
        throw runtime_error("n != p * q");
}

结果是:

P: 
15737705590244743839558616502896029191493197327877753279847020015603526753735923
90718294084119093232085749598005372477289597182368848096852332845373492076546615
30801859889389455120932077199406250387226339056140578989122526711937239401762061
949364440402067108084155200696015505170135950332209194782224750221639.

Q: 
12992175256740635899099334754006444501823007340248226099417932857332386190837921
12746269565434716649972371852989646481333243433270528522640603220881224011247812
49085873464824282666514908127141915943024862618996371026577302203267804867959037
802770797169483022132210859867700312376409633383772189122488119155159.

d mod p-1， d mod q-1和 inv q mod p留给读者练习(但它们很容易，尤其是在Crypto++中)。您修改后的 RSA_solve可能如下所示:

void RSA_solve(const Integer& n, const Integer& e, const Integer& d,
               Integer& p, Integer& q,
               Integer& dmodp1, Integer& dmodq1, Integer& invqmodp)

现在，使用您的Base 10(十进制)字符串切换到OpenSSL:

const char nz[] =
    "20446702916744654562596343388758805860065209639960173505037453331270270518732245"
    "08977372301204320323609709562340204469011575537734525469644875960570778896584888"
    "95017468362112062706438336639499925362469853626937363871851454247879222415857219"
    "92924045675229348655595626434390043002821512765630397723028023792577935108185822"
    "75369257422156693093780503115582009714681996492027000881132703628678639279359312"
    "17624250488602118597634417704467037220158572506211078553986931332640811506974231"
    "88751482418465308470313958250757758547155699749157985955379381294962058862159085"
    "915015369381046959790476428631998204940879604226680285601";

const char ez[] = "65537";

const char dz[] =
    "23583109899396195101799862623499368829246520235662137651186064319555667005065389"
    "11356936879137503597382515919515633242482643314423192704128296593672966061810149"
    "31632061789402182278402640746140338406535182197235078430096761014345948432406842"
    "76746396884059179774424728049430754391920261073195321175575450790865379829879825"
    "22396626690057355718157403493216553255260857777965627529169195827622139772389760"
    "13057175483467867984218114225248961766503010944557397801270779301059273764049922"
    "00150833924259148778478404572782464027609558833769999511998277062853834711506435"
    "61410605789710883438795588594095047409018233862167884701";

const char pz[] =
    "15737705590244743839558616502896029191493197327877753279847020015603526753735923"
    "90718294084119093232085749598005372477289597182368848096852332845373492076546615"
    "30801859889389455120932077199406250387226339056140578989122526711937239401762061"
    "949364440402067108084155200696015505170135950332209194782224750221639";

const char qz[] =
    "12992175256740635899099334754006444501823007340248226099417932857332386190837921"
    "12746269565434716649972371852989646481333243433270528522640603220881224011247812"
    "49085873464824282666514908127141915943024862618996371026577302203267804867959037"
    "802770797169483022132210859867700312376409633383772189122488119155159";

using BN_ptr = std::unique_ptr<BIGNUM, decltype(&::BN_free)>;
using RSA_ptr = std::unique_ptr<RSA, decltype(&::RSA_free)>;
using EVP_PKEY_ptr = std::unique_ptr<EVP_PKEY, decltype(&::EVP_PKEY_free)>;
using EVP_MD_CTX_ptr = std::unique_ptr<EVP_MD_CTX, decltype(&::EVP_MD_CTX_destroy)>;

#define UNUSED(x) ((void)x)

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

    int rc;
    long err;

