创建ECDSA公钥给定曲线和公共点？

我正在努力从公钥的字符串表示形式创建 ECDSA 公钥，即

string     devicePublicKey("86FB5EB3CA0507226BE7197058B9EC041D3A3758D9D9C91902ACA3391F4E58AEF13AFF63CC4EF68942B9B94904DC1B890EDBEABD16B992110624968E894E560E");

之前我发现我必须在这个键前加上“04”​​前缀，所以不确定这次是否需要？

我正在尝试生成它以用于验证签名

string ecs04b2ExpSignature("0199E984CEC75DDCA7F1DDF6E53E2E67352A2BE38A4B66F8ED596606FAB983FF300CAA76DE88CED9D563A5C03E8F3A7C000780F3F2061C611E9AA0B18B460D77");

要签名的数据在哪里

string      ecs04b2SigningData("020000000000000001FFFFFFFFFFFFFFFE123456789ABCDEF000B3DA2000000100000300000003030003000300");

我现在的粗略代码如下所示

SecByteBlock message(convertHexStrToSecByteBlock(messageIn));
SecByteBlock signature(convertHexStrToSecByteBlock(signatureIn));

ECDSA<ECP, SHA256>::PublicKey publicKey;
string inPublicKey("04");
inPublicKey.append(pubKeyIn);
SecByteBlock pubKey = encryptBase::convertHexStrToSecByteBlock(inPublicKey);



ECP::Point p;
publicKey.AccessGroupParameters().Initialize(CryptoPP::ASN1::secp256r1());
publicKey.GetGroupParameters().GetCurve().DecodePoint(p, pubKey, publicKey.GetGroupParameters().GetCurve().EncodedPointSize(true));
publicKey.SetPublicElement(p);

//ByteQueue qt;
//qt.Put((byte*)exp.c_str(),(size_t)exp.size());
AutoSeededRandomPool prng;
bool result = publicKey.Validate(prng, 3);
if (result) 
{  
    // Load public key (in ByteQueue, X509 format)
    ECDSA<ECP, SHA256>::Verifier verifier(publicKey);

    bool result = verifier.VerifyMessage(message.data(), messageIn.size(), signature.data(), signature.size());
    if (result)
        cout << "Verified signature on message" << endl;
    else
        cerr << "Failed to verify signature on message" << endl;
}
else
{
    cout << "Failed to validate key" << endl;
}

这是一起切碎的，所以不会建造。任何帮助都会很棒

PS我在这里问了一个与私钥相关的类似问题创建给定曲线和私有指数的 ECDSA 私钥？ https://stackoverflow.com/questions/27232053/creation-of-ecdsa-private-key-given-curve-and-private-exponent

答案详细在ECDSA 维基页面 http://www.cryptopp.com/wiki/Ecdsa#Public_Key_2，但其并不明显。您需要执行以下操作来初始化publicKey给定曲线和公共点：

string pt = "2DB45A3F21889438B42C8F464C75292BACF5FDDB5DA0B492501B299CBFE92D8F"
            "DB90FC8FF4026129838B1BCAD1402CAE47FE7D8084E409A41AFCE16D63579C5F";

HexDecoder decoder;
decoder.Put((byte*)pt.data(), pt.size());
decoder.MessageEnd();

ECP::Point q;
size_t len = decoder.MaxRetrievable();
// len should be GetField().MaxElementByteLength()

q.identity = false;
q.x.Decode(decoder, len/2);
q.y.Decode(decoder, len/2);

ECDSA<ECP, SHA256>::PublicKey publicKey;
publicKey.Initialize(ASN1::secp256r1(), q);

bool result = publicKey.Validate( prng, 3 );
if( result )
{
    cout << "Validated public key" << endl;
}
else
{
    cerr << "Failed to validate public key" << endl;
    exit(1);
}

const ECP::Point& qq = publicKey.GetPublicElement();
cout << "Q.x: " << std::hex << qq.x << endl;
cout << "Q.y: " << std::hex << qq.y << endl;

上面的程序产生以下结果。

$ ./cryptopp-test.exe
Validated public key
Q.x: 2db45a3f21889438b42c8f464c75292bacf5fddb5da0b492501b299cbfe92d8fh
Q.y: db90fc8ff4026129838b1bcad1402cae47fe7d8084e409a41afce16d63579c5fh

你不能使用GetField().MaxElementByteLength()因为唯一可用的是x and y坐标。在初始化底层之前，诸如字段大小之类的东西将不可用DL_GroupParameters_EC< EC > http://www.cryptopp.com/docs/ref/class_d_l___group_parameters___e_c.html在公钥中。

例如，以下情况会导致分段错误：

ECDSA<ECP, SHA256>::PublicKey publicKey;
unsigned int u = publicKey.GetGroupParameters().GetCurve().GetField().MaxElementByteLength();
cout << "Field element length: " << u << endl;

您可以通过以下方式篡改公钥以确保验证失败：

q.y.Decode(decoder, len/2);
q.y++;