International Association
for Cryptologic Research

We present a novel stateless zero-knowledge rollup (ZK-rollup) protocol with client-side validation called Intmax2. Our architecture distinctly diverges from existing ZK-rollup approaches since essentially all of the data availability and computational costs are shifted to the client-side as opposed to imposing heavy computational requirements on the rollup aggregators. Moreover, the data storage and computation in our approach is parallelizable for each user. Therefore, there are no specific nodes to validate the contents of transactions. In effect, only block producers, who periodically submit a Merkle tree root containing all the transactions, are necessary.

Recently, many cryptographic primitives such as homomorphic encryption (HE), multi-party computation (MPC) and zero-knowledge (ZK) protocols have been proposed in the literature which operate on prime field $\mathbb{F}_p$ for some large prime $p$. Primitives that are designed using such operations are called arithmetization-oriented primitives. As the concept of arithmetization-oriented primitives is new, a rigorous cryptanalysis of such primitives is yet to be done. In this paper, we investigate arithmetization-oriented APN functions. More precisely, we investigate APN permutations in the CCZ-classes of known families of APN power functions over prime field $\mathbb{F}_p$. Moreover, we present a new class of APN binomials over $\mathbb{F}_q$ obtained by modifying the planar function $x^2$ over $\mathbb{F}_q$. We also present a class of binomials having differential uniformity at most $5$ defined via the quadratic character over finite fields of odd characteristic. We give sufficient conditions for which this family of binomials is permutation. Computationally it is confirmed that the latter family contains new APN functions for some small parameters. We conjecture it to contain an infinite subfamily of APN functions.

REAMC Report-007(2023) ACORN-QRE: Specification and Analysis of a Method of Generating Secure One-time Pads for Use in Encryption Roy S Wikramaratna (email: rwikramaratna@gmail.com) Abstract

The Additive Congruential Random Number (ACORN) generator is straightforward to implement; it has been demonstrated in previous papers to give rise to sequences with long period which can be proven from theoretical considerations to approximate to being uniform in up to k dimensions (for any given k).

The ACORN-QRE algorithm is a straightforward modification of ACORN which effectively avoids the linearity of the original algorithm, while preserving the uniformity of the modified sequence. It provides a new method for generating one-time pads that are resistant to attack either by current computers or by future computing developments, including quantum computers. The pads can use any alphabet (including both binary and alphanumeric) and can be used with a Vernam-type cypher to securely encrypt both files and communications.

This report explains how the ACORN-QRE algorithm works and provides evidence for the claim that the resulting one-time pads are inherently not susceptible to cryptanalysis and that they will remain secure against foreseeable developments in computing, including the potential development of quantum computers.

The ACORN-QRE algorithm is patented in the UK under Patent No. GB2591467; patent applied for in the US under Application No. 17/795632. The patents are owned by REAMC Limited, 4 Nuthatch Close, Poole, Dorset BH17 7XR, United Kingdom

Towards building more scalable blockchains, an approach known as data availability sampling (DAS) has emerged over the past few years. Even large blockchains like Ethereum are planning to eventually deploy DAS to improve their scalability. In a nutshell, DAS allows the participants of a network to ensure the full availability of some data without any one participant downloading it entirely. Despite the significant practical interest that DAS has received, there are currently no formal definitions for this primitive, no security notions, and no security proofs for any candidate constructions. For a cryptographic primitive that may end up being widely deployed in large real-world systems, this is a rather unsatisfactory state of affairs.

In this work, we initiate a cryptographic study of data availability sampling. To this end, we define data availability sampling precisely as a clean cryptographic primitive. Then, we show how data availability sampling relates to erasure codes. We do so by defining a new type of commitment schemes which naturally generalizes vector commitments and polynomial commitments. Using our framework, we analyze existing constructions and prove them secure. In addition, we give new constructions which are based on weaker assumptions, computationally more efficient, and do not rely on a trusted setup, at the cost of slightly larger communication complexity. Finally, we evaluate the trade-offs of the different constructions.

Efficient power management is critical for embedded devices, both for extending their lifetime and ensuring safety. However, this can be a challenging task due to the unpredictability of the batteries commonly used in such devices. To address this issue, dedicated Integrated Circuits known as "fuel gauges" are often employed outside of the System-On-Chip. These devices provide various metrics about the available energy source and are highly accurate. However, their precision can also be exploited by malicious actors to compromise platform confidentiality if the Operating System fails to intervene. Depending on the fuel gauge and OS configuration, several attack scenarios are possible. In this article, we focus on Android and demonstrate how it is possible to bypass application isolation to recover PINs entered in other processes.

