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International Symposium on Computing and Networking

An Efficient MQ-Based Signature in the QROM

Hiroki Furue, Dung Hoang Duong, Tsuyoshi Takagi

Published Nov 1, 2019• 0 citations
Publisher

Abstract

At PKC 2018, Chen et al. proposed SOFIA, the first MQ-based digital signature scheme secure in the quantum random oracle model (QROM). SOFIA is constructed by applying an extended version of the Unruh transform (EUROCRYPT 2015) to the MQ-based 5-pass identification scheme (IDS) proposed by Sakumoto et al. (CRYPTO 2011). In this paper, we propose an MQ-based 3-pass IDS with impersonation probability of 1/2 and apply the original version of the Unruh transform to it to obtain a more efficient MQ-based digital signature scheme secure in the QROM. The signature size with our digital signature scheme decreases by about 30% compared with SOFIA.

DOI
10.1109/candar.2019.00010

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•Apr 7, 2020•0 citations
At PKC 2018, Chen et al. proposed SOFIA, the first MQ-based digital signature scheme secure in the quantum random oracle model (QROM). SOFIA is constructed by applying an extended version of the Unruh transform (EUROCRYPT 2015) to the MQ-based 5-pass identification scheme (IDS) proposed by Sakumoto et al. (CRYPTO 2011). In this paper, we propose an MQ-based 3-pass IDS with impersonation probability of 1/2 and apply the original version of the Unruh transform to it to obtain a more efficient MQ-based digital signature scheme secure in the QROM. The signature size with our digital signature scheme decreases by about 30% compared with SOFIA.
At PKC 2018, Chen et al. proposed SOFIA, the first MQ-based digital signature scheme having tight security in the quantum random oracle model (QROM). SOFIA is constructed by applying an extended version of the Unruh transform (EUROCRYPT 2015) to the mathcal MQ-based 5-pass identification scheme (IDS) proposed by Sakumoto et al. (CRYPTO 2011). In this paper, we propose an MQ-based 3-pass IDS with impersonation probability of 1/2 and apply the original version of the Unruh transform to it to obtain a more efficient MQ-based digital signature scheme tightly secure in the QROM. The signature size of our digital signature scheme decreases by about 35% compared with SOFIA in the level I of NIST PQC security category, and is supposed to be the shortest among that of MQ-based signatures tightly secure in the QROM.
SOFIA: MQ\mathcal {MQ}MQ-Based Signatures in the QROM
We propose SOFIA, the first MQ\mathcal {MQ}MQ -based signature scheme provably secure in the quantum-accessible random oracle model (QROM). Our construction relies on an extended version of Unruh’s transform for 5-pass identification schemes that we describe and prove secure both in the ROM and QROM. Based on a detailed security analysis, we provide concrete parameters for SOFIA that achieve 128-bit post-quantum security. The result is SOFIA-4-128 with parameters carefully optimized to minimize signature size and maximize performance. SOFIA-4-128 comes with an implementation targeting recent Intel processors with the AVX2 vector-instruction set; the implementation is fully protected against timing attacks.
The Fiat-Shamir transformation is a famous technique to turn identification schemes into signature schemes. The derived scheme is provably secure in the random-oracle model against classical adversaries. Still, the technique has also been suggested to be used in connection with quantum-immune identification schemes, in order to get quantum-immune signature schemes. However, a recent paper by Boneh et al. (Asiacrypt 2011) has raised the issue that results in the random-oracle model may not be immediately applicable to quantum adversaries, because such adversaries should be allowed to query the random oracle in superposition. It has been unclear if the Fiat-Shamir technique is still secure in this quantum oracle model (QROM). Here, we discuss that giving proofs for the Fiat-Shamir transformation in the QROM is presumably hard. We show that there cannot be black-box extractors, as long as the underlying quantum-immune identification scheme is secure against active adversaries and the first message of the prover is independent of its witness. Most schemes are of this type. We then discuss that for some schemes one may be able to resurrect the Fiat-Shamir result in the QROM by modifying the underlying protocol first. We discuss in particular a version of the Lyubashevsky scheme which is provably secure in the QROM.
Quantum secure signature schemes have a lot of attention recently, in particular because of the NIST call to standardize quantum safe cryptography. However, only few signature schemes can have concrete quantum security because of technical difficulties associated with the Quantum Random Oracle Model (QROM). In this paper, we show that code-based signature schemes based on the full domain hash paradigm can behave very well in the QROM i.e. that we can have tight security reductions. We also study quantum algorithms related to the underlying code-based assumption. Finally, we apply our reduction to a concrete example: the SURF signature scheme. We provide parameters for 128 bits of quantum security in the QROM and show that the obtained parameters are competitive compared to other similar quantum secure signature schemes.
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.
Recently, in order to guarantee security against quantum adversaries, several identification (ID) schemes based on computational problems which are supposed to be hard even for quantum computers have been proposed. However, their security are only proven against non-quantum adversaries. In this paper, we proposed a novel four-pass code-based identification scheme. By using quantum random oracle model, we provide a security proof for our scheme against quantum adversaries which aim to impersonate the prover under concurrent active attacks, based on the hardness assumption of syndrome decoding (SD) problem. Our security proof is interesting in its own right, since it only requires a non-programmable quantum random oracle, in contrast to existing security proofs of digital signatures generated from ID scheme via Fiat-Shamir transform which require programmable quantum random oracles.