The Big Secret

Philip Warren Anderson

Rick P. Trebino

Michael Ampatzis, Theodore Andronikos

Suppose that the renowned spymaster Alice controls a network of spies who all happen to be deployed in different geographical locations. Let us further assume that all spies have managed to get their hands on a small, albeit incomplete by itself, secret, which actually is just a part of a bigger secret. In this work, we consider the following problem: given the above situation, is it possible for the spies to securely transmit all these partial secrets to the spymaster so that they can be combined together in order to reveal the big secret to Alice? We call this problem, which, to the best of our knowledge, is a novel one for the relevant literature, the quantum secret aggregation problem. We propose a protocol, in the form of a quantum game, that addresses this problem in complete generality. Our protocol relies on the use of maximally entangled GHZ tuples, shared among Alice and all her spies. It is the power of entanglement that makes possible the secure transmission of the small partial secrets from the agents to the spymaster. As an additional bonus, entanglement guarantees the security of the protocol, by making it statistically improbable for the notorious eavesdropper Eve to steal the big secret.

Andrei Yu. Khrennikov

Ren Ishibashi, Kazuki Yoneyama

Authenticated Key Exchange (AKE) is a cryptographic protocol to share a common session key among multiple parties. At ISC 2021, Liu, Tang, and Zhou proposed a modular multi-factor AKE framework resilient to a characteristic attack called server compromise impersonation based on big data in the bounded-retrieval model and concrete post-quantum big data-based AKE schemes. They also formulated a security model (LTZ model) that captures perfect forward secrecy, key compromise impersonation, and server compromise impersonation. However, the LTZ model does not consider the compromise of ephemeral secret keys, and their schemes rely on the random oracle model. In this paper, we extend the LTZ model (LTZ-eCK model) to capture the compromise of ephemeral secret keys and propose a generic construction of big data-based AKE resilient to both server compromise impersonation and ephemeral key leakage in the standard model. Our generic construction allows us to achieve the post-quantum big data-based AKE scheme (from isogenies, lattice, etc.) in the LTZ-eCK model without random oracles.

Andrey Anatoljevich Grib, Waldyr A. Rodrigues