帮我写一段的不使用相关库的NTRU数字签名的java语言代码

好的，以下是一段不使用相关库的NTRU数字签名的java语言代码：

import java.math.BigInteger;
import java.util.Random;

public class NTRU {

    private static final BigInteger p = new BigInteger("3");
    private static final BigInteger q = new BigInteger("128");
    private static final BigInteger a = new BigInteger("2");
    private static final BigInteger t = new BigInteger("30");
    private static final BigInteger x = new BigInteger("2");

    public static void main(String[] args) {
        BigInteger[] keyPair = generateKeyPair();
        BigInteger message = new BigInteger("123456789");
        BigInteger signature = sign(message, keyPair[0]);
        boolean verified = verify(message, signature, keyPair[1]);
        System.out.println("Signature verified: " + verified);
    }

    public static BigInteger[] generateKeyPair() {
        BigInteger[] publicKey = new BigInteger[2];
        BigInteger[] privateKey = new BigInteger[2];

        BigInteger f, fp, fq, g, h, pMinus1, qMinus1;
        do {
            f = generateRandomPolynomial(t);
            fp = f.subtract(BigInteger.ONE);
            fq = f.add(BigInteger.ONE);
            pMinus1 = p.subtract(BigInteger.ONE);
            qMinus1 = q.subtract(BigInteger.ONE);
        } while (pMinus1.mod(fp).equals(BigInteger.ZERO) || qMinus1.mod(fq).equals(BigInteger.ZERO));

        g = generateRandomPolynomial(t);
        h = g.multiply(f.modInverse(p)).mod(q);

        publicKey[0] = p;
        publicKey[1] = h;
        privateKey[0] = f;
        privateKey[1] = g;

        BigInteger[] keyPair = new BigInteger[2];
        keyPair[0] = privateKey[0];
        keyPair[1] = publicKey[1];
        return keyPair;
    }

    private static BigInteger generateRandomPolynomial(BigInteger degree) {
        BigInteger polynomial = new BigInteger(degree.bitCount(), new Random());
        polynomial = polynomial.setBit(degree.intValue());
        polynomial = polynomial.setBit(0);
        return polynomial;
    }

    public static BigInteger sign(BigInteger message, BigInteger privateKey) {
        BigInteger hash = hash(message);
        BigInteger signature = hash.modPow(privateKey, p);
        return signature;
    }

    public static boolean verify(BigInteger message, BigInteger signature, BigInteger publicKey) {
        BigInteger hash = hash(message);
        BigInteger m1 = signature.modPow(publicKey, p);
        BigInteger m2 = hash.mod(a);
        return m1.equals(m2);
    }

    private static BigInteger hash(BigInteger message) {
        BigInteger hash = message.mod(x);
        return hash;
    }
}

这段代码是通过 NTRU 算法生成公钥和私钥，对消息进行签名并验证签名的过程。真实应用中还需要对 NTRU 算法的参数进行调整以提高安全性。