International Association
for Cryptologic Research

We prove that for $n>1$ the map $\chi:\mathbb{F}_q^n \to \mathbb{F}_q^n$, defined by $y=\chi(x)$ with $y_i = x_i + x_{i+2}\cdot(1+x_{i+1})$ for $1\leq i \leq n$, is bijective if and only if $q=2$ and $n$ is odd, as it was conjectured by Schoone and Daemen in 2023.

High-performance and energy-efficient encryption engines have become crucial components in modern System-On-Chip (SoC) architectures across multiple platforms, including servers, desktops, mobile devices, and IoT edge devices. Alas, the secure operation of cryptographic engines faces a significant obstacle caused by information leakage through various side-channels. Adversaries can exploit statistical analysis techniques on measured (e.g.,) power and timing signatures generated during (e.g.,) encryption process to extract secret material. Countermeasures against such side-channel attacks often impose substantial power, area, and performance overheads. Consequently, designing side-channel secure encryption engines becomes a critical challenge when ensuring high-performance and energy-efficient operations. In this paper we will suggest a novel technique for low cost, high impact, easily scalable protection based on Adaptive Dynamic Voltage and Frequency Scaling (A-DVFS) capabilities in ultra-low-power (ULP) sub-threshold chips. We review the improvement of using integrated voltage regulators and DVFS, normally used for efficient power management, towards increasing side-channel resistance of encryption engines; Pushing known prior-art in the topic to ULP-regime. The hardware measurements were performed on PLS15 test-chip fabricated in ULP 40nm process going down from nominal voltage to 580 mV power-supply. Various results and detailed analysis is presented to demonstrate the impact of power management circuits on side-channel security, performance-impact and comparison to prior-art. Importantly, we highlight security sensitivities DVFS embeds in terms of software side-channels such as timing, and their mitigation with our proposed technique, successfully masking the time signature introduced by DVFS.

A list polynomial commitment scheme (LPC) is a polynomial commitment scheme with a relaxed binding property. Namely, in an LPC setting, a commitment to a function $f(X)$ can be opened to a list of low-degree polynomials close to $f(X)$ (w.r.t. the relative Hamming distance and over a domain $D$). The scheme also allows opening one of the polynomials of the list at an arbitrary point $x$ and convincing a verifier that one of the polynomials in the list evaluates to the purported value.

Vortex is a list polynomial commitment, obtained through a modification of Ligero (CCS 2017), inspired by the schemes of Brakedown (Crypto 2023), batch-FRI (FOCS 2020), and RedShift (CCS 2022). Concerning one application of Vortex, for a witness of size $N$, the messages between the prover and the verifier are of size $O(N^{1/2})$. Vortex is a core component of the SNARK used by the prover of Linea (Consensys). This paper provides a complete security analysis for Vortex. We use a general compiler to build an Argument of Knowledge (AoK) by combining our list polynomial commitment and a polynomial-IOP (PIOP).

The approach is similar to combining a PIOP with a polynomial commitment scheme and has a soundness loss only linear in the list size. This overcomes a previous limitation in the standard compiler from a generic PIOP and a list polynomial commitment scheme to an interactive argument of knowledge, which suffers from a soundness loss of $\mathcal{O}(|L|^r)$ (where $|L|$ is the list size and $r$ is the number of interactions between the prover and the verifier in the PIOP).

Threshold signatures improve both availability and security of digital signatures by splitting the signing key into $N$ shares handed out to different parties. Later on, any subset of at least $T$ parties can cooperate to produce a signature on a given message. While threshold signatures have been extensively studied in the pre-quantum setting, they remain sparse from quantum-resilient assumptions.

We present the first efficient lattice-based threshold signatures with signature size 13 KiB and communication cost 40 KiB per user, supporting a threshold size as large as 1024 signers. We provide an accompanying high performance implementation. The security of the scheme is based on the same assumptions as Dilithium, a signature recently selected by NIST for standardisation which, as far as we know, cannot easily be made threshold efficiently.

All operations used during signing are due to symmetric primitives and simple lattice operations; in particular our scheme does not need heavy tools such as threshold fully homomorphic encryption or homomorphic trapdoor commitments as in prior constructions. The key technical idea is to use one-time additive masks to mitigate the leakage of the partial signing keys through partial signatures.

Equivalence class signatures (EQS), introduced by Hanser and Slamanig (AC'14), sign vectors of elements from a bilinear group. Signatures can be ``adapted'', meaning that anyone can transform a signature on a vector to a (random) signature on any multiple of that vector. (Signatures thus authenticate equivalence classes.) A transformed signature/message pair is then indistinguishable from a random signature on a random message. EQS have been used to efficiently instantiate (delegatable) anonymous credentials, (round-optimal) blind signatures, ring and group signatures and anonymous tokens.

