The Fischlin transform yields non-interactive zero-knowledge proofs with straight-line extractability in the classical random oracle model. This is done by forcing a prover to generate multiple accepting transcripts through a proof-of-work mechanism. Whether the Fischlin transform is straight-line extractable against quantum adversaries has remained open due to the difficulty of reasoning about the likelihood of query transcripts in the quantum-accessible random oracle model (QROM), even when using the compressed oracle methodology. In this work, we prove that the Fischlin transform remains straight-line extractable in the QROM, via an extractor based on the compressed oracle. This establishes the post-quantum security of the Fischlin transform, providing a post-quantum straight-line extractable NIZK alternative to Pass' transform with smaller proof size. Our techniques include tail bounds for sums of independent random variables and for martingales as well as symmetrization, query amplitude and quantum union bound arguments.
The Fischlin transform yields non-interactive zero-knowledge proofs with straight-line extractability in the classical random oracle model. This is done by forcing a prover to generate multiple accepting transcripts through a proof-of-work mechanism. Whether the Fischlin transform is straight-line extractable against quantum adversaries has remained open due to the difficulty of reasoning about the likelihood of query transcripts in the quantum-accessible random oracle model (QROM), even when using the compressed oracle methodology. In this work, we prove that the Fischlin transform remains straight-line extractable in the QROM, via an extractor based on the compressed oracle. This establishes the post-quantum security of the Fischlin transform, providing a post-quantum straight-line extractable NIZK alternative to Pass' transform with smaller proof size. Our techniques include tail bounds for sums of independent random variables and for martingales as well as symmetrization, query amplitude and quantum union bound arguments.
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.
In a recent breakthrough, Yamakawa and Zhandry (J. ACM 2024) constructed a proof of quantumness in the quantum random oracle model (QROM) in which the quantum prover samples a codeword preimage of a publicly computable function H. They conjectured that given any H, a successful prover must sample their preimage from a high-entropy distribution over possible answers. If true, this would give a certifiable randomness protocol in the quantum random oracle model. As partial evidence for their conjecture, Yamakawa and Zhandry proved the security of their certifiable randomness protocol assuming the Aaronson-Ambainis conjecture.
We prove the security of the certifiable randomness protocol of Yamakawa-Zhandry unconditionally, without relying on the unproven Aaronson-Ambainis conjecture, against low query-depth quantum adversaries: specifically, adversaries that make up to o(\log λ) adaptive quantum queries to the random oracle.
With the rapid advance in quantum computing, quantum security is now an indispensable property for any cryptographic system. In this paper, we study how to prove the security of a complex cryptographic system in the quantum random oracle model. We first give a variant of Zhandry’s compressed quantum random oracle (CStO), called compressed quantum random oracle with adaptive special points (CStOs). Then, we extend the on-line extraction technique of Don et al (EUROCRYPT’22) from CStO to CStOs. We also extend the random experiment technique of Liu and Zhandry (CRYPTO’19) for extracting the CStO query that witnesses the future adversarial output. With these preparations, a systematic security proof in the quantum random oracle model can start with a random CStO experiment (that extracts the witness for the future adversarial output) and then convert this game to one involving CStOs. Next, the on-line extraction technique for CStOs can be applied to extract the witness for any on-line commitment. With this strategy, we give a security proof of our recent compact multi-signature framework that is converted from any weakly secure linear ID scheme. We also prove the quantum security of our recent lattice realization of this linear ID scheme, by iteratively applying the weakly collapsing protocol technique of Liu and Zhandry (CRYPTO 2019). Combining these two results, we obtain the first quantum security proof for a compact multi-signature.
