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Lecture notes in computer science

Quantum-Access Security of Hash-Based Signature Schemes

Quan Yuan, Mehdi Tibouchi, Masayuki Abe

Published Jan 1, 2023• 8 citations
Publisher
DOI
10.1007/978-3-031-35486-1_16

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Quantum-access security, where an attacker is granted superposition access to secret-keyed functionalities, is a fundamental security model and its study has inspired results in post-quantum security. We revisit, and fill a gap in, the quantum-access security analysis of the Lamport one-time signature scheme (OTS) in the quantum random oracle model (QROM) by Alagic et al.~(Eurocrypt 2020). We then go on to generalize the technique to the Winternitz OTS. Along the way, we develop a tool for the analysis of hash chains in the QROM based on the superposition oracle technique by Zhandry (Crypto 2019) which might be of independent interest.
Abstract In response to information security issues present in quantum information query scenarios, this paper proposes a quantum information query scheme based on quantum digital signatures. This scheme addresses the security vulnerabilities of existing quantum queries lacking strong authentication, trusted behavior binding, and unified access controllers. Using key-controlled single particle rotation operations, the user identity is jointly encoded with the query information into a quantum state constitutive signature and sent to the access controller, constructing a physically inseparable signature binding. The access controller uses hash verification to verify the legitimacy of the identity before forwarding the signature state. The verifier restores the query information parameters through reverse rotation and Bell measurements and completes the final verification, ensuring that the query behavior is demonstrable, non-falsifiable, and irrefutable throughout the process. The scheme requires only local single-particle operations throughout the process, while significantly reducing the complexity of implementation. It integrates privacy protection, identity authentication, and signature security into an organic whole, forming a trusted security closed loop of quantum information queries supported by a trusted access controller at the core.
Since the seminal result of Kilian, Oblivious Transfer (OT) has proven to be a fundamental primitive in cryptography. In such a scheme, a user is able to gain access to an element owned by a server, without learning more than this single element, and without the server learning which element the user has accessed. The NIST call for post-quantum encryption and signature schemes has revived the interest for cryptographic protocols based on post-quantum assumptions and the need for secure post-quantum OT schemes. In this paper, we show how to construct an OT scheme based on lattices, from a collision-resistant chameleon hash scheme (CH) and a CCA encryption scheme accepting a smooth projective hash function (SPHF). Note that our scheme does not rely on random oracles and provides UC security against adaptive corruptions assuming reliable erasures.