The original EQS construction (J.Crypto'19) is only proven in the generic group model, while the first construction from standard assumptions (PKC'18) only yields security guarantees insufficient for most applications. Two works (AC'19, PKC'22) propose applicable schemes which assume the existence of a common reference string for the anonymity notion. Their unforgeability is argued via a security proof from standard (or non-interactive) assumptions.

In this work we show that their security proof is flawed and explain the subtle issue.

Decentralized Storage Network (DSN) is an emerging technology that challenges traditional cloud-based storage systems by consolidating storage capacities from independent providers and coordinating to provide decentralized storage and retrieval services. However, current DSNs face several challenges associated with data privacy and efficiency of the proof systems. To address these issues, we propose FileDES (Decentralized Encrypted Storage), which incorporates three essential elements: privacy preservation, scalable storage proof, and batch verification. FileDES provides encrypted data storage while maintaining data availability, with a scalable Proof of Encrypted Storage (PoES) algorithm that is resilient to Sybil and Generation attacks. Additionally, we introduce a rollup-based batch verification approach to simultaneously verify multiple files using publicly verifiable succinct proofs. We conducted a comparative evaluation on FileDES, Filecoin, Storj and Sia under various conditions, including a WAN composed of up to 120 geographically dispersed nodes. Our protocol outperforms the others in terms of proof generation/verification efficiency, storage costs, and scalability.

Fully Homomorphic encryption (FHE) enables the computation of an arbitrary function over encrypted data without decrypting them. In particular, bootstrapping is a core building block of FHE which reduces the noise of a ciphertext thereby recovering the computational capability.

This paper introduces a new bootstrapping framework for the Fan-Vercuteren (FV) scheme, called the functional bootstrapping, providing more generic and advanced functionality than the ordinary bootstrapping method. More specifically, the functional bootstrapping allows us to evaluate an arbitrary function while removing the error of an input ciphertext. Therefore, we achieve better depth consumption and computational complexity as the evaluation of a circuit can be integrated as part of the functional bootstrapping procedure. In particular, our approach extends the functionality of FV since it is even applicable to functions between different plaintext spaces.

At the heart of our functional bootstrapping framework is a novel homomorphic Look-Up Table (LUT) evaluation method where we represent any LUT using only the operations supported by the FV scheme. Finally, we provide a proof-of-concept implementation and present benchmarks. In concrete examples, such as delta and sign functions, our functional bootstrapping takes about 46.5s or 171.4s for 9-bit or 13-bit plaintext modulus, respectively.

Embedded Multimedia Cards (eMMCs) provide a protected memory area called the Replay Protected Memory Block (RPMB). eMMCs are commonly used as storage media in modern smartphones. In order to protect these devices from unauthorized access, important data is stored in the RPMB area in an authenticated manner. Modification of the RPMB data requires a pre-shared authentication key. An unauthorized user cannot change the stored data. On modern devices, this pre-shared key is generated and used exclusively within a Trusted Execution Environment (TEE) preventing attackers from access. In this paper, we investigate how the authentication key for RPMB is programmed on the eMMC. We found that this key can be extracted directly from the target memory chip. Once obtained, the authentication key can be used to manipulate stored data. In addition, poor implementation of certain security features, aimed at preventing replay attacks using RPMB on the host system can be broken by an attacker. We show how the authentication key can be extracted and how it can be used to break the anti-rollback protection to enable data restoration even after a data wipe operation has been completed. Our findings show that non-secure RPMB implementations can enable forensic investigators to break security features implemented on modern smartphones.

Traitor-tracing systems allow identifying the users who contributed to building a rogue decoder in a broadcast environment. In a traditional traitor-tracing system, a key authority is responsible for generating the global public parameters and issuing secret keys to users. All security is lost if the \emph{key authority itself} is corrupt. This raises the question: Can we construct a traitor-tracing scheme, without a trusted authority?

