arXiv subjects

Sam Gunn

Publications and source records attributed to Sam Gunn.

17 recordsLinked to original sources

arXiv2026

How to sketch a learning algorithm

How does the choice of training data influence an AI model? This broad question is of central importance to interpretability, privacy, and basic science. At its technical core is the data deletion problem: after a reasonable amount of precomputation, quickly predict how the model would behave in a given situation if a given subset of training data had been excluded from the learning algorithm. We present a data deletion scheme capable of predicting model outputs with vanishing error $\varepsilon$ and failure probability $\delta$ in the deep learning setting. Our precomputation and prediction algorithms are only $\tilde{O}(\log(1/\delta)/\varepsilon^2)$ factors slower than regular training and inference, respectively. The storage requirements are those of $\tilde{O}(\log(1/\delta)/\varepsilon^2)$ models. Our proof is based on an assumption that we call stability. In contrast to the assumptions made by prior work, stability appears to be fully compatible with learning powerful AI models. In support of this, we show that stability is satisfied in a minimal set of experiments with microgpt. Our code is available at https://github.com/SamSpo1/microgpt-sketch. At a technical level, our work is based on a new method for locally sketching an arithmetic circuit by computing higher-order derivatives in random complex directions. Forward-mode automatic differentiation allows cheap computation of these derivatives.

cs.LG↗

arXiv2025

Improved Pseudorandom Codes from Permuted Puzzles

Watermarks are an essential tool for identifying AI-generated content. Recently, Christ and Gunn (CRYPTO '24) introduced pseudorandom error-correcting codes (PRCs), which are equivalent to watermarks with strong robustness and quality guarantees. A PRC is a pseudorandom encryption scheme whose decryption algorithm tolerates a high rate of errors. Pseudorandomness ensures quality preservation of the watermark, and error tolerance of decryption translates to the watermark's ability to withstand modification of the content. In the short time since the introduction of PRCs, several works (NeurIPS '24, RANDOM '25, STOC '25) have proposed new constructions. Curiously, all of these constructions are vulnerable to quasipolynomial-time distinguishing attacks. Furthermore, all lack robustness to edits over a constant-sized alphabet, which is necessary for a meaningfully robust LLM watermark. Lastly, they lack robustness to adversaries who know the watermarking detection key. Until now, it was not clear whether any of these properties was achievable individually, let alone together. We construct pseudorandom codes that achieve all of the above: plausible subexponential pseudorandomness security, robustness to worst-case edits over a binary alphabet, and robustness against even computationally unbounded adversaries that have the detection key. Pseudorandomness rests on a new assumption that we formalize, the permuted codes conjecture, which states that a distribution of permuted noisy codewords is pseudorandom. We show that this conjecture is implied by the permuted puzzles conjecture used previously to construct doubly efficient private information retrieval. To give further evidence, we show that the conjecture holds against a broad class of simple distinguishers, including read-once branching programs.

cs.CR↗

arXiv2025

Black-Box Crypto is Useless for Pseudorandom Codes

A pseudorandom code is a keyed error-correction scheme with the property that any polynomial number of encodings appear random to any computationally bounded adversary. We show that the pseudorandomness of any code tolerating a constant rate of random errors cannot be based on black-box reductions to almost any generic cryptographic primitive: for instance, anything that can be built from random oracles, generic multilinear groups, and virtual black-box obfuscation. Our result is optimal, as Ghentiyala and Guruswami (2024) observed that pseudorandom codes tolerating any sub-constant rate of random errors exist using a black-box reduction from one-way functions. The key technical ingredient in our proof is the hypercontractivity theorem for Boolean functions, which we use to prove our impossibility in the random oracle model. It turns out that this easily extends to an impossibility in the presence of ``crypto oracles,'' a notion recently introduced -- and shown to be capable of implementing all the primitives mentioned above -- by Lin, Mook, and Wichs (EUROCRYPT 2025).

cs.CR↗

arXiv2024

SoK: Watermarking for AI-Generated Content

As the outputs of generative AI (GenAI) techniques improve in quality, it becomes increasingly challenging to distinguish them from human-created content. Watermarking schemes are a promising approach to address the problem of distinguishing between AI and human-generated content. These schemes embed hidden signals within AI-generated content to enable reliable detection. While watermarking is not a silver bullet for addressing all risks associated with GenAI, it can play a crucial role in enhancing AI safety and trustworthiness by combating misinformation and deception. This paper presents a comprehensive overview of watermarking techniques for GenAI, beginning with the need for watermarking from historical and regulatory perspectives. We formalize the definitions and desired properties of watermarking schemes and examine the key objectives and threat models for existing approaches. Practical evaluation strategies are also explored, providing insights into the development of robust watermarking techniques capable of resisting various attacks. Additionally, we review recent representative works, highlight open challenges, and discuss potential directions for this emerging field. By offering a thorough understanding of watermarking in GenAI, this work aims to guide researchers in advancing watermarking methods and applications, and support policymakers in addressing the broader implications of GenAI.

