Verification of correct exponentiation or other operations in cryptographic applications

An apparatus for implementing a cryptographic protocol between multiple parties including at least a prover and a verifier, the apparatus comprising:

• a processor associated with the prover and operative to generate at least one signal corresponding to information representative of first and second proofs performed by the prover based on an operation associated with the cryptographic protocol, wherein the first proof is a proof that the operation has been correctly performed, and the second proof is a proof that the first proof has been correctly performed, wherein the proof information signal is transmitted from the prover to the verifier and used to determine if the operation associated with the cryptographic protocol is valid;
• and
• a memory coupled to the processor for at least temporarily storing at least a portion of the proof information signal.

A method for implementing a cryptographic protocol between multiple parties including at least a prover and a verifier, the method being implemented in a digital data processor including a processor and a memory and the method comprising the steps of:

• applying a key transformation protocol which takes an input of the form (g, y, m, s), for which loggy=logms, and produces a pair (G, Y) wherein G is a generator and Y is a public key, such that X=logGY can only be computed if loggy=logms;
• and
• generating a digital signature using the pair (G, Y).

An apparatus for implementing a cryptographic protocol between multiple parties including at least a prover and a verifier, the apparatus comprising:

• a processor associated with the prover and operative:
• (i) to apply a key transformation protocol which takes an input of the form (g, y, m, s), for which loggy=logms, so as to produce a pair (G, y) wherein G is a generator and Y is a public key, such that X=logGY can only be computed if loggy=logms;
• and (ii) to generate a digital signature using the pair (G, Y).

A method of implementing a cryptographic protocol between multiple parties including at least a prover and a verifier, the method being implemented in a digital data processor including a processor and a memory and the method comprising the steps of:

• receiving at least one signal corresponding to information representative of first and second proofs performed by the prover based on an operation associated with the cryptographic protocol, wherein the first proof is a proof that the operation has been correctly performed, and the second proof is a proof that the first proof has been correctly performed;
• and
• determining if the operation associated with the cryptographic protocol is valid based at least in part on the proof information signal.