rsa find e ref: https://www.v2ex.com/t/379974

finde.java

import java.math.BigInteger;
import java.util.function.Function;

/**
 * @author yinheli
 */
public class RSATest {

    private static BigInteger[] commonE = new BigInteger[]{
            new BigInteger("3"),
            new BigInteger("5"),
            new BigInteger("17"),
            new BigInteger("257"),
            new BigInteger("65537"),
    };

    public static void main(String[] args) {
        // calculate e

        BigInteger p = new BigInteger("CF642C412E5D7FC1BAA9AF0CC9EF0B7B", 16);
        BigInteger q = new BigInteger("D051E350D4E7D727456E1C75354201E3", 16);
        BigInteger dp = new BigInteger("15B66F5FC9E669CEE51DF9CD7FFB1685C8B6FAF84E0BA12B97A743158BB422C201F437260B2A495627ACE33450DAF4DB", 16);
        BigInteger dq = new BigInteger("15CF52899A283C4B0BD44967AAC7AE586A4AAACEF2233E4E8C627CE9BA1415953259B4F933D86E02D3614F7F4F886843", 16);

        BigInteger e = findE(p, q, dp, dq);
        System.out.println(e);
    }

    public static BigInteger findE(BigInteger p, BigInteger q, BigInteger dp, BigInteger dq) {
        BigInteger p1 = p.subtract(BigInteger.ONE);
        BigInteger q1 = q.subtract(BigInteger.ONE);
        BigInteger n = p.multiply(q);
        BigInteger phiN = p1.multiply(q1);

        Function<BigInteger, Boolean> isValidE = (e) -> {
            if (e.gcd(phiN).equals(BigInteger.ONE)) {
                BigInteger d = calculateD(e, phiN);
                if (d.multiply(p).equals(dp) && d.multiply(q).equals(dq)) {
                    return true;
                }
            }
            return false;
        };

        for (BigInteger e : commonE) {
            if (isValidE.apply(e)) {
                return e;
            }
        }

        BigInteger e = BigInteger.ONE;
        while (e.compareTo(n) < 0) {
            e = e.nextProbablePrime();
            if (isValidE.apply(e)) {
                return e;
            }
        }

        return null;
    }

    private static BigInteger calculateD(BigInteger e, BigInteger phiN) {
        return e.modInverse(phiN);
    }
}