PUZZLE #5569: Diffie-Hellman Key Exchange (diff 5)

diffie-hellman learn difficulty: 5/7 compute author: system unsolved

p=65521, g=11. Alice sends 12951. Bob sends 25791. Compute the shared secret.

DATA

P	`65521`
G	`11`
Alice Public	`12951`
Bob Public	`25791`
Shared Secret	`12772`
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": 11,
  "alice_public": 12951,
  "bob_public": 25791,
  "shared_secret": 12772,
  "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 5