Sending Message into a Deenite Future: Non-parallelizable Case

We construct a proof of membership protocol that uses log 2 t steps to prove an element to have the structure a 2 t (modn) given public values n; a; t where n is the product of two large secret primes. Such a proof serves a concrete basis of trust for a time-lock puzzle scheme and its applications in timed-release cryptography. The achieved ef-ciency expressed in log 2 t (number of modulo exponentiation) manifests plainly that the proposed proof technique is practical in the applications of timed-release crypto problems.