Using Dual Generalized Rebalanced - RSA, there is very less (could be said as 0) probability to crack Key(Public Key & Private Key) using Brute Force attack.
Here is Java implementation of it.
For more details about Dual RSA:
import java.math.BigInteger;
import java.security.SecureRandom;
/*
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/**
*
* @author 311
*/
public class RebalancedRSA {
public static void main(String[] args) {
int ne=50,nd=75,nk=25,n=200;//ne<n and n/2-ne = nd - nk
BigInteger e = new BigInteger(ne,new SecureRandom());
BigInteger temp = new BigInteger("65536");
BigInteger two = new BigInteger("2");
if(e.mod(two).equals(BigInteger.ZERO))
{
//System.out.println("e if " + e);
e = e.add(BigInteger.ONE);
}
//System.out.println("e " + e);
int k = (n/2 - ne)/nk;
BigInteger pa[] = new BigInteger[k];
for(int i=1;i<=k-1;i++) // we are starting array index from 1
{
pa[i] = new BigInteger(n/2-ne,new SecureRandom());
}
BigInteger paa = new BigInteger(n/2-ne,new SecureRandom());
while(true)
{
paa = new BigInteger(n/2-ne,new SecureRandom());
temp = paa.mod(two);
boolean b;
b = temp.equals(BigInteger.ZERO);
if(!b){
paa = paa.add(BigInteger.ONE);
}
temp = paa.gcd(e);
// System.out.println("temp " + temp);
if((temp.equals(BigInteger.ONE)))
break;
}
/* System.out.println("e = " + e);
System.out.println("paa = "+ paa);
System.out.println("gcd " +paa.gcd(e));*/
BigInteger kp1;
BigInteger pb,dp,p1,p2;
// while(true)
//{
while(true)
{
kp1 = new BigInteger(nk,new SecureRandom());
temp = kp1.gcd(e);
if((temp.equals(BigInteger.ONE)))
break;
}
// System.out.println("kp1 = " + kp1 + " " + nk );
while(true)
{
int i=0;
pb = new BigInteger(ne,new SecureRandom());
if(pb.compareTo(e) == -1) // if pb < e then continue
continue;
temp = e.multiply(two);
if(pb.compareTo(temp)==1) // if pb > 2e then continut
continue;
// e < pb < 2e is satisfied
temp = pb.multiply(kp1);
temp = temp.multiply(paa); //kp1*pa*pb+1
temp = temp.add(BigInteger.ONE);
dp = temp.divide(e);
BigInteger t1,t2;
t1 = kp1.multiply(paa); //t1 = kp1*pa
t2 = t1.multiply(two); //t2 = 2*kp1*pa
if(t1.compareTo(dp)==-1) //if t1 < dp
{
if(t2.compareTo(dp)==1) // & dp < 2t1 == correct dp
{
}
}
else
{
continue;
}
p1 = paa.multiply(pb);
p1 = p1.add(BigInteger.ONE);
if(p1.isProbablePrime(1))
{
}
else
{
continue;
}
int flag=0;
p2 = new BigInteger("1");
for(i=1;i<=k-1;i++)
{
temp = paa.multiply(pb);
temp = temp.multiply(kp1);
//System.out.println("temp = " + temp);
//System.out.println("pa[0] = " + pa[i]);
temp = temp.divide(pa[i]);
p2 = temp.add(BigInteger.ONE);
//System.out.println("p2 " + p2);
if(p2.isProbablePrime(1))
{
//System.out.println("NO break");
}
else
{
flag = 1;
// System.out.println("break");
break;
}
}
if(flag==0)
break;
}
BigInteger qa[] = new BigInteger[k];
for(int i=1;i<=k-1;i++) // we are starting array index from 1
{
qa[i] = new BigInteger(n/2-ne,new SecureRandom());
}
BigInteger qaa = new BigInteger(n/2-ne,new SecureRandom());
while(true)
{
qaa = new BigInteger(n/2-ne,new SecureRandom());
temp = qaa.mod(two);
boolean b;
b = temp.equals(BigInteger.ZERO);
if(!b){
qaa = qaa.add(BigInteger.ONE);
}
temp = qaa.gcd(e);
// System.out.println("temp " + temp);
if((temp.equals(BigInteger.ONE)))
break;
}
/* System.out.println("e = " + e);
System.out.println("paa = "+ qaa);
System.out.println("gcd " +qaa.gcd(e));*/
BigInteger kq1;
BigInteger qb,dq,q1,q2;
// while(true)
//{
while(true)
{
kq1 = new BigInteger(nk,new SecureRandom());
temp = kq1.gcd(e);
if((temp.equals(BigInteger.ONE)))
break;
}
// System.out.println("kq1 = " + kq1 + " " + nk );
while(true)
{
int i=0;
qb = new BigInteger(ne,new SecureRandom());
if(qb.compareTo(e) == -1) // if pb < e then continue
continue;
temp = e.multiply(two);
if(qb.compareTo(temp)==1) // if pb > 2e then continut
continue;
// e < qb < 2e is satisfied
temp = qb.multiply(kq1);
temp = temp.multiply(qaa); //kp1*pa*pb+1
temp = temp.add(BigInteger.ONE);
dq = temp.divide(e);
BigInteger t1,t2;
t1 = kq1.multiply(qaa); //t1 = kp1*pa
t2 = t1.multiply(two); //t2 = 2*kp1*pa
if(t1.compareTo(dq)==-1) //if t1 < dp
{
if(t2.compareTo(dq)==1) // & dp < 2t1 == correct dp
{
}
}
else
{
continue;
}
q1 = qaa.multiply(qb);
q1 = q1.add(BigInteger.ONE);
if(q1.isProbablePrime(1))
{
}
else
{
continue;
}
int flag=0;
q2 = new BigInteger("1");
for(i=1;i<=k-1;i++)
{
temp = qaa.multiply(qb);
temp = temp.multiply(kq1);
//System.out.println("temp = " + temp);
//System.out.println("qa[0] = " + qa[i]);
temp = temp.divide(qa[i]);
q2 = temp.add(BigInteger.ONE);
//System.out.println("q2 " + q2);
if(q2.isProbablePrime(1))
{
//System.out.println("NO break");
}
else
{
flag = 1;
// System.out.println("break");
break;
}
}
if(flag==0)
break;
}
BigInteger N1,N2,kp2,kq2;
N1 = p1.multiply(q1);
N2 = p2.multiply(q2);
kp1 = pa[1];
kq1 = pa[1];
System.out.println("N1 = " + N1);
System.out.println("N2 = " + N2);
System.out.println("e = " + e);
System.out.println("dp = " + dp);
System.out.println("dq = " + dq);
System.out.println("p1 = " + p1);
System.out.println("q1 = " + q1);
System.out.println("p2 = " + p2);
System.out.println("q2 = " + q2);
}
}
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