“d”是什么格式?PEM格式还是二进制格式?
该格式为Base64URL编码或“Base 64编码与URL和文件名安全字母表”
RFC 4648(请参见第5节,第7页的表2)。
如何将其加载到RSA结构中?
好的,所以OpenSSL确实很痛苦。要将其加载到RSA结构中,您需要将n、e和d从Base64URL转换为Base64。以下是我在Crypto++中的做法(您可以在OpenSSL中完成,但这会很困难):
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;
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(), '_', '/');
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)));
< p > < em > < strong >编辑 :Crypto++现在有
Base64URLEncoder和
Base64URLDecoder类,因此您不需要进行查找/替换操作。
< p >运行上面的代码后,< code > nn ,< code > ee 和< code > 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< code > Integer 中,并使用以下命令获取基数为10的字符串:
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
用于私钥操作。 d mod p-1
、d mod q-1
和 inv q mod p
是可选的。只有 n
、e
、d
,您需要解决缺失的参数(至少是 p
和 q
)。其中两个难点是 p
和 q
。以下是 Crypto++ 代码来解决它们(可以自由转换为 OpenSSL):
Integer p, q;
RSA_solve(n, e, d, p, q);
cout << "P: " << endl << p << endl << endl;
cout << "Q: " << endl << q << endl << endl;
而且:
void RSA_solve(const Integer& n, const Integer& e, const Integer& d, Integer& p, Integer& q)
这会导致:
P:
15737705590244743839558616502896029191493197327877753279847020015603526753735923
90718294084119093232085749598005372477289597182368848096852332845373492076546615
30801859889389455120932077199406250387226339056140578989122526711937239401762061
949364440402067108084155200696015505170135950332209194782224750221639.
Q:
12992175256740635899099334754006444501823007340248226099417932857332386190837921
12746269565434716649972371852989646481333243433270528522640603220881224011247812
49085873464824282666514908127141915943024862618996371026577302203267804867959037
802770797169483022132210859867700312376409633383772189122488119155159.
"
d mod p-1
,d mod q-1
和inv q mod p
留给读者自己练习(但它们很容易,在Crypto ++中尤其如此)。您修改后的RSA_solve
可能如下:
"
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]
...
}
以下是您需要在
<openssl dir>/crypto/rsa/rsa.h
中提供的
struct rsa
字段:
struct rsa_st
{
...
ENGINE *engine;
BIGNUM *n;
BIGNUM *e;
BIGNUM *d;
BIGNUM *p;
BIGNUM *q;
BIGNUM *dmp1;
BIGNUM *dmq1;
BIGNUM *iqmp;
...
};
因此,我可以将其输入到EVP_SignFinal调用中...
EVP_SignFinal
需要一个EVP_PKEY
,而您拥有一个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
表示对 RSA*
的引用计数被增加了,这是可以接受的。如果是 set0
,你必须释放你的副本(也就是使用 rsa.release()
而不是 rsa.get()
),以避免重复释放。
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;
这里是上面使用的Crypto++代码的Pastebin链接:
http://pastebin.com/9Rm7bxZp。
这里是上面使用的OpenSSL代码的Pastebin链接:
http://pastebin.com/aGVpj4FW。
这里是OpenSSL程序的输出:
$ ./openssl-test.exe
Signature: 78f2c9af23b9a2a42e3b57dec454fa43ea6627992f48d40a33da6a7c93f98b4
PRSA
。也许你在想另一个库? - jwwRSA_check_key
是有问题的),以及没有p和q就无法执行任何私钥操作,因此OpenSSL可能会很麻烦。对于基本的东西,如编码转换、密钥验证和私钥操作,Crypto++可能是更好的选择。 - jww