International Association
for Cryptologic Research

Distributed Point Function (DPF) provides a way for a dealer to split a point function $f_{\alpha, \beta}$ into multiple succinctly described function-shares, where the function $f_{\alpha, \beta}$ for a special input $\alpha$, returns a special output value $\beta$, and returns a fixed value $0$ otherwise. As the security requirement, any strict subset of the function-shares reveals nothing about the function $f_{\alpha,\beta}$. However, each function-share can be individually evaluated on the common input $x$, and these evaluation results can then be merged together to reconstruct the value $f_{\alpha, \beta}(x)$.

Recently, Servan-Schreiber et al. (S&P 2023) investigate the access control problem for DPF; namely, the DPF evaluators can ensure that the DPF dealer is authorized to share the given function with privacy assurance. In this work, we revisit this problem, introducing a new notion called DPF with constraints; meanwhile, we identify that there exists a subtle flaw in their privacy definition as well as a soundness issue in one of their proposed schemes due to the lack of validation of the special output value $\beta$. Next, we show how to reduce both the storage size of the constraint representation and the server's computational overhead from $O(N)$ to $O(\log N)$, where $N$ is the number of authorized function sets. In addition, we show how to achieve fine-grained private access control, that is, the wildcard-style constraint for the choice of the special output $\beta$. Our benchmarks show that the amortized running time of our logarithmic storage scheme is $2\times$ - $3\times$ faster than the state-of-the-art when $N=2^{15}$. Furthermore, we provide the first impossibility and feasibility results of the DPF with constraints where the evaluators do not need to communicate with each other.

A common drawback of secure vector summation protocols in the single-server model is that they impose at least one synchronization point between all clients contributing to the aggregation. This results in clients waiting on each other to advance through the rounds of the protocol, leading to large latency even if the protocol is computationally efficient. In this paper we propose protocols in the single-server model where clients contributing data to the aggregation send a single message to the server in an asynchronous fashion, i.e., without the need for synchronizing their reporting time with any other clients. Our approach is based on a committee of parties, called decryptors, that aid in the computation. Decryptors run a setup phase before data collection starts, and a decryption phase once it ends. Unlike existing committee-based protocols such as Flamingo (S&P 2023), the cost for committee members can be made sub-linear in the number of clients, and does not depend on the size of the input data. Our experimental evaluation shows that our protocol, even while enabling asynchronous client contributions,is competitive with the state of the art protocols that do not have that feature in both computation and communication.

Nair and Song (USENIX 2023) introduce the concept of a Multi-Factor Key Derivation Function (MFKDF), along with constructions and a security analysis. MFKDF integrates dynamic authentication factors, such as HOTP and hardware tokens, into password-based key derivation. The aim is to improve the security of password-derived keys, which can then be used for encryption or as an alternative to multi-factor authentication. The authors claim an exponential security improvement compared to traditional password-based key derivation functions (PBKDF).

We show that the MFKDF constructions proposed by Nair and Song fall short of the stated security goals. Underspecified cryptographic primitives and the lack of integrity of the MFKDF state lead to several attacks, ranging from full key recovery when an HOTP factor is compromised, to bypassing factors entirely or severely reducing their entropy. We reflect on the different threat models of key-derivation and authentication, and conclude that MFKDF is always weaker than plain PBKDF and multi-factor authentication in each setting.

In this work we first present an explicit forking lemma that distills the information-theoretic essence of the high-moment technique introduced by Rotem and Segev (CRYPTO '21), who analyzed the security of identification protocols and Fiat-Shamir signature schemes. Whereas the technique of Rotem and Segev was particularly geared towards two specific cryptographic primitives, we present a stand-alone probabilistic lower bound, which does not involve any underlying primitive or idealized model. The key difference between our lemma and previous ones is that instead of focusing on the tradeoff between the worst-case or expected running time of the resulting forking algorithm and its success probability, we focus on the tradeoff between higher moments of its running time and its success probability. Equipped with our lemma, we then establish concrete security bounds for the BN and BLS multi-signature schemes that are significantly tighter than the concrete security bounds established by Bellare and Neven (CCS '06) and Boneh, Drijvers and Neven (ASIACRYPT '18), respectively. Our analysis does not limit adversaries to any idealized algebraic model, such as the algebraic group model in which all algorithms are assumed to provide an algebraic justification for each group element they produce. Our bounds are derived in the random-oracle model based on the standard-model second-moment hardness of the discrete logarithm problem (for the BN scheme) and the computational co-Diffie-Hellman problem (for the BLS scheme). Such second-moment assumptions, asking that the success probability of any algorithm in solving the underlying computational problems is dominated by the second moment of the algorithm's running time, are particularly plausible in any group where no better-than-generic algorithms are currently known.

