I'm using bouncycastle's implimentation of NTRU, here is my code:
NTRUEncryptionKeyGenerationParameters ntruEncryptionKeyGenerationParameters = NTRUEncryptionKeyGenerationParameters.EES1087EP2;
NTRUEncryptionKeyPairGenerator ntruEncryptionKeyPairGenerator = new NTRUEncryptionKeyPairGenerator();
ntruEncryptionKeyPairGenerator.init(ntruEncryptionKeyGenerationParameters);
AsymmetricCipherKeyPair asymmetricCipherKeyPair = ntruEncryptionKeyPairGenerator.generateKeyPair();
NTRUEncryptionPrivateKeyParameters ntruEncryptionPrivateKeyParameters = (NTRUEncryptionPrivateKeyParameters) asymmetricCipherKeyPair.getPrivate();
NTRUEncryptionPublicKeyParameters ntruEncryptionPublicKeyParameters = (NTRUEncryptionPublicKeyParameters) asymmetricCipherKeyPair.getPublic();
NTRUEngine ntruEngine = new NTRUEngine();
ntruEngine.init(true, ntruEncryptionPublicKeyParameters);
The question is how can I get f polynomial and basis, because I've found only fp(inverse of f, and they don't have inverse methods) and Basis? I've looked up javadocs but no result.
You can find it from the class NTRUEncryptionKeyPairGenerator
public AsymmetricCipherKeyPair generateKeyPair()
{
int N = params.N;
int q = params.q;
int df = params.df;
int df1 = params.df1;
int df2 = params.df2;
int df3 = params.df3;
int dg = params.dg;
boolean fastFp = params.fastFp;
boolean sparse = params.sparse;
Polynomial t;
IntegerPolynomial fq;
IntegerPolynomial fp = null;
// choose a random f that is invertible mod 3 and q
while (true)
{
IntegerPolynomial f;
// choose random t, calculate f and fp
if (fastFp)
{
// if fastFp=true, f is always invertible mod 3
t = params.polyType == NTRUParameters.TERNARY_POLYNOMIAL_TYPE_SIMPLE ? Util.generateRandomTernary(N, df, df, sparse, params.getRandom()) : ProductFormPolynomial.generateRandom(N, df1, df2, df3, df3, params.getRandom());
f = t.toIntegerPolynomial();
f.mult(3);
f.coeffs[0] += 1;
}
else
{
t = params.polyType == NTRUParameters.TERNARY_POLYNOMIAL_TYPE_SIMPLE ? Util.generateRandomTernary(N, df, df - 1, sparse, params.getRandom()) : ProductFormPolynomial.generateRandom(N, df1, df2, df3, df3 - 1, params.getRandom());
f = t.toIntegerPolynomial();
fp = f.invertF3();
if (fp == null)
{
continue;
}
}
fq = f.invertFq(q);
if (fq == null)
{
continue;
}
break;
}
// if fastFp=true, fp=1
if (fastFp)
{
fp = new IntegerPolynomial(N);
fp.coeffs[0] = 1;
}
// choose a random g that is invertible mod q
DenseTernaryPolynomial g;
while (true)
{
g = DenseTernaryPolynomial.generateRandom(N, dg, dg - 1, params.getRandom());
if (g.invertFq(q) != null)
{
break;
}
}
IntegerPolynomial h = g.mult(fq, q);
h.mult3(q);
h.ensurePositive(q);
g.clear();
fq.clear();
NTRUEncryptionPrivateKeyParameters priv = new NTRUEncryptionPrivateKeyParameters(h, t, fp, params.getEncryptionParameters());
NTRUEncryptionPublicKeyParameters pub = new NTRUEncryptionPublicKeyParameters(h, params.getEncryptionParameters());
return new AsymmetricCipherKeyPair(pub, priv);
}
f is the polynomial you are after. What do you mean by the basis?
The inverse method is described in NTRU Report 014: Almost Inverses and Fast NTRU Key Creation
https://www.securityinnovation.com/uploads/Crypto/NTRUTech014.pdf
It is done via several steps for optimization
find inverse of f over Z/2Z/(x^N-1)
lift it to Z/2^rZ/(x^N-1)
repeat until 2^r = q