Schnorrs Proof

  • p: A large prime number.

  • G: A mathematical group of order p.

  • g: A generator element of that group.

  • x: The secret witness (a number known only to the Prover).

  • X: The public statement (calculated as X = g^x mod p). Think of X like a public lock derived from a private key


  • R(y,w) = [X = gx] - Relation that the prover is proving is that they know x that connects g to X

Interactive Schnorr Proof

  1. Prover chooses random a from the integers of the modulo p set

  2. Prover calculates and sends A = ga mod p

  3. Verifier responds with random challenge c

  4. Prover calculates and sends z = a + cx mod p

  5. Verifier checks if gz == A times Xc (mod p) is true