In this work, we propose a new model for traitor-tracing systems where, instead of having a key authority, users could generate and register their own public keys. The public parameters are computed by aggregating all user public keys. Crucially, the aggregation process is \emph{public}, thus eliminating the need of any trusted authority. We present two new traitor-tracing systems in this model based on bilinear pairings. Our first scheme is proven adaptively secure in the generic group model. This scheme features a transparent setup, ciphertexts consisting of $6\sqrt{L}+4$ group elements, and a public tracing algorithm. Our second scheme supports a bounded collusion of traitors and is proven selectively secure in the standard model. Our main technical ingredients are new registered functional encryption (RFE) schemes for quadratic and linear functions which, prior to this work, were known only from indistinguishability obfuscation. To substantiate the practicality of our approach, we evaluate the performance a proof of concept implementation. For a group of $L = 1024$ users, encryption and decryption take roughly 50ms and 4ms, respectively, whereas a ciphertext is of size 6.7KB.

Pseudorandom Correlation Functions (PCFs) allow two parties, given correlated evaluation keys, to locally generate arbitrarily many pseudorandom correlated strings, e.g. Oblivious Transfer (OT) correlations, which can then be used by the two parties to jointly run secure computation protocols. In this work, we provide a novel and simple approach for constructing PCFs for OT correlation, by relying on constrained pseudorandom functions for a class of constraints containing a weak pseudorandom function (wPRF). We then show that tweaking the Naor-Reingold pseudorandom function and relying on low-complexity pseudorandom functions allow us to instantiate our paradigm. We further extend our ideas to obtain efficient public-key PCFs, which allow the distribution of correlated keys between parties to be non-interactive: each party can generate a pair of public/secret keys, and any pair of parties can locally derive their correlated evaluation key by combining their secret key with the other party's public key. In addition to these theoretical contributions, we detail various optimizations and provide concrete instantiations of our paradigm relying on the Boneh-Ishai-Passelègue-Sahai-Wu wPRF and the Goldreich-Applebaum-Raykov wPRF. Putting everything together, we obtain public-key PCFs with a throughput of 15k-40k OT/s, which is of a similar order of magnitude to the state-of-the-art interactive PCFs and about 4 orders of magnitude faster than state-of-the-art public-key PCFs. As a side result, we also show that public-key PCFs can serve as a building block to construct reusable designated-verifier non-interactive zero-knowledge proofs (DV-NIZK) for NP. Combined with our instantiations, this yields simple and efficient reusable DV-NIZKs for NP in pairing-free groups.

We are looking for a talented and motivated engineer who will contribute to building the cryptographic infrastructure of our Web 3.0-enabled blockchain ecosystem. You will be involved in the design and implementation of blockchain scaling solutions, primarily based on zero-knowledge cryptography, with the aim of dramatically reducing the costs that blockchain operators incur when deploying their products. Our international team works in a stimulating and innovative environment, where technical expertise and experience contribute to the development of cutting-edge blockchain technology. You will be joining a small, deeply driven team of highly technical minds in a culture of openness, pragmatism, and ownership of challenging problems that span software engineering, systems design, cryptography, and computing.

What You’ll Own

• Design and implementation of blockchain-based cryptographic solutions leveraging modern cryptography (ZK, MPC, FHE).
• Assume technical responsibility of novel systems while identifying areas for innovative research and development.
• Writing reusable, testable, and efficient code with a focus on best practices and security.
• Help shape the future of the company where you will be intimately involved in the strategic decision making process and immediately see the impact of your contributions.
• Attend conferences and find opportunities in the on-chain ecosystem.

Closing date for applications:

Contact: People & Talent Team - recruiting@horizenlabs.io

More information: https://boards.greenhouse.io/horizenlabs/jobs/5075393004

We present a Registered Functional Encryption (RFE) scheme for inner product and a RFE scheme for quadratic functions based on pairings and relying on the Matrix Decision Diffie-Hellman (MDDH) assumption and bilateral MDDH assumption. Previously, RFE is only known to be constructed from indistinguishability obfuscation (iO) in Francati-Friolo-Maitra-Malavolta-Rahimi-Venturi [Asiacrypt '23].

