Computationally Relaxed Locally Decodable Codes, Revisited

We revisit computationally relaxed locally decodable codes (crLDCs) (Blocki et al., Trans. Inf. Theory '21) and give two new constructions. Our first construction is a Hamming crLDC that is conceptually simpler than prior constructions, leveraging digital signature schemes and an appropriately chosen Hamming code. Our second construction is an extension of our Hamming crLDC to handle insertion-deletion (InsDel) errors, yielding an InsDel crLDC. This extension crucially relies on the noisy binary search techniques of Block et al. (FSTTCS '20) to handle InsDel errors. Both crLDC constructions have binary codeword alphabets, are resilient to a constant fraction of Hamming and InsDel errors, respectively, and under suitable parameter choices have poly-logarithmic locality and encoding length linear in the message length and polynomial in the security parameter. These parameters compare favorably to prior constructions in the poly-logarithmic locality regime

Honest Majority Multi-Prover Interactive Arguments

Interactive arguments, and their (succinct) non-interactive and zero-knowledge counterparts, have seen growing deployment in real world applications in recent years. Unfortunately, for large and complex statements, concrete proof generation costs can still be quite expensive. While recent work has sought to solve this problem by outsourcing proof computation to a group of workers in a privacy preserving manner, current solutions still require each worker to do work on roughly the same order as a single-prover solution. We introduce the Honest Majority Multi-Prover (HMMP) model for interactive arguments. In these arguments, we distribute prover computation among $M$ collaborating, but distrusting, provers. All provers receive the same inputs and have no private inputs, and we allow any $t < M/2$ provers to be statically corrupted before generation of public parameters, and all communication is done via an authenticated broadcast channel. In contrast with the recent works of Ozdemir and Boneh (USENIX \u2722) and Dayama et al. (PETS \u2722), we target prover efficiency over privacy. We show that: (1) any interactive argument where the prover computation is suitably divisible into $M$ sub-computations can be transformed into an interactive argument in the HMMP model; and (2) arguments that are obtained via compiling polynomial interactive oracle proofs with polynomial commitment schemes admit HMMP model constructions that experience a (roughly) $1/M$ speedup over a single-prover solution. The transformation of (1) preserves computational (knowledge) soundness, zero-knowledge, and can be made non-interactive via the Fiat-Shamir transformation. The constructions of (2) showcase that there are efficiency gains in proof distribution when privacy is not a concern

Locally Decodable/Correctable Codes for Insertions and Deletions

Recent efforts in coding theory have focused on building codes for insertions and deletions, called insdel codes, with optimal trade-offs between their redundancy and their error-correction capabilities, as well as efficient encoding and decoding algorithms. In many applications, polynomial running time may still be prohibitively expensive, which has motivated the study of codes with super-efficient decoding algorithms. These have led to the well-studied notions of Locally Decodable Codes (LDCs) and Locally Correctable Codes (LCCs). Inspired by these notions, Ostrovsky and Paskin-Cherniavsky (Information Theoretic Security, 2015) generalized Hamming LDCs to insertions and deletions. To the best of our knowledge, these are the only known results that study the analogues of Hamming LDCs in channels performing insertions and deletions. Here we continue the study of insdel codes that admit local algorithms. Specifically, we reprove the results of Ostrovsky and Paskin-Cherniavsky for insdel LDCs using a different set of techniques. We also observe that the techniques extend to constructions of LCCs. Specifically, we obtain insdel LDCs and LCCs from their Hamming LDCs and LCCs analogues, respectively. The rate and error-correction capability blow up only by a constant factor, while the query complexity blows up by a poly log factor in the block length. Since insdel locally decodable/correctble codes are scarcely studied in the literature, we believe our results and techniques may lead to further research. In particular, we conjecture that constant-query insdel LDCs/LCCs do not exist