    RSA_ptr rsa(RSA_new(), ::RSA_free);
    BIGNUM *n = NULL, *e = NULL, *d = NULL, *p = NULL, *q = NULL;

    rc = BN_dec2bn(&n, nz);
    if(rc == 0 || n == NULL) {
        cerr << "BN_dec2bn failed for n" << endl;
        exit(1);
    }
    rsa->n = n;

    rc = BN_dec2bn(&e, ez);
    if(rc == 0 || e == NULL) {
        cerr << "BN_dec2bn failed for e" << endl;
        exit(1);
    }
    rsa->e = e;

    rc = BN_dec2bn(&d, dz);
    if(rc == 0 || d == NULL) {
        cerr << "BN_dec2bn failed for d" << endl;
        exit(1);
    }
    rsa->d = d;

    rc = BN_dec2bn(&p, pz);
    if(rc == 0 || p == NULL) {
        cerr << "BN_dec2bn failed for p" << endl;
        exit(1);
    }
    rsa->p = p;

    rc = BN_dec2bn(&q, qz);
    if(rc == 0 || q == NULL) {
        cerr << "BN_dec2bn failed for q" << endl;
        exit(1);
    }
    rsa->q = q;

    [Exercise left to the reader]

    rc = RSA_check_key(rsa.get());
    err = ERR_get_error();
    if(rc != 1) {
        cerr << "RSA_check_key failed, error 0x" << std::hex << err << endl;
        exit(1);
    }

    [Continues at next question below]
    ...
}

这是您需要在 struct rsa中提供的字段(来自 <openssl dir>/crypto/rsa/rsa.h):

struct rsa_st
    {
    ...
    /* functional reference if 'meth' is ENGINE-provided */
    ENGINE *engine;
    BIGNUM *n;
    BIGNUM *e;
    BIGNUM *d;
    BIGNUM *p;
    BIGNUM *q;
    BIGNUM *dmp1;
    BIGNUM *dmq1;
    BIGNUM *iqmp;
    ...
    };

so that I can feed this into an EVP_SignFinal call...

EVP_SignFinal需要一个 EVP_PKEY，而您有一个 RSA。所以:

EVP_PKEY_ptr pkey(EVP_PKEY_new(), ::EVP_PKEY_free);

rc = EVP_PKEY_set1_RSA(pkey.get(), rsa.get());
err = ERR_get_error();
if(rc != 1) {
    cerr << "EVP_PKEY_set1_RSA failed, error 0x" << std::hex << err << endl;
    exit(1);
}

set1表示引用计数在 RSA*上增加了。没关系。如果它是 set0，则必须释放您的副本(也就是说，使用 rsa.release()而不是 rsa.get())以避免双重释放。

EVP_MD_CTX_ptr ctx(EVP_MD_CTX_create(), ::EVP_MD_CTX_destroy);
EVP_MD_CTX_init(ctx.get());

const EVP_MD* md = EVP_sha256();
rc = EVP_SignInit(ctx.get(), md);
err = ERR_get_error();
if(rc != 1) {
    cerr << "EVP_SignInit_ex failed, error 0x" << std::hex << err << endl;
    exit(1);
}

const char message[] = "Now is the time for all good men...";

rc = EVP_SignUpdate(ctx.get(), message, (unsigned int)sizeof(message));
err = ERR_get_error();
if(rc != 1) {
    cerr << "EVP_SignUpdate failed, error 0x" << std::hex << err << endl;
    exit(1);
}

const unsigned int req = std::max(EVP_MD_size(md), EVP_PKEY_size(pkey.get()));
unique_ptr<unsigned char[]> signature(new unsigned char[req]);
unsigned int size = req;

rc = EVP_SignFinal(ctx.get(), signature.get(), &size, pkey.get());
err = ERR_get_error();
if(rc != 1) {
    cerr << "EVP_SignFinal failed, error 0x" << std::hex << err << endl;
    exit(1);
}

size = std::min(size, (unsigned int)EVP_MD_size(md));

cout << "Signature: ";
for(unsigned i = 0; i < size; i++)
    cout << std::hex << (signature[i] & 0xFF);
cout << endl;

这是上面使用的Crypto++代码的Pastebin: http://pastebin.com/9Rm7bxZp。

这是上面使用的OpenSSL代码的Pastebin: http://pastebin.com/aGVpj4FW。

这是OpenSSL程序的输出:

$ ./openssl-test.exe 
Signature: 78f2c9af23b9a2a42e3b57dec454fa43ea6627992f48d40a33da6a7c93f98b4