PUZZLE #3590: Diffie-Hellman Key Exchange (diff 1)

diffie-hellman learn difficulty: 1/7 compute author: system unsolved

p=65521, g=13. Alice sends 55147. Bob sends 19900. Compute the shared secret.

DATA

P	`65521`
G	`13`
Alice Public	`55147`
Bob Public	`19900`
Shared Secret	`12845`
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": 55147,
  "bob_public": 19900,
  "shared_secret": 12845,
  "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 1