On Soundness Notions for Interactive Oracle Proofs

Interactive oracle proofs (IOPs) (Ben-Sasson et al., TCC 2016) have emerged as a powerful model for proof systems which generalizes both Interactive Proofs (IPs) and Probabilistically Checkable Proofs (PCPs). While IOPs are not any more powerful than PCPs from a complexity theory perspective, their potential to create succinct proofs and arguments has been demonstrated by many recent constructions achieving better parameters such as total proof length, alphabet size, and query complexity. In this work, we establish new results on the relationship between various notions of soundness for IOPs. First, we formally generalize the notion of round-by-round soundness (Canetti et al., STOC 2019) and round-by-round knowledge soundness (Chiesa et al., TCC 2019). Given this generalization, we then examine its relationship to the notions of generalized special soundness (Attema et al., CRYPTO 2021) and generalized special unsoundness (Attema et al., TCC 2022). We show that: 1. generalized special soundness implies generalized round-by-round soundness; 2. generalized round-by-round knowledge soundness implies generalized special soundness; 3. generalized special soundness does not imply generalized round-by-round knowledge soundness; 4. generalized round-by-round soundness (resp., special unsoundness) is an upper bound (resp., a lower bound) on standard soundness, and that this relationship is tight when the round-by-round soundness and special unsoundness errors are equal; and 5. any special sound IOP can be transformed via (a variant of) the Fiat-Shamir transformation into a non-interactive proof that is adaptively sound in the Quantum Random Oracle Model

Public-Coin Zero-Knowledge Arguments with (almost) Minimal Time and Space Overheads

Zero-knowledge protocols enable the truth of a mathematical statement to be certified by a verifier without revealing any other information. Such protocols are a cornerstone of modern cryptography and recently are becoming more and more practical. However, a major bottleneck in deployment is the efficiency of the prover and, in particular, the space-efficiency of the protocol. For every $\mathsf{NP}$ relation that can be verified in time $T$ and space $S$, we construct a public-coin zero-knowledge argument in which the prover runs in time $T \cdot \mathrm{polylog}(T)$ and space $S \cdot \mathrm{polylog}(T)$. Our proofs have length $\mathrm{polylog}(T)$ and the verifier runs in time $T \cdot \mathrm{polylog}(T)$ (and space $\mathrm{polylog}(T)$). Our scheme is in the random oracle model and relies on the hardness of discrete log in prime-order groups. Our main technical contribution is a new space efficient polynomial commitment scheme for multi-linear polynomials. Recall that in such a scheme, a sender commits to a given multi-linear polynomial $P \colon \mathbb{F}^n \rightarrow \mathbb{F}$ so that later on it can prove to a receiver statements of the form $P(x) = y$ . In our scheme, which builds on the commitment schemes of Bootle et al. (Eurocrypt 2016) and Bünz et al. (S&P 2018), we assume that the sender is given multi-pass streaming access to the evaluations of $P$ on the Boolean hypercube and w show how to implement both the sender and receiver in roughly time $2^n$ and space $n$ and with communication complexity roughly $n$

Fiat-Shamir Security of FRI and Related SNARKs

We establish new results on the Fiat-Shamir (FS) security of several protocols that are widely used in practice, and we provide general tools for establishing similar results for others. More precisely, we: (1) prove the FS security of the FRI and batched FRI protocols; (2) analyze a general class of protocols, which we call $\delta$-correlated, that use low-degree proximity testing as a subroutine (this includes many Plonk-like protocols (e.g., Plonky2 and Redshift), ethSTARK, RISC Zero, etc.); and (3) prove FS security of the aforementioned Plonk-like protocols, and sketch how to prove the same for the others. We obtain our first result by analyzing the round-by-round (RBR) soundness and RBR knowledge soundness of FRI. For the second result, we prove that if a $\delta$-correlated protocol is RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials, then it is RBR (knowledge) sound in general. Equipped with this tool, we prove our third result by formally showing that Plonk-like protocols are RBR (knowledge) sound under the assumption that adversaries always send low-degree polynomials. We then outline analogous arguments for the remainder of the aforementioned protocols. To the best of our knowledge, ours is the first formal analysis of the Fiat-Shamir security of FRI and widely deployed protocols that invoke it