cs.CR↗

arXiv2024

Ideal Pseudorandom Codes

Pseudorandom codes are error-correcting codes with the property that no efficient adversary can distinguish encodings from uniformly random strings. They were recently introduced by Christ and Gunn [CRYPTO 2024] for the purpose of watermarking the outputs of randomized algorithms, such as generative AI models. Several constructions of pseudorandom codes have since been proposed, but none of them are robust to error channels that depend on previously seen codewords. This stronger kind of robustness is referred to as adaptive robustness, and it is important for meaningful applications to watermarking. In this work, we show the following. - Adaptive robustness: We show that the pseudorandom codes of Christ and Gunn are adaptively robust, resolving a conjecture posed by Cohen, Hoover, and Schoenbach [S&P 2025]. - Ideal security: We define an ideal pseudorandom code as one which is indistinguishable from the ideal functionality, capturing both the pseudorandomness and robustness properties in one simple definition. We show that any adaptively robust pseudorandom code for single-bit messages can be bootstrapped to build an ideal pseudorandom code with linear information rate, under no additional assumptions. - CCA security: In the setting where the encoding key is made public, we define a CCA-secure pseudorandom code in analogy with CCA-secure encryption. We show that any adaptively robust public-key pseudorandom code for single-bit messages can be used to build a CCA-secure pseudorandom code with linear information rate, in the random oracle model. These results immediately imply stronger robustness guarantees for generative AI watermarking schemes, such as the practical quality-preserving image watermarks of Gunn, Zhao, and Song (2024).

cs.CR↗

arXiv2024

Quantum One-Time Protection of any Randomized Algorithm

The meteoric rise in power and popularity of machine learning models dependent on valuable training data has reignited a basic tension between the power of running a program locally and the risk of exposing details of that program to the user. At the same time, fundamental properties of quantum states offer new solutions to data and program security that can require strikingly few quantum resources to exploit, and offer advantages outside of mere computational run time. In this work, we demonstrate such a solution with quantum one-time tokens. A quantum one-time token is a quantum state that permits a certain program to be evaluated exactly once. One-time security guarantees, roughly, that the token cannot be used to evaluate the program more than once. We propose a scheme for building quantum one-time tokens for any randomized classical program, which include generative AI models. We prove that the scheme satisfies an interesting definition of one-time security as long as outputs of the classical algorithm have high enough min-entropy, in a black box model. Importantly, the classical program being protected does not need to be implemented coherently on a quantum computer. In fact, the size and complexity of the quantum one-time token is independent of the program being protected, and additional quantum resources serve only to increase the security of the protocol. Due to this flexibility in adjusting the security, we believe that our proposal is parsimonious enough to serve as a promising candidate for a near-term useful demonstration of quantum computing in either the NISQ or early fault tolerant regime.

quant-ph↗

arXiv2024

Provably Robust Watermarks for Open-Source Language Models

The recent explosion of high-quality language models has necessitated new methods for identifying AI-generated text. Watermarking is a leading solution and could prove to be an essential tool in the age of generative AI. Existing approaches embed watermarks at inference and crucially rely on the large language model (LLM) specification and parameters being secret, which makes them inapplicable to the open-source setting. In this work, we introduce the first watermarking scheme for open-source LLMs. Our scheme works by modifying the parameters of the model, but the watermark can be detected from just the outputs of the model. Perhaps surprisingly, we prove that our watermarks are unremovable under certain assumptions about the adversary's knowledge. To demonstrate the behavior of our construction under concrete parameter instantiations, we present experimental results with OPT-6.7B and OPT-1.3B. We demonstrate robustness to both token substitution and perturbation of the model parameters. We find that the stronger of these attacks, the model-perturbation attack, requires deteriorating the quality score to 0 out of 100 in order to bring the detection rate down to 50%.

cs.CR↗

arXiv2024

An Undetectable Watermark for Generative Image Models

We present the first undetectable watermarking scheme for generative image models. Undetectability ensures that no efficient adversary can distinguish between watermarked and un-watermarked images, even after making many adaptive queries. In particular, an undetectable watermark does not degrade image quality under any efficiently computable metric. Our scheme works by selecting the initial latents of a diffusion model using a pseudorandom error-correcting code (Christ and Gunn, 2024), a strategy which guarantees undetectability and robustness. We experimentally demonstrate that our watermarks are quality-preserving and robust using Stable Diffusion 2.1. Our experiments verify that, in contrast to every prior scheme we tested, our watermark does not degrade image quality. Our experiments also demonstrate robustness: existing watermark removal attacks fail to remove our watermark from images without significantly degrading the quality of the images. Finally, we find that we can robustly encode 512 bits in our watermark, and up to 2500 bits when the images are not subjected to watermark removal attacks. Our code is available at https://github.com/XuandongZhao/PRC-Watermark.