YOSO-style MPC protocols (Gentry et al., Crypto'21), are a promising framework where the overall computation is partitioned into small, short-lived pieces, delegated to subsets of one-time stateless parties. Such protocols enable gaining from the security benefits provided by using a large community of participants where "mass corruption" of a large fraction of participants is considered unlikely, while keeping the computational and communication costs manageable. However, fully realizing and analyzing YOSO-style protocols has proven to be challenging: While different components have been defined and realized in various works, there is a dearth of protocols that have reasonable efficiency and enjoy full end to end security against adaptive adversaries.

The YOSO model separates the protocol design, specifying the short-lived responsibilities, from the mechanisms assigning these responsibilities to machines participating in the computation. These protocol designs must then be translated to run directly on the machines, while preserving security guarantees. We provide a versatile and modular framework for analyzing the security of YOSO-style protocols, and show how to use it to compile any protocol design that is secure against static corruptions of $t$ out of $c$ parties, into protocols that withstand adaptive corruption of $T$ out of $N$ machines (where $T/N$ is closely related to $t/c$, specifically when $t/c<0.5$, we tolerate $T/N \leq 0.29$) at overall communication cost that is comparable to that of the traditional protocol even when $c << N$.

Furthermore, we demonstrate how to minimize the use of costly non-committing encryption, thereby keeping the computational and communication overhead manageable even in practical terms, while still providing end to end security analysis. Combined with existing approaches for transforming stateful protocols into stateless ones while preserving static security (e.g. Gentry et al. 21, Kolby et al. 22), we obtain end to end security.

The BBS+ signature scheme is one of the most prominent solutions for realizing anonymous credentials. In particular, due to properties like selective disclosure and efficient protocols for creating and showing possession of credentials. In recent years, research in cryptography has increasingly focused on the distribution of cryptographic tasks to mitigate attack surfaces and remove single points of failure.

In this work, we present a threshold BBS+ protocol in the preprocessing model. Our protocol supports an arbitrary $t$-out-of-$n$ threshold and achieves non-interactive signing in the online phase. It relies on a new pseudorandom correlation-based offline protocol producing preprocessing material with sublinear communication complexity in the number of signatures. Both our offline and online protocols are actively secure under the Universal Composability framework. Finally, we estimate the concrete efficiency of our protocol, including an implementation of the online phase. The online protocol without network latency takes less than $15 ms$ for $t \leq 30$ and credentials sizes up to $10$. Further, our results indicate that the influence of $t$ on the online signing is insignificant, $< 6 \%$ for $t \leq 30$, and the overhead of the thresholdization occurs almost exclusively in the offline phase.

The random oracle model is an instrument used for proving that protocol has no structural flaws when settling with standard hash properties is impossible or fairly difficult. In practice, however, random oracles have to be instantiated with some specific hash functions, which are not random oracles. Hence, in the real world, an adversary has broader capabilities than considered in the random oracle proof — it can exploit the peculiarities of a specific hash function to achieve its goal. In a case when a hash function is based on some building block, one can go further and show that even if the adversary has access to that building block, the hash function still behaves like a random oracle under some assumptions made about the building block. Thereby, the protocol can be proved secure against more powerful adversaries under less complex assumptions. The indifferentiability notion formalizes that approach.

In this paper we study whether Streebog, a Russian standardized hash function, can instantiate a random oracle from that point of view. We prove that Streebog is indifferentiable from a random oracle under an ideal cipher assumption for the underlying block cipher.

The post-quantum digital signature scheme CRYSTALS-Dilithium has been recently selected by the NIST for standardization. Implementing CRYSTALS-Dilithium, and other post-quantum cryptography schemes, on embedded devices raises a new set of challenges, including ones related to performance in terms of speed and memory requirements, but also related to side-channel and fault injection attacks security. In this work, we investigated the latter and describe a differential fault attack on the randomized and deterministic versions of CRYSTALS-Dilithium. Notably, the attack requires a few instructions skips and is able to reduce the MLWE problem that Dilithium is based on to a smaller RLWE problem which can be practically solved with lattice reduction techniques. Accordingly, we demonstrated key recoveries using hints extracted on the secret keys from the same faulted signatures using the LWE with side-information framework introduced by Dachman-Soled et al. at CRYPTO’20. As a final contribution, we proposed algorithmic countermeasures against this attack and in particular showed that the second one can be parameterized to only induce a negligible overhead over the signature generation.