Visual onset expands subjective time

We report a distortion of subjective time perception in which the duration of a first interval is perceived to be longer than the succeeding interval of the same duration. The amount of time expansion depends on the onset type defining the first interval. When a stimulus appears abruptly, its duration is perceived to be longer than when it appears following a stationary array. The difference in the processing time for the stimulus onset and motion onset, measured as reaction times, agrees with the difference in time expansion. Our results suggest that initial transient responses for a visual onset serve as a temporal marker for time estimation, and a systematic change in the processing time for onsets affects perceived time

Post-stroke inhibition of induced NADPH oxidase type 4 prevents oxidative stress and neurodegeneration

Ischemic stroke is the second leading cause of death worldwide. Only one moderately effective therapy exists, albeit with contraindications that exclude 90% of the patients. This medical need contrasts with a high failure rate of more than 1,000 pre-clinical drug candidates for stroke therapies. Thus, there is a need for translatable mechanisms of neuroprotection and more rigid thresholds of relevance in pre-clinical stroke models. One such candidate mechanism is oxidative stress. However, antioxidant approaches have failed in clinical trials, and the significant sources of oxidative stress in stroke are unknown. We here identify NADPH oxidase type 4 (NOX4) as a major source of oxidative stress and an effective therapeutic target in acute stroke. Upon ischemia, NOX4 was induced in human and mouse brain. Mice deficient in NOX4 (Nox4(-/-)) of either sex, but not those deficient for NOX1 or NOX2, were largely protected from oxidative stress, blood-brain-barrier leakage, and neuronal apoptosis, after both transient and permanent cerebral ischemia. This effect was independent of age, as elderly mice were equally protected. Restoration of oxidative stress reversed the stroke-protective phenotype in Nox4(-/-) mice. Application of the only validated low-molecular-weight pharmacological NADPH oxidase inhibitor, VAS2870, several hours after ischemia was as protective as deleting NOX4. The extent of neuroprotection was exceptional, resulting in significantly improved long-term neurological functions and reduced mortality. NOX4 therefore represents a major source of oxidative stress and novel class of drug target for stroke therapy

Obscured Activity: AGN, Quasars, Starbursts and ULIGs observed by the Infrared Space Observatory

Some of the most active galaxies in the Universe are obscured by large quantities of dust and emit a substantial fraction of their bolometric luminosity in the infrared. Observations of these infrared luminous galaxies with the Infrared Space Observatory (ISO) have provided a relatively unabsorbed view to the sources fuelling this active emission. The improved sensitivity, spatial resolution and spectroscopic capability of ISO over its predecessor Infrared Astronomical Satellite (IRAS), has enabled significant advances in the understanding of the infrared properties of active galaxies. ISO surveyed a wide range of active galaxies which, in the context of this review, includes those powered by intense bursts of star-formation as well as those containing a dominant active galactic nucleus (AGN). Mid infrared imaging resolved for the first time the dust enshrouded nuclei in many nearby galaxies, while a new era in infrared spectroscopy was opened by probing a wealth of atomic, ionic and molecular lines as well as broad band features in the mid and far infrared. This was particularly useful since it resulted in the understanding of the power production, excitation and fuelling mechanisms in the nuclei of active galaxies including the intriguing but so far elusive ultraluminous infrared galaxies. Detailed studies of various classes of AGN and quasars greatly improved our understanding of the unification scenario. Far-infrared imaging and photometry also revealed the presence of a new very cold dust component in galaxies and furthered our knowledge of the far-infrared properties of faint starbursts, ULIGs and quasars. We summarise almost nine years of key results based upon ISO data spanning the full range of luminosity and type of active galaxies.Comment: Accepted for publication in 'ISO science legacy - a compact review of ISO major achievements', Space Science Reviews - dedicated ISO issue. To be published by Springer in 2005. 62 pages (low resolution figures version). Higher resolution PDFs available from http://users.physics.uoc.gr/~vassilis/papers/VermaA.pdf or http://www.iso.vilspa.esa.es/science/SSR/Verma.pd