cs.CR↗

arXiv2024

Classical Commitments to Quantum States

We define the notion of a classical commitment scheme to quantum states, which allows a quantum prover to compute a classical commitment to a quantum state, and later open each qubit of the state in either the standard or the Hadamard basis. Our notion is a strengthening of the measurement protocol from Mahadev (STOC 2018). We construct such a commitment scheme from the post-quantum Learning With Errors (LWE) assumption, and more generally from any noisy trapdoor claw-free function family that has the distributional strong adaptive hardcore bit property (a property that we define in this work). Our scheme is succinct in the sense that the running time of the verifier in the commitment phase depends only on the security parameter (independent of the size of the committed state), and its running time in the opening phase grows only with the number of qubits that are being opened (and the security parameter). As a corollary we obtain a classical succinct argument system for QMA under the post-quantum LWE assumption. Previously, this was only known assuming post-quantum secure indistinguishability obfuscation. As an additional corollary we obtain a generic way of converting any X/Z quantum PCP into a succinct argument system under the quantum hardness of LWE.

quant-ph↗

arXiv2024

Pseudorandom Error-Correcting Codes

We construct pseudorandom error-correcting codes (or simply pseudorandom codes), which are error-correcting codes with the property that any polynomial number of codewords are pseudorandom to any computationally-bounded adversary. Efficient decoding of corrupted codewords is possible with the help of a decoding key. We build pseudorandom codes that are robust to substitution and deletion errors, where pseudorandomness rests on standard cryptographic assumptions. Specifically, pseudorandomness is based on either $2^{O(\sqrt{n})}$-hardness of LPN, or polynomial hardness of LPN and the planted XOR problem at low density. As our primary application of pseudorandom codes, we present an undetectable watermarking scheme for outputs of language models that is robust to cropping and a constant rate of random substitutions and deletions. The watermark is undetectable in the sense that any number of samples of watermarked text are computationally indistinguishable from text output by the original model. This is the first undetectable watermarking scheme that can tolerate a constant rate of errors. Our second application is to steganography, where a secret message is hidden in innocent-looking content. We present a constant-rate stateless steganography scheme with robustness to a constant rate of substitutions. Ours is the first stateless steganography scheme with provable steganographic security and any robustness to errors.

cs.CR↗

arXiv2023

How to Use Quantum Indistinguishability Obfuscation

Quantum copy protection, introduced by Aaronson, enables giving out a quantum program-description that cannot be meaningfully duplicated. Despite over a decade of study, copy protection is only known to be possible for a very limited class of programs. As our first contribution, we show how to achieve "best-possible" copy protection for all programs. We do this by introducing quantum state indistinguishability obfuscation (qsiO), a notion of obfuscation for quantum descriptions of classical programs. We show that applying qsiO to a program immediately achieves best-possible copy protection. Our second contribution is to show that, assuming injective one-way functions exist, qsiO is concrete copy protection for a large family of puncturable programs -- significantly expanding the class of copy-protectable programs. A key tool in our proof is a new variant of unclonable encryption (UE) that we call coupled unclonable encryption (cUE). While constructing UE in the standard model remains an important open problem, we are able to build cUE from one-way functions. If we additionally assume the existence of UE, then we can further expand the class of puncturable programs for which qsiO is copy protection. Finally, we construct qsiO relative to an efficient quantum oracle.

quant-ph↗

arXiv2023

Undetectable Watermarks for Language Models

Recent advances in the capabilities of large language models such as GPT-4 have spurred increasing concern about our ability to detect AI-generated text. Prior works have suggested methods of embedding watermarks in model outputs, by noticeably altering the output distribution. We ask: Is it possible to introduce a watermark without incurring any detectable change to the output distribution? To this end we introduce a cryptographically-inspired notion of undetectable watermarks for language models. That is, watermarks can be detected only with the knowledge of a secret key; without the secret key, it is computationally intractable to distinguish watermarked outputs from those of the original model. In particular, it is impossible for a user to observe any degradation in the quality of the text. Crucially, watermarks should remain undetectable even when the user is allowed to adaptively query the model with arbitrarily chosen prompts. We construct undetectable watermarks based on the existence of one-way functions, a standard assumption in cryptography.

