I put together some test code to generate a 28 byte (224bit) signature
on a constant public message using ASN1::secp112r1(), and I have two
questions.
First, is calling VerifyMessage (initialized with the public keys) on
the signature and a constant public message enough to verify that the
signature represent a valid product key that can't be generated
without knowledge of the private key? I don't understand if making
the message public is a security risk, or if I need to add a hash or
something to the product key like I've seen mentioned in a couple
places.
Second, will ECDSA work with curves of fewer bits than secp112? I'd
rather use a smaller curve to get a shorter signature so the product
key isn't so long, but when I used a smaller curve generated with
Elliptic Curve Builder, I get the error "Crypto++ Error:
CryptoMaterial: this object contains invalid values" when SignMessage
is called.
Thanks, and I hope these are easy questions for the experts out there,
cause I've been having a hard time finding much information on this
subject.
Here's the test code I'm working with:
ECIESNullT< CryptoPP::ECP >::PrivateKey PrivateKey;
/*
This is the curve generated by Elliptic Curve Builder that works with
ECIESNullT< CryptoPP::ECP >::Decryptor Decryptor( PrivateKey );
but not with ECDSA< CryptoPP::ECP >::Signer signer(PrivateKey);
CryptoPP::Integer p("147088164709569533");
CryptoPP::Integer a("6094329446842148");
CryptoPP::Integer b("-57162508610850246");
CryptoPP::Integer n("147088163948218061"); // R from ECB
CryptoPP::Integer h("1"); // S from ECB, must be
<= 4
CryptoPP::Integer x("71002669261090523");
CryptoPP::Integer y("11469141678568184");
CryptoPP::AutoSeededRandomPool rng;
CryptoPP::ECP ec( p, a, b );
PrivateKey.Initialize( ec,CryptoPP::ECP::Point( x, y ), n , h );
*/
PrivateKey.AccessGroupParameters().Initialize(ASN1::secp112r1());
PrivateKey.SetPrivateExponent(CryptoPP::Integer("4127861661178866478914975717021461"));
CryptoPP::ECDSA< CryptoPP::ECP >::Signer signer(PrivateKey);
ECDSA<ECP>::Verifier verifier(signer);
// sign
byte message[] = "test";
unsigned int messageLen = sizeof(message);
SecByteBlock signature(signer.MaxSignatureLength(messageLen));
AutoSeededRandomPool rng;
unsigned int signatureLen = signer.SignMessage(rng, message,
messageLen, signature);
// verify
std::cout << "Verify: " << verifier.VerifyMessage(message, messageLen,
signature, signatureLen) << "\r\n";
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