The analysis of real-life incidents has revealed that state-level efforts are made to camouflage the intentional flaws in the mathematical layer of an S-Box to exploit the information-theoretic properties, i.e., Kuznyechik. To extract and investigate the common features in the backdoored S-Box(es), this research thoroughly examines them from the perspective of 24 cryptanalytic attack vectors available in the open literature. We have debunked the earlier claims by the backdoor engineers that their designs are stealthy against statistical distinguishers. A backdoored architecture fulfils the notions of randomness but lacks the strength to resist sophisticated cryptanalytic attacks. Our analysis has revealed that during the backdoor insertion phase, a malicious designer compromises vital cryptographic properties, prominently the algebraic degree, differential trails, avalanche characteristics and leaving the open ground for hybrid attacks. It is observed that these mappings attain the upper bound of BCT, FBCT and DLCT, thus paving the way for hybrid attacks with high probability.

We present a simple and lightweight single-server sublinear private information retrieval scheme based on new techniques in hint construction and usage. Our scheme has small amortized response and close to optimal online response, which is only twice that of simply fetching the desired entry without privacy. For a 128 GB database with 64-byte entries, each query consumes only 117 KB of communication and 7.5 milliseconds of computation, amortized.

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.

Privacy-preserving payment systems face the difficult task of balancing privacy and accountability: on one hand, users should be able to transact privately and anonymously, on the other hand, no illegal activities should be tolerated. The challenging question of finding the right balance lies at the core of the research on accountable privacy that stipulates the use of cryptographic techniques for policy enforcement, but still allows an authority to revoke the anonymity of transactions whenever such an automatic enforcement is technically not supported. Current state-of-the-art systems are only able to enforce rather limited policies, such as spending or transaction limits, or assertions about participants, but are unable to enforce more complex policies that for example jointly evaluate both, the private credentials of sender and recipient-let alone to do this without an auditor in the loop during payment. This limits the cases where privacy revocation can be avoided as the method to fulfill regulations, which is unsatisfactory from a data-protection viewpoint and shows the need for cryptographic solutions that are able to elevate accountable privacy to a more fine-grained level.

In this work, we present such a solution. We show how to enforce complex policies while offering strong privacy and anonymity guarantees by enhancing the notion of policy-compliant signatures (PCS) introduced by Badertscher, Matt and Waldner (TCC'21). In more detail, we first define the notion of unlinkable PCS (ul-PCS) and show how this cryptographic primitive can be generically integrated with a wide range of systems including UTxO-based ledgers, privacy-preserving protocols like Monero or Zcash, and central-bank digital currencies. We give a generic construction for ul-PCS for any policy, and optimized constructions tailored for special policy classes, such as role-based policies and separable policies.

To bridge the gap between theory and practice, we provide prototype implementations for all our schemes. We give the first benchmarks for policy-compliant signatures in general, and demonstrate their feasibility for reasonably sized attribute sets for the special cases.

URL shorteners are a common online service that allows the shortening of a long URL (often a Google Maps URL or similar) into a much shorter one, to use for example on social media or in QR codes. However, URL shorteners are free to behave dishonestly: they can, for instance, map a short URL into a long URL honestly for one party, while redirecting some other party into a different malicious long URL for the same short URL.

DuckyZip is the first provably honest URL shortening service which cannot selectively provide different "long URLs" to different parties undetected. DuckyZip uses a combination of Verifiable Random Function (VRF) constructions and a smart contract in order to provide a URL shortening service with strong security guarantees: despite the transparency of the smart contract log, observers cannot feasibly create a mapping of all short URLs to long URLs that is faster than classical enumeration.

Although power LEDs have been integrated in various devices that perform cryptographic operations for decades, the cryptanalysis risk they pose has not yet been investigated. In this paper, we present optical cryptanalysis, a new form of cryptanalytic side-channel attack, in which secret keys are extracted by using a photodiode to measure the light emitted by a device’s power LED and analyzing subtle fluctuations in the light intensity during cryptographic operations. We analyze the optical leakage of power LEDs of various consumer devices and the factors that affect the optical SNR. We then demonstrate end-to-end optical cryptanalytic attacks against a range of consumer devices (smartphone, smartcard, and Raspberry Pi, along with their USB peripherals) and recover secret keys (RSA, ECDSA, SIKE) from prior and recent versions of popular cryptographic libraries (GnuPG, Libgcrypt, PQCrypto-SIDH) from a maximum distance of 25 meters

Most succinct arguments (SNARKs) are initially only proven knowledge sound (KS). We show that the commonly employed compilation strategy from polynomial interactive oracle proofs (PIOP) via polynomial commitments to knowledge sound SNARKS actually also achieves other desirable properties: weak unique response (WUR) and trapdoorless zero-knowledge (TLZK); and that together they imply simulation extractability (SIM-EXT).

