PUZZLE #2454: Diffie-Hellman Key Exchange (diff 7)

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

p=65521, g=3. Alice sends 45606. Bob sends 40895. Compute the shared secret.

DATA

P	`65521`
G	`3`
Alice Public	`45606`
Bob Public	`40895`
Shared Secret	`32479`
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": 3,
  "alice_public": 45606,
  "bob_public": 40895,
  "shared_secret": 32479,
  "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: Audited: diffie-hellman diff 7