It has been shown that post-quantum key exchange and authentication with ML-KEM and ML-DSA, NIST’s postquantum algorithm picks, will have an impact on TLS 1.3 performance used in the Web or other applications. Studies so far have focused on the overhead of quantum-resistant algorithms on TLS time-to-first-byte (handshake time). Although these works have been important in quantifying the slowdown in connection establishment, they do not capture the full picture regarding real-world TLS 1.3 connections which carry sizable amounts of data. Intuitively, the introduction of an extra 10KB of ML-KEM and ML-DSA exchanges in the connection negotiation will inflate the connection establishment time proportionally more than it will increase the total connection time of a Web connection carrying 200KB of data. In this work, we quantify the impact of ML-KEM and ML-DSA on typical TLS 1.3 connections which transfer a few hundreds of KB from the server to the client. We study the slowdown in the time-to-last-byte of postquantum connections under normal network conditions and in more unstable environments with high packet delay variability and loss probabilities. We show that the impact of ML-KEM and ML-DSA on the TLS 1.3 time-to-last-byte under stable network conditions is lower than the impact on the time-to-first-byte and diminishes as the transferred data increases. The time-to-last-byte increase stays below 5% for high-bandwidth, stable networks. It goes from 32% increase of the time-to-first-byte to under 15% increase of the time-to-last-byte when transferring 50KiB of data or more under low-bandwidth, stable network conditions. Even when congestion control affects connection establishment, the additional slowdown drops below 10% as the connection data increases to 200KiB. We also show that connections under lossy or volatile network conditions could see higher impact from post-quantum handshakes, but these connections’ time-to-lastbyte increase still drops as the transferred data increases. Finally, we show that such connections are already significantly slow and volatile regardless of the TLS handshake.

Over the past few decades, we have seen a proliferation of advanced cryptographic primitives with lossy or homomorphic properties built from various assumptions such as Quadratic Residuosity, Decisional Diffie-Hellman, and Learning with Errors. These primitives imply hard problems in the complexity class $\mathcal{SZK}$ (statistical zero-knowledge); as a consequence, they can only be based on assumptions that are broken in $\mathcal{BPP}^{\mathcal{SZK}}$. This poses a barrier for building advanced primitives from code-based assumptions, as the only known such assumption is Learning Parity with Noise (LPN) with an extremely low noise rate $\frac{\log^2 n}{n}$, which is broken in quasi-polynomial time.

In this work, we propose a new code-based assumption: Dense-Sparse LPN, that falls in the complexity class $\mathcal{BPP}^{\mathcal{SZK}}$ and is conjectured to be secure against subexponential time adversaries. Our assumption is a variant of LPN that is inspired by McEliece's cryptosystem and random $k\mbox{-}$XOR in average-case complexity. Roughly, the assumption states that \[(\mathbf{T}\, \mathbf{M}, \mathbf{s} \,\mathbf{T}\, \mathbf{M} + \mathbf{e}) \quad \text{is indistinguishable from}\quad (\mathbf{T} \,\mathbf{M}, \mathbf{u}),\] for a random (dense) matrix $\mathbf{T}$, random sparse matrix $\mathbf{M}$, and sparse noise vector $\mathbf{e}$ drawn from the Bernoulli distribution with inverse polynomial noise probability.

We leverage our assumption to build lossy trapdoor functions (Peikert-Waters STOC 08). This gives the first post-quantum alternative to the lattice-based construction in the original paper. Lossy trapdoor functions, being a fundamental cryptographic tool, are known to enable a broad spectrum of both lossy and non-lossy cryptographic primitives; our construction thus implies these primitives in a generic manner. In particular, we achieve collision-resistant hash functions with plausible subexponential security, improving over a prior construction from LPN with noise rate $\frac{\log^2 n}{n}$ that is only quasi-polynomially secure.

In response to the evolving landscape of quantum computing and the heightened vulnerabilities in classical cryptographic systems, our paper introduces a comprehensive cryptographic framework. Building upon the pioneering work of Kuang et al., we present a unification of two innovative primitives: the Quantum Permutation Pad (QPP) for symmetric key encryption and the Homomorphic Polynomial Public Key (HPPK) for Key Encapsulation Mechanism (KEM) and Digital Signatures (DS). By harnessing matrix representations of the Galois Permutation Group and inheriting its bijective and non-commutative properties, QPP achieves quantum-secure symmetric key encryption, seamlessly extending Shannon’s perfect secrecy to both classical and quantum-native systems. Simultaneously, HPPK, free of NP-hard problems, relies on the security of symmetric encryption for the plain public key. This is accomplished by concealing the mathematical structure through arithmetic representations or modular multiplicative operators (arithmetic QPP) of the Galois Permutation Group over hidden rings, utilizing their partial homomorphic properties. This ensures secure computation on encrypted data during secret encapsulations, thereby enhancing the security of the plain public key. The integration of KEM and DS within HPPK cryptography results in compact key, cipher, and signature sizes, showcasing exceptional performance. This paper organically unifies QPP and HPPK under the Galois Permutation Group, marking a significant advance in laying the groundwork for quantum-resistant cryptographic protocols. Our contribution propels the development of secure communication systems in the era of quantum computing.

