Generate RSA public and Private Key

RSA Algorithm

RSA is an algorithm for public-key cryptography that is based on the presumed difficulty of factoring large integers, the factoring problem. RSA stands for Ron Rivest, Adi Shamir and Leonard Adleman, who first publicly described the algorithm in 1977

  • Choose p = 3 and q = 11
  • Compute n = p * q = 3 * 11 = 33
  • Compute φ(n) = (p - 1) * (q - 1) = 2 * 10 = 20
  • Choose e such that 1 < e < φ(n) and e and n are coprime. Let e = 7
  • Compute a value for d such that (d * e) % φ(n) = 1. One solution is d = 3 [(3 * 7) % 20 = 1]
  • Public key is (e, n) => (7, 33)
  • Private key is (d, n) => (3, 33)
  • The encryption of m = 2 is c = 27 % 33 = 29
  • The decryption of c = 29 is m = 293 % 33 = 2