arXiv subjects

Garazi Muguruza

Publications and source records attributed to Garazi Muguruza.

7 recordsLinked to original sources

arXiv2026

Amplifying Randomized Encodings & Applications

A randomized encoding for a promise problem is a randomized reduction whose outcome distribution on input $x$ can be simulated within some distance $d$, called privacy, using only one bit of information about $x$: whether it is a YES or NO instance. The encoding is one-sided if this holds only for YES instances. Our main contribution is showing that (classical and quantum) one-sided randomized encodings have privacy and correctness amplification: any problem with an encoding with privacy $1-1/poly(n)$ and error $1/2-1/poly(n)$ also has one with negligible privacy and error. We use this result to show: - NISZK, the class of problems with non-interactive (statistical) zero-knowledge proofs, has strong zero-knowledge amplification: every problem with such a proof with zero-knowledge error $1-1/poly(n)$ also has one with negligible zero-knowledge error. This solves a problem open since Goldreich, Sahai, and Vadhan (CRYPTO '99). - The worst-case hardness of a problem with a perfect (zero-error) one-sided encoding implies one-way functions (OWFs), and, if the encoding is quantum, one-way state generators (OWSGs). We then conclude that removing the error from one-sided randomized encodings would make the worst-case hardness of SZK sufficient for OWFs. - Weak and imperfect indistinguishability obfuscation (iO) implies OWFs assuming the Polynomial Hierarchy does not collapse to its third level. Here, weak means the computational distance between the obfuscated and original circuits is $1-1/poly(n)$, and imperfect means the error is $1/2-1/poly(n)$. To achieve this amplification, we study randomized encodings through the lens of lossy reductions (Ball et al. ITCS 2020): we introduce an extended, flexible notion of lossy reductions and show it is equivalent to randomized encodings. This equivalence underlies our main results and may be of independent interest.

cs.CR↗

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.

quant-ph↗

arXiv2024

Port-Based State Preparation and Applications

We introduce Port-Based State Preparation (PBSP), a teleportation task where Alice holds a complete classical description of the target state and Bob's correction operations are restricted to only tracing out registers. We show a protocol that implements PBSP with error decreasing exponentially in the number of ports, in contrast to the polynomial trade-off for the related task of Port-Based Teleportation, and we prove that this is optimal when a maximally entangled resource state is used. As an application, we introduce approximate Universal Programmable Hybrid Processors (UPHP). Here the goal is to encode a unitary as a quantum state, and the UPHP can apply this unitary to a quantum state when knowing its classical description. We give a construction that needs strictly less memory in terms of dimension than the optimal approximate Universal Programmable Quantum Processor achieving the same error. Additionally, we provide lower bounds for the optimal trade-off between memory and error of UPHPs.

quant-ph↗

arXiv2024

All $S_p$ notions of quantum expansion are equivalent

In a recent work Li, Qiao, Wigderson, Wigderson and Zhang introduced notions of quantum expansion based on $S_p$ norms and posed as an open question if they were all equivalent. We give an affirmative answer to this question.

math.CO↗

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).

quant-ph↗

arXiv2023

Oblivious Transfer from Zero-Knowledge Proofs, or How to Achieve Round-Optimal Quantum Oblivious Transfer and Zero-Knowledge Proofs on Quantum States

We provide a generic construction to turn any classical Zero-Knowledge (ZK) protocol into a composable (quantum) oblivious transfer (OT) protocol, mostly lifting the round-complexity properties and security guarantees (plain-model/statistical security/unstructured functions...) of the ZK protocol to the resulting OT protocol. Such a construction is unlikely to exist classically as Cryptomania is believed to be different from Minicrypt. In particular, by instantiating our construction using Non-Interactive ZK (NIZK), we provide the first round-optimal (2-message) quantum OT protocol secure in the random oracle model, and round-optimal extensions to string and k-out-of-n OT. At the heart of our construction lies a new method that allows us to prove properties on a received quantum state without revealing additional information on it, even in a non-interactive way, without public-key primitives, and/or with statistical guarantees when using an appropriate classical ZK protocol. We can notably prove that a state has been partially measured (with arbitrary constraints on the set of measured qubits), without revealing any additional information on this set. This notion can be seen as an analog of ZK to quantum states, and we expect it to be of independent interest as it extends complexity theory to quantum languages, as illustrated by the two new complexity classes we introduce, ZKstatesQIP and ZKstatesQMA.

quant-ph↗

arXiv2022

An efficient combination of quantum error correction and authentication

When sending quantum information over a channel, we want to ensure that the message remains intact. Quantum error correction and quantum authentication both aim to protect (quantum) information, but approach this task from two very different directions: error-correcting codes protect against probabilistic channel noise and are meant to be very robust against small errors, while authentication codes prevent adversarial attacks and are designed to be very sensitive against any error, including small ones. In practice, when sending an authenticated state over a noisy channel, one would have to wrap it in an error-correcting code to counterbalance the sensitivity of the underlying authentication scheme. We study the question of whether this can be done more efficiently by combining the two functionalities in a single code. To illustrate the potential of such a combination, we design the threshold code, a modification of the trap authentication code which preserves that code's authentication properties, but which is naturally robust against depolarizing channel noise. We show that the threshold code needs polylogarithmically fewer qubits to achieve the same level of security and robustness, compared to the naive composition of the trap code with any concatenated CSS code. We believe our analysis opens the door to combining more general error-correction and authentication codes, which could improve the practicality of the resulting scheme.

quant-ph↗