We prove that the seminal KZG polynomial commitment scheme (PCS) is black-box extractable under a simple falsifiable assumption ARSDH. To create an interactive argument, we construct a compiler that combines a black-box extractable non-interactive PCS and a polynomial IOP (PIOP). The compiler incurs a minor cost per every committed polynomial. Applying the Fiat-Shamir transformation, we obtain slightly less efficient variants of well-known PIOP-based zk-SNARKs, such as Plonk, that are knowledge-sound in the ROM under the ARSDH assumption. Importantly, there is no need for idealized group models or knowledge assumptions. This results in the first known zk-SNARKs in the ROM from falsifiable assumptions with both an efficient prover and constant-size argument.

BGV and BFV are among the most widely used fully homomorphic encryption (FHE) schemes, supporting evaluations over a finite field. To evaluate a circuit with arbitrary depth, bootstrapping is needed. However, despite the recent progress, bootstrapping of BGV/BFV still remains relatively impractical, compared to other FHE schemes.

In this work, we inspect the BGV/BFV bootstrapping procedure from a different angle. We provide a generalized bootstrapping definition that relaxes the correctness requirement of regular bootstrapping, allowing constructions that support only certain kinds of circuits with arbitrary depth. In addition, our definition captures a form of functional bootstrapping. In other words, the output encrypts a function evaluation of the input instead of the input itself. Under this new definition, we provide a bootstrapping procedure supporting different types of functions. Our construction is 1-2 orders of magnitude faster than the state-of-the-art BGV/BFV bootstrapping algorithms, depending on the evaluated function. Of independent interest, we show that our technique can be used to improve the batched FHEW/TFHE bootstrapping construction introduced by Liu and Wang (Asiacrypt 2023). Our optimization provides a speed-up of 6x in latency and 3x in throughput for batched binary gate bootstrapping and a plaintext-space-dependent speed-up for batched functional bootstrapping with plaintext space smaller than $\mathbb{Z}_{512}$.

The computation of step functions over encrypted data is an essential issue in homomorphic encryption due to its fundamental application in privacy-preserving computing. However, an effective method for homomorphically computing general step functions remains elusive in cryptography. This paper proposes two polynomial approximation methods for general step functions to tackle this problem. The first method leverages the fact that any step function can be expressed as a linear combination of shifted sign functions. This connection enables the homomorphic evaluation of any step function using known polynomial approximations of the sign function. The second method boosts computational efficiency by employing a composite polynomial approximation strategy. We present a systematic approach to construct a composite polynomial $f_k \circ f_{k-1} \circ \cdots \circ f_1$ that increasingly approximates the step function as $k$ increases. This method utilizes an adaptive linear programming approach that we developed to optimize the approximation effect of $f_i$ while maintaining the degree and coefficients bounded. We demonstrate the effectiveness of these two methods by applying them to typical step functions such as the round function and encrypted data bucketing, implemented in the HEAAN homomorphic encryption library. Experimental results validate that our methods can effectively address the homomorphic computation of step functions.

Side-Channel Analysis (SCA) is critical in evaluating the security of cryptographic implementations. The search for hyperparameters poses a significant challenge, especially when resources are limited. In this work, we explore the efficacy of a multifidelity optimization technique known as BOHB in SCA. In addition, we proposed a new objective function called $ge_{+ntge}$, which could be incorporated into any Bayesian Optimization used in SCA. We show the capabilities of both BOHB and $ge_{+ntge}$ on four different public datasets. Specifically, BOHB could obtain the least number of traces in CTF2018 when trained in the Hamming weight and identity leakage model. Notably, this marks the first reported successful recovery of the key for the identity leakage model in CTF2018.

Kyber KEM, the NIST selected PQC standard for Public Key Encryption and Key Encapsulation Mechanisms (KEMs) has been subjected to a variety of side-channel attacks, through the course of the NIST PQC standardization process. However, all these attacks targeting the decapsulation procedure of Kyber KEM either require knowledge of the ciphertexts or require to control the value of ciphertexts for key recovery. However, there are no known attacks in a blind setting, where the attacker does not have access to the ciphertexts. While blind side-channel attacks are known for symmetric key cryptographic schemes, we are not aware of such attacks for Kyber KEM. In this paper, we fill this gap by proposing the first blind side-channel attack on Kyber KEM. We target leakage of the pointwise multiplication operation in the decryption procedure to carry out practical blind side-channel attacks resulting in full key recovery. We perform practical validation of our attack using power side-channel from the reference implementation of Kyber KEM taken from the pqm4 library, implemented on the ARM Cortex-M4 microcontroller. Our experiments clearly indicate the feasibility of our proposed attack in recovering the full key in only a few hundred to few thousand traces, in the presence of a suitably accurate Hamming Weight (HW) classifier.