cs.CR↗

arXiv2022

Approaching the Quantum Singleton Bound with Approximate Error Correction

It is well known that no quantum error correcting code of rate $R$ can correct adversarial errors on more than a $(1-R)/4$ fraction of symbols. But what if we only require our codes to *approximately* recover the message? We construct efficiently-decodable approximate quantum codes against adversarial error rates approaching the quantum Singleton bound of $(1-R)/2$, for any constant rate $R$. Moreover, the size of the alphabet is a constant independent of the message length and the recovery error is exponentially small in the message length. Central to our construction is a notion of quantum list decoding and an implementation involving folded quantum Reed-Solomon codes.

quant-ph↗

arXiv2022

Commitments to Quantum States

What does it mean to commit to a quantum state? In this work, we propose a simple answer: a commitment to quantum messages is binding if, after the commit phase, the committed state is hidden from the sender's view. We accompany this new definition with several instantiations. We build the first non-interactive succinct quantum state commitments, which can be seen as an analogue of collision-resistant hashing for quantum messages. We also show that hiding quantum state commitments (QSCs) are implied by any commitment scheme for classical messages. All of our constructions can be based on quantum-cryptographic assumptions that are implied by but are potentially weaker than one-way functions. Commitments to quantum states open the door to many new cryptographic possibilities. Our flagship application of a succinct QSC is a quantum-communication version of Kilian's succinct arguments for any language that has quantum PCPs with constant error and polylogarithmic locality. Plugging in the PCP theorem, this yields succinct arguments for NP under significantly weaker assumptions than required classically; moreover, if the quantum PCP conjecture holds, this extends to QMA. At the heart of our security proof is a new rewinding technique for extracting quantum information.

quant-ph↗

arXiv2021

On Certified Randomness from Fourier Sampling or Random Circuit Sampling

Certified randomness has a long history in quantum information, with many potential applications. Recently Aaronson (2018, 2020) proposed a novel public certified randomness protocol based on existing random circuit sampling (RCS) experiments. The security of his protocol, however, relies on non-standard complexity-theoretic conjectures which were not previously studied in the literature. Inspired by Aaronson's work, we study certified randomness in the quantum random oracle model (QROM). We show that quantum Fourier Sampling can be used to define a publicly verifiable certified randomness protocol with black-box security without any computational assumptions. In addition to giving a certified randomness protocol in the QROM, our work can also be seen as supporting Aaronson's conjectures for RCS-based randomness generation, as our protocol is in some sense the "black-box version" of Aaronson's protocol. In further support of Aaronson's proposal, we prove a Fourier Sampling version of Aaronson's conjecture by extending Raz and Tal's separation of BQP vs PH. Our work complements the subsequent certified randomness protocol of Yamakawa and Zhandry (2022) in the QROM. Whereas the security of that protocol relied on the Aaronson-Ambainis conjecture, ours does not rely on any computational assumption - at the expense of requiring exponential-time classical verification. Our protocol also has a simple heuristic implementation.

quant-ph↗

arXiv2019

On the Classical Hardness of Spoofing Linear Cross-Entropy Benchmarking

Recently, Google announced the first demonstration of quantum computational supremacy with a programmable superconducting processor. Their demonstration is based on collecting samples from the output distribution of a noisy random quantum circuit, then applying a statistical test to those samples called Linear Cross-Entropy Benchmarking (Linear XEB). This raises a theoretical question: how hard is it for a classical computer to spoof the results of the Linear XEB test? In this short note, we adapt an analysis of Aaronson and Chen [2017] to prove a conditional hardness result for Linear XEB spoofing. Specifically, we show that the problem is classically hard, assuming that there is no efficient classical algorithm that, given a random n-qubit quantum circuit C, estimates the probability of C outputting a specific output string, say 0^n, with variance even slightly better than that of the trivial estimator that always estimates 1/2^n. Our result automatically encompasses the case of noisy circuits.

quant-ph↗

arXiv2019

Review of a Quantum Algorithm for Betti Numbers

We looked into the algorithm for calculating Betti numbers presented by Lloyd, Garnerone, and Zanardi (LGZ). We present a new algorithm in the same spirit as LGZ with the intent of clarifying quantum algorithms for computing Betti numbers. Our algorithm is simpler and slightly more efficient than that presented by LGZ. We present a thorough analysis of our algorithm, pointing out reasons that both our algorithm and that presented by LGZ do not run in polynomial time for most inputs. However, the algorithms do run in polynomial time for calculating an approximation of the Betti number to polynomial multiplicative error, when applied to some class of graphs for which the Betti number is exponentially large.

quant-ph↗