karatsugaMulti.java

import java.math.BigInteger;
class KaratsubaMulti{
    
    public static BigInteger compute(String x,String y)
    {
        int n = 0;
        int n1 = x.length();
        int n2 = y.length();
        if(n1>=n2)n=n2;
        else n = n1;
        
        if(n == 1)
        {
            BigInteger a = new BigInteger(x);
            BigInteger b = new BigInteger(y);
            return a.multiply(b);
        }
        int nm = n/2;
        String a = x.substring(0,n1-nm);
        String b = x.substring(n1-nm,n1);
        
        String u = y.substring(0,n2-nm);
        String v = y.substring(n2-nm,n2);
        
        
        BigInteger r1 = compute(a,u);
        BigInteger r2 = compute(b,v);
        BigInteger r3 = compute((new BigInteger(a)).add(new BigInteger(b)).toString(),(new BigInteger(u)).add(new BigInteger(v)).toString()).subtract(r1).subtract(r2);

        String xx = "";
        for(int i=0;i<nm;i++)
        xx=xx+"0";
        
        String s1 = r1.toString().concat(xx).concat(xx);
        String s3 = r3.toString().concat(xx);

        return((new BigInteger(s1)).add(r2).add(new BigInteger(s3)));
        
    }

    public static void main(String args[])
    {
        String a = "12345";
        String b = "123";
        System.out.println(compute(a,b));
    }
}

Please let me know if there any better way to do this . Since , with my logic I have to inter-convert between big integer and string hectic number of times and this adds to complexity.For your information , inbuilt multiply() function for big integers in java uses karatsuga multiplication .