We prove near-optimal lower bounds for preprocessing attacks on quantum cryptography in the random oracle model. Specifically, we show that a T-query adversary with S qubits of non-uniform advice can recover a random key k from the n-qubit binary phase state ∣ψk⟩∝∑xR(k,x)∣x⟩ with probability at most O(NT2+ST) for N=2n. In contrast, the best known bound for post-quantum one-way functions is O(NT2+ST), with a trivial attack at S=N. This demonstrates a new advantage of quantum cryptography over classical cryptography: n qubits of communication suffice for security against preprocessing attacks with space up to N2 rather than N. Our methodology is simple: express the optimal preprocessing attack as the operator norm of a random matrix, and bound this value in expectation over the random oracle via the trace-moment method. These trace moments have a natural interpretation using compressed oracles [Zhandry, Crypto 2019], which we then analyze. This can be viewed as a simplification and generalization of the approach of Liu [Eurocrypt 2023] for proving the security of post-quantum cryptography against preprocessing attacks. We also prove the following results: (1) We tighten Liu's analysis of post-quantum PRGs in QROM, achieving a distinguishing advantage bound of O(NT2+NST). (2) For unitary synthesis, we extend the one-query lower bound of Lombardi-Ma-Wright [STOC 2024] to hold against adversaries that can make one arbitrary function query along with polynomially many (adaptive) queries to the random oracle, either before or after the function query. This also interprets the original LMW24 result in terms of compressed oracles. (3) Finally, we prove a tight O(NS) bound for the pseudorandomness of random binary phase states against space S distinguishers.
Succinct arguments are a fundamental cryptographic primitive for verifying computational claims with small communication. In the classical setting, succinct arguments for NP can be constructed from unstructured hardness alone (e.g., hash functions) by compiling probabilistically checkable proofs (PCPs) or interactive oracle proofs (IOPs) for NP via the commit-and-open paradigm. In contrast, known succinct arguments for QMA rely on ``structured'' cryptographic primitives, or on the quantum PCP conjecture.
We construct the first succinct argument for QMA in the quantum random oracle model (QROM) without relying on additional cryptographic assumptions or unproven conjectures. This yields succinct arguments for QMA from unstructured hardness alone, showing that ideal hash functions not only suffice for succinct arguments for NP but also for QMA.
Underlying our result is an efficiency-preserving transformation that compiles quantum interactive oracle proofs (QIOPs), a recently introduced interactive generalization of quantum PCPs, into quantum arguments for the same language, via a natural quantum commit-and-open paradigm. Our transformation applies to every QIOP with public-query soundness, a notion that we formalize to capture a natural requirement of the commit-and-open paradigm and is satisfied by a known QIOP for QMA. As a key ingredient in our transformation, we formalize and construct extractable vector commitments for quantum states with local openings in the QROM, which may be of independent interest.
Recent developments in quantum computers pose an imminent threat to cryptography since many widely used cryptographic schemes will no longer be secure. This worrisome scenario motivated a growing interest in the field of post-quantum cryptography, which aims to design cryptosystems that are postquantum secure, i.e. secure against quantum-capable adversaries. While finding post-quantum computational hardness assumptions is pivotal to achieve this goal, an issue that is often overlooked is provable security. In fact, to prove that the post-quantum computational hardness necessarily implies post-quantum security of the derived cryptosystem, the reduction argument that establishes this implication also needs to be post-quantum. As such, many new methods have been devised in the last few years to handle this adaptation to the quantum setting. In particular, the quantum analogue of the Random Oracle Model has garnered special interest, as it is the foundation of many cryptographic schemes, from public-key encryption to digital signatures. It is also very problematic and usually the main culprit of the failure of security proofs when transitioning to the quantum setting. This work offers a comprehensive exposition on the most influential techniques developed in the last decade to enable or facilitate the construction of security proofs in the Quantum Random Oracle Model (QROM). Each presented technique offers an unique purpose and a solution to a problem provoked by the QROM, and, as such, as a whole, this works allows for an understanding of the most common strategies to construct these type of security proofs. This is accomplished by presenting and analyzing the security proof of three cryptographic schemes set in this model, which underlines the central role these techniques take in provable quantum security.