Random Oracles in a Quantum World (1008.0931v2)

Abstract: The interest in post-quantum cryptography - classical systems that remain secure in the presence of a quantum adversary - has generated elegant proposals for new cryptosystems. Some of these systems are set in the random oracle model and are proven secure relative to adversaries that have classical access to the random oracle. We argue that to prove post-quantum security one needs to prove security in the quantum-accessible random oracle model where the adversary can query the random oracle with quantum states. We begin by separating the classical and quantum-accessible random oracle models by presenting a scheme that is secure when the adversary is given classical access to the random oracle, but is insecure when the adversary can make quantum oracle queries. We then set out to develop generic conditions under which a classical random oracle proof implies security in the quantum-accessible random oracle model. We introduce the concept of a history-free reduction which is a category of classical random oracle reductions that basically determine oracle answers independently of the history of previous queries, and we prove that such reductions imply security in the quantum model. We then show that certain post-quantum proposals, including ones based on lattices, can be proven secure using history-free reductions and are therefore post-quantum secure. We conclude with a rich set of open problems in this area.

• The paper introduces history-free reductions, enabling classical cryptographic proofs to extend to quantum-accessible random oracle models.
• It delineates the separation between classical and quantum models by showing how protocols secure in classical settings can be vulnerable under quantum queries.
• The study evaluates signature and encryption schemes under quantum conditions, highlighting the practical pathway to post-quantum cryptographic resilience.

Random Oracles in a Quantum World

The paper addresses the intersection of post-quantum cryptography and the random oracle model, focusing on the challenges and implications of quantum-accessible random oracles. It presents a significant discourse on the necessity of adapting cryptographic proofs to withstand quantum adversaries, a pertinent topic given the advancing threat of quantum computing to classical cryptosystems.

Summary and Analysis

Separation of Models

The authors initiate the discussion by delineating the distinction between classical and quantum-accessible random oracle models. They illustrate this separation through a protocol that remains secure in a classical setting but becomes vulnerable under quantum conditions. The core insight is the necessity for quantum-accessible queries to maintain security against quantum adversaries.

History-free Reductions

A primary contribution of this work is the introduction of "history-free reductions", a framework where classical proofs of security can extend to quantum-accessible models. The history-free reduction concept implies that results from classical random oracle models may stand in the quantum field, provided specific criteria are met. This approach significantly impacts the protocol development landscape, as it offers a pathway to adapt existing protocols for quantum resilience without extensive redesign.

Concrete Schemes and Security

The paper evaluates several cryptographic schemes under these quantum-accessible conditions:

• Signature Schemes: Using history-free reductions, the security of the Full Domain Hash (FDH) signature scheme and others based on claw-free permutations is assessed. It demonstrates that schemes proven secure in the classical model maintain their security in the quantum model under certain conditions.
• Encryption Schemes: The paper further evaluates encryption schemes such as Bellare-Rogaway (BR) encryption. It establishes their security within the quantum-accessible model, contingent on the existence of quantum-accessible pseudorandom functions.

Implications and Open Problems

The implications of this work are profound in both theoretical and practical dimensions. Theoretically, it challenges current assumptions about cryptographic security in the face of quantum threats, advocating for proofs adaptable to quantum settings. Practically, these findings influence the future design and evaluation of post-quantum cryptographic systems, emphasizing the importance of considering quantum-accessible oracles from the outset.

The paper concludes with open problems, particularly regarding generic transformations in the quantum random oracle model, such as CPA to CCA transformations. These problems present fertile ground for further research to enhance the robustness of cryptosystems against quantum adversaries.

Speculation on Future AI Developments

As quantum computing evolves, AI's role in cryptography may involve developing models to automatically identify and resolve vulnerabilities in existing protocols. Furthermore, AI could potentially drive the creation of quantum-resistant cryptographic algorithms that inherently account for the complexities of quantum-accessible interactions. The pursuit of such advances reflects the ongoing need to secure digital infrastructures against the emerging capabilities of quantum technologies.

Overall, this paper lays crucial groundwork in defining the path towards resilient cryptographic solutions in the face of quantum advancements, urging the cryptographic community to rethink established models through a quantum-accessible lens.