On Classical Cryptographic Protocols in Post-Quantum World

In post-quantum approach, we consider classical (non-quantum) protocols and primitives which are run by honest parties on classical computers and our aim is to keep their security in an environment where the adversary can rely on quantum computers [3]. In particular, even a harder goal is set by requiring provable security guaranties in a concurrent running environment as we aim computational UC-security. Unruh [16] conjectured that classical arguments of computational UC-security remain usable in a post-quantum world as long as the underlying computational UC-secure primitives are also computationally quantum UC-secure. Our proposed technique (full factorization) aims at reducing the original protocol into a statistically-secure protocol by turning the protocol into a hybrid one where all cryptographic primitives are substituted by appropriate ideal functionalities. The considered set of primitives consists of secret key and public key encryption as well as digital signature. This way and by applying the Unruh's Quantum Lifting Theorem as well as the Quantum Universal Composition Theorem we gain a computationally quantum UC-secure protocol from a classical UC-secure protocol. We consider quantum standard-security, where the adversary can send only classical inputs to honest algorithms, i.e. honest machines cannot receive quantum superposition of inputs If we add also the practical need of efficiency our example is the class of protocols built from symmetric key primitives. A practical (fast) implementation could be based on AES encryption algorithm with appropriate key size as long as we live with the wide belief that this algorithm is secure against a quantum adversary.