The factoring of SIM-EXT into KS + WUR + TLZK is becoming a cornerstone of the analysis of non-malleable SNARK systems. We show how to prove WUR and TLZK for PIOP compiled SNARKs under mild falsifiable assumptions on the polynomial commitment scheme. This means that the analysis of knowledge soundness from PIOP properties that inherently relies on non-falsifiable or idealized assumption such as the algebraic group model (AGM) or generic group model (GGM) need not be repeated.

While the proof of WUR requires only mild assumptions on the PIOP, TLZK is a different matter. As perfectly hiding polynomial commitments sometimes come at a substantial performance premium, SNARK designers prefer to employ deterministic commitments with some leakage. This results in the need for a stronger zero-knowledge property for the PIOP.

The modularity of our approach implies that any analysis improvements, e.g. in terms of tightness, credibility of the knowledge assumption and model of the KS analysis, or the precision of capturing real-world optimizations for TLZK also benefits the SIM-EXT guarantees.

In this paper, we provide a systematic treatment for the batch arithmetic circuit satisfiability and evaluation problem. Building on the core idea which treats circuit inputs/outputs as a low-degree polynomials, we explore various interactive argument and proof schemes that can produce succinct proofs with short verification time. In particular, for the batch satisfiability problem, we provide a construction of succinct interactive argument of knowledge for generic log-space uniform circuits based on the bilinear pairing and common reference string assumption. Our argument has size in $O(poly(\lambda) \cdot (|\mathbf{w}| + d \log |C|))$, where $\lambda$ is the security parameter, $|\mathbf{w}|$ is the size of the witness, and $d$ and $|C|$ are the depth and size of the circuit, respectively. Note that the argument size is independent of the batch size. To the best of our knowledge, asymptotically it is the smallest among all known batch argument schemes that allow public verification. The batch satisfiablity problem simplifies to a batch evaluation problem when the circuit only takes in public inputs (i.e., no witness). For the evaluation problem, we construct statistically sound interactive proofs for various special yet highly important types of circuits, including linear circuits, and circuits representing sum of polynomials. Our proposed protocols are able to achieve proof sizes independent of the batch size. We also describe protocols optimized specifically for batch FFT and batch matrix multiplication which achieve desirable properties, including lower prover time and better composability. We believe these protocols are of interest in their own right and can be used as primitives in more complex applications.

We show that the key agreement scheme [IEEE Internet Things J., 9(12), 2022, 9918--9933] is flawed. In order to authenticate each other, all participants use message authentication code (MAC) to generate tags for exchanged data. But MAC is a cryptographic technique which requires that the sender and receiver share a symmetric key. The scheme tries to establish a new shared key by using an old shared key, which results in a vicious circle. To the best of our knowledge, it is the first time to discuss such a flaw in the related literatures.

We prove that the problem of decoding a quasi-cyclic code is NPhard, and the corresponding decision problem is NP-complete. Our proof is based on a new characterization of quasi-cyclic codes closely related to linear random codes. We also discuss the cryptographic significance of this result.

We design DiStefano: an efficient framework for generating private commitments over TLS-encrypted web traffic for a designated, untrusted third-party. DiStefano provides many improvements over previous TLS commitment systems, including: a modular security model that is applicable to TLS 1.3 traffic, and support for generating verifiable claims using applicable zero-knowledge systems; inherent 1-out-of-n privacy for the TLS server that the client communicates with; and various cryptographic optimisations to ensure fast online performance of the TLS session. We build an open-source implementation of DiStefano integrated into the BoringSSL cryptographic library, that is used within Chromium-based Internet browsers. We show that DiStefano is practical for committing to facts in arbitrary TLS traffic, with online times that are comparable with existing TLS 1.2 solutions. We also make improvements to certain cryptographic primitives used inside DiStefano, leading to 3x and 2x improvements in online computation time and bandwidth in specific situations.