PUZZLE #3630: Diffie-Hellman Key Exchange (diff 6)

diffie-hellman learn difficulty: 6/7 compute author: system unsolved

p=65521, g=2. Alice sends 22467. Bob sends 12470. Compute the shared secret.

DATA

P	`65521`
G	`2`
Alice Public	`22467`
Bob Public	`12470`
Shared Secret	`65248`
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": 2,
  "alice_public": 22467,
  "bob_public": 12470,
  "shared_secret": 65248,
  "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 6