Hello.
I'm trying to use elliptic curves to generate serial numbers for my
audio software which cannot be generated by a keygen.
The serial number will be 30 chars, which mean 150 bits. Obviously
this means that I cannot use ECIES or stuff like that because it's
simply too big. I need to use only the encryption primitive, with no
padding or stuff like that.
I've managed to do that with RSA. The code is like this:
====
RSAFunction pub;
InvertibleRSAFunction priv;
priv.Initialize(randPool, keyLength);
pub.Initialize(priv.GetModulus(), priv.GetPublicExponent());
Integer Data, Cipher, Plain;
Data.Decode(DataBuf.begin(), DataBuf.size(), Integer::UNSIGNED);
Cipher = priv.CalculateInverse(randPool, Data);
Plain = pub.ApplyFunction(Cipher);
====
The serial number will be Cipher written like an ASCII string.
The problem is that I cannot do thatn with EC.
After digging through header files I've managed to get this code
out of ECIES:
====
DL_PublicKey_EC<ECP> pub;
DL_PrivateKey_EC<ECP> priv;
priv.Initialize(randPool, ASN1::secp256k1());
priv.MakePublicKey(pub);
SecByteBlock data;
SecByteBlock plain;
SecByteBlock cipher;
int K = pub.AccessGroupParameters().GetEncodedElementSize(false);
data.CleanNew(3 * K); // make sure we have enough space
plain.CleanNew(3 * K);
cipher.CleanNew(3 * K);
strcpy((char *) data.begin(), "Encrypt Test");
Integer DataInteger(data.begin(), data.size(), Integer::UNSIGNED);
ECPPoint DataElement;
ECPPoint PlainElement;
ECPPoint CipherElement;
ECPPoint RandomElement;
DataElement.identity = false;
DataElement.x = DataInteger;
DataElement.y = DataInteger;
//Integer RandomInteger(randPool, Integer::One(),
pub.GetAbstractGroupParameters().GetMaxExponent());
Integer RandomInteger = DataInteger;
RandomElement = pub.GetAbstractGroupParameters().ExponentiateBase(RandomInteger);
//Element z = agreeAlg.AgreeWithEphemeralPrivateKey(params,
key.GetPublicPrecomputation(), x);
CipherElement = pub.GetPublicPrecomputation().Exponentiate(
pub.GetAbstractGroupParameters().GetGroupPrecomputation(),
RandomInteger * pub.GetAbstractGroupParameters().GetCofactor());
pub.GetAbstractGroupParameters().EncodeElement(true, CipherElement, cipher.begin());
//Element z = agreeAlg.AgreeWithStaticPrivateKey(params, q, true,
key.GetPrivateExponent());
PlainElement = priv.AccessGroupParameters().ExponentiateElement(RandomElement,
priv.GetPrivateExponent() * priv.AccessGroupParameters().GetCofactor());
====
The code works, at the end PlainElement = CipherElement (I've made a
bad choice of names, they should be named something like
AgreedSecretElement).
The thing is that instead of a RandomInteger from which to derivate a
key, I want to put my plaintext data. But when I decrypt the data,
I need RandomInteger! So I'm stuck.
I don't understand the math behind EC, so I have no idea what
ExponentiateBase does and how to play with this to do what I intend.
To resume: i want to encrypt a Integer (smaller that key size) with
the private key (not the public one as usual). The cipher text length
should be close to key length (like in RSA). Than I want to decrypt
the cipher text using the public key. All these using elliptic curves.
Could anybody help me? Or point me to some sample code which uses raw
elliptic curves?
Thanks.
