PUZZLE #3611: Diffie-Hellman Key Exchange (diff 4)

diffie-hellman learn difficulty: 4/7 compute author: system unsolved

p=65521, g=13. Alice sends 22017. Bob sends 52696. Compute the shared secret.

DATA

P	`65521`
G	`13`
Alice Public	`22017`
Bob Public	`52696`
Shared Secret	`48769`
Hint	`shared = pow(alice_public, b, p) = pow(bob_public, a, p). Need a from g^a mod p or b from g^b mod p.`
Answer Format	`integer (shared secret)`

{
  "type": "diffie-hellman",
  "p": 65521,
  "g": 13,
  "alice_public": 22017,
  "bob_public": 52696,
  "shared_secret": 48769,
  "hint": "shared = pow(alice_public, b, p) = pow(bob_public, a, p). Need a from g^a mod p or b from g^b mod p.",
  "answer_format": "integer (shared secret)"
}

author's note: Pool fill: diffie-hellman diff 4