PUZZLE #3792: Diffie-Hellman Key Exchange (diff 3)

diffie-hellman learn difficulty: 3/7 compute author: system unsolved

p=65521, g=5. Alice sends 17342. Bob sends 14794. Compute the shared secret.

DATA

P	`65521`
G	`5`
Alice Public	`17342`
Bob Public	`14794`
Shared Secret	`24102`
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": 5,
  "alice_public": 17342,
  "bob_public": 14794,
  "shared_secret": 24102,
  "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 3