Java 如何获取NTRU参数

我正在使用bouncycastle的NTRU实现，下面是我的代码：

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);

---

问题是如何得到f多项式和基，因为我只找到了fp（f的逆，他们没有逆方法）和基？我已经查找了javadocs，但没有结果。

您可以从NTRUEncryptionKeyPairGenerator类中找到它

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是你要找的多项式。 你所说的基础是什么意思

NTRU报告014中描述了反向方法： 几乎相反和快速NTRU密钥创建

这是通过几个优化步骤完成的

求f在Z/2Z/（x^N-1）上的倒数

将其提升至Z/2^rZ/（x^N-1）

重复，直到2^r=q