I want to know if you can see Beauty
even when it is not pretty
every day.
And if you can source your own life
from its presence.
even when it is not pretty
every day.
And if you can source your own life
from its presence.
I almost wish I hadn't gone down that rabbit-hole — and yet — and yet — it's rather curious, you know, this sort of life!
1105 is composite with witness 2 294409 is composite with witness 2 118901509 is prime 118901521 is composite with witness 2 118901527 is prime 118915387 is composite with witness 2
Points in E(F13) are : (-Infinity,-Infinity) (1.0,5.0) (1.0,8.0) (2.0,3.0) (2.0,10.0) (9.0,6.0) (9.0,7.0) (12.0,2.0) (12.0,11.0) Addition test-> (9.0,7.0) + (1.0,8.0) =(2.0,10.0) double-and-add algorithm for elliptic curve-> 947*(6.0,730.0) mod 3623= (3492.0,60.0)
Find prime factors of 48356747: 2^19! -1 = 13944673 (mod 48356747) gcd(2^19!-1,48356747) = 6917 factors of 48356747, p=6917, and q=48356747/6917=6991 The prime factorization of 6916 is: 2, 2, 7, 13, 19 The prime factorization of 6990 is: 2, 3, 5, 233
public class RSA { //find x from x^e = c (mod p) public static long findRoot(long e, long c, long p) { long x = 0; //find e^-1 (mod p-1) long eInverse = crypto.inverse(p-1, e); //x = c^d (mod p) x = crypto.fastSq(p, c, eInverse); return x; } //test: answer = 6059 public static void main(String[] args) { long e = 1583; long c = 4714; long p = 7919; long x = RSA.findRoot(e,c, p); System.out.println("Solution to x^"+e+" = "+c+" (mod "+p+"): x= "+x); } }
Solution to x^1583 = 4714 (mod 7919): x= 6059
Step:0->x=2+3*5=17 Step:1->x=17+21*7=164 Solution:164
[u,y,d] = gcd(x,p); y = mod(y,p);