arXiv subjects

Samuel Bouaziz--Ermann

Publications and source records attributed to Samuel Bouaziz--Ermann.

4 recordsLinked to original sources

arXiv2026

On Limits on the Provable Consequences of Quantum Pseudorandomness

There are various notions of quantum pseudorandomness, such as pseudorandom unitaries (PRUs), pseudorandom state generators (PRSGs), pseudorandom function-like state generators (PRFSGs) and quantum-computable PRGs. Unlike the different notions of classical pseudorandomness, which are known to be existentially equivalent to each other, the relations among quantum pseudorandomness have yet to be fully established. We present evidence suggesting that some forms of quantum pseudorandomness are unlikely to be constructed from the others. This indicates that quantum pseudorandomness behaves quite differently from classical pseudorandomness. Our main result is a unitary oracle separation where log-length output PRFSGs exist but quantum-computable pseudorandom generators (QPRGs) with negligible correctness error do not. This result suggests that the inverse-polynomial error in the state-of-the-art construction of QPRGs from log-length PRSGs is inherent. To achieve this, we prove a novel differential geometric barrier theorem for the product Haar measure on quantum states which replaces the usual concentration inequalities by certifying a non-negligible ``gap'' between two large trace-separated sets. Our separation is based on an oracle that outputs Haar random quantum states for each bit string, which can be viewed as a quantum version of the random oracle model, where output strings are replaced by quantum states. Variations of this oracle can be used to study other relationships between quantum cryptographic primitives, and we use it to achieve partial separations, that highlight technical difficulties when dealing with ancillary registers, measurements, and adaptivity in the quantum setting.

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arXiv2024

Quantum Pseudorandomness Cannot Be Shrunk In a Black-Box Way

Pseudorandom Quantum States (PRS) were introduced by Ji, Liu and Song as quantum analogous to Pseudorandom Generators. They are an ensemble of states efficiently computable but computationally indistinguishable from Haar random states. Subsequent works have shown that some cryptographic primitives can be constructed from PRSs. Moreover, recent classical and quantum oracle separations of PRS from One-Way Functions strengthen the interest in a purely quantum alternative building block for quantum cryptography, potentially weaker than OWFs. However, our lack of knowledge of extending or shrinking the number of qubits of the PRS output still makes it difficult to reproduce some of the classical proof techniques and results. Short-PRSs, that is PRSs with logarithmic size output, have been introduced in the literature along with cryptographic applications, but we still do not know how they relate to PRSs. Here we answer half of the question, by showing that it is not possible to shrink the output of a PRS from polynomial to logarithmic qubit length while still preserving the pseudorandomness property, in a relativized way. More precisely, we show that relative to Kretschmer's quantum oracle (TQC 2021) short-PRSs cannot exist (while PRSs exist, as shown by Kretschmer's work).

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arXiv2023

Towards the Impossibility of Quantum Public Key Encryption with Classical Keys from One-Way Functions

There has been a recent interest in proposing quantum protocols whose security relies on weaker computational assumptions than their classical counterparts. Importantly to our work, it has been recently shown that public-key encryption (PKE) from one-way functions (OWF) is possible if we consider quantum public keys. Notice that we do not expect classical PKE from OWF given the impossibility results of Impagliazzo and Rudich (STOC'89). However, the distribution of quantum public keys is a challenging task. Therefore, the main question that motivates our work is if quantum PKE from OWF is possible if we have classical public keys. Such protocols are impossible if ciphertexts are also classical, given the impossibility result of Austrin et al. (CRYPTO'22) of quantum enhanced key-agreement (KA) with classical communication. In this paper, we focus on black-box separation for PKE with classical public key and quantum ciphertext from OWF under the polynomial compatibility conjecture, first introduced in Austrin et al.. More precisely, we show the separation when the decryption algorithm of the PKE does not query the OWF. We prove our result by extending the techniques of Austrin et al. and we show an attack for KA in an extended classical communication model where the last message in the protocol can be a quantum state.

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arXiv2023

Quantum security of subset cover problems

The subset cover problem for $k \geq 1$ hash functions, which can be seen as an extension of the collision problem, was introduced in 2002 by Reyzin and Reyzin to analyse the security of their hash-function based signature scheme HORS. The security of many hash-based signature schemes relies on this problem or a variant of this problem (e.g. HORS, SPHINCS, SPHINCS+, $\dots$). Recently, Yuan, Tibouchi and Abe (2022) introduced a variant to the subset cover problem, called restricted subset cover, and proposed a quantum algorithm for this problem. In this work, we prove that any quantum algorithm needs to make $Ω\left((k+1)^{-\frac{2^{k}}{2^{k+1}-1}}\cdot N^{\frac{2^{k}-1}{2^{k+1}-1}}\right)$ queries to the underlying hash functions with codomain size $N$ to solve the restricted subset cover problem, which essentially matches the query complexity of the algorithm proposed by Yuan, Tibouchi and Abe. We also analyze the security of the general $(r,k)$-subset cover problem, which is the underlying problem that implies the unforgeability of HORS under a $r$-chosen message attack (for $r \geq 1$). We prove that a generic quantum algorithm needs to make $Ω\left(N^{k/5}\right)$ queries to the underlying hash functions to find a $(1,k)$-subset cover. We also propose a quantum algorithm that finds a $(r,k)$-subset cover making $O\left(N^{k/(2+2r)}\right)$ queries to the $k$ hash functions.

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