We construct an adaptively-sound succinct non-interactive argument (SNARG) for NP in the CRS model from sub-exponentially-secure indistinguishability obfuscation ($i\mathcal{O}$) and sub-exponentially-secure one-way functions. Previously, Waters and Wu (STOC 2024), and subsequently, Waters and Zhandry (CRYPTO 2024) showed how to construct adaptively-sound SNARGs for NP by relying on sub-exponentially-secure indistinguishability obfuscation, one-way functions, and an additional algebraic assumption (i.e., discrete log, factoring, or learning with errors). In this work, we show that no additional algebraic assumption is needed and vanilla (sub-exponentially-secure) one-way functions already suffice in combination with $i\mathcal{O}$.

We first give a direct construction of an adaptively-sound SNARG for NP assuming (sub-exponentially-secure) $i\mathcal{O}$ and an injective one-way function. Then, we show that it suffices to have an injective one-way function that has an inefficient sampler (i.e., sampling a challenge for the one-way function requires super-polynomial time). Because we rely on the existence of injective one-way functions only in the security proof and not in the actual construction, having an inefficient sampling procedure does not impact correctness. We then show that injective one-way functions with an inefficient sampler can be built generically from any vanilla one-way function. Our approach may be independently useful in other settings to replace injective one-way functions with standard one-way functions in applications of $i\mathcal{O}$.

Software based cryptographic implementations provide flexibility but they face performance limitations. In contrast, hardware based cryptographic accelerators utilize application-specific customization to provide real-time security solutions. Cryptographic instruction-set extensions (CISE) combine the advantages of both hardware and software based solutions to provide higher performance combined with the flexibility of atomic-level cryptographic operations. While CISE is widely used to develop security solutions, side-channel analysis of CISE-based devices is in its infancy. Specifically, it is important to evaluate whether the power usage and electromagnetic emissions of CISE-based devices have any correlation with its internal operations, which an adversary can exploit to deduce cryptographic secrets. In this paper, we propose a test vector leakage assessment framework to evaluate the pre-silicon prototypes at the early stages of the design life-cycle. Specifically, we first identify functional units with the potential for leaking information through power side-channel signatures and then evaluate them on system prototypes by generating the necessary firmware to maximize the side-channel signature. Our experimental results on two RISC-V based cryptographic extensions, RISCV-CRYPTO and XCRYPTO, demonstrated that seven out of eight prototype AES- and SHA-related functional units are vulnerable to leaking cryptographic secrets through their power side-channel signature even in full system mode with a statistical significance of $\alpha = 0.05$.

Fully homomorphic signatures are a significant strengthening of digital signatures, enabling computations on \emph{secretly} signed data. Today, we have multiple approaches to design fully homomorphic signatures such as from lattices, or succinct functional commitments, or indistinguishability obfuscation, or mutable batch arguments. Unfortunately, all existing constructions for homomorphic signatures suffer from one or more limitations. We do not have homomorphic signatures with features such as multi-hop evaluation, context hiding, and fast amortized verification, while relying on standard falsifiable assumptions.

In this work, we design homomorphic signatures satisfying all above properties. We construct homomorphic signatures for polynomial-sized circuits from a variety of standard assumptions such as sub-exponential DDH, standard pairing-based assumptions, or learning with errors. We also discuss how our constructions can be easily extended to the multi-key setting.

We revisit the problem of private information retrieval (PIR) in the shuffle model, where queries can be made anonymously by multiple clients. We present the first single-server PIR protocol in this model that has sublinear per-client communication and information-theoretic security. Moreover, following one-time preprocessing on the server side, our protocol only requires sublinear per-client computation. Concretely, for every $\gamma>0$, the protocol has $O(n^{\gamma})$ communication and computation costs per (stateless) client, with $1/\text{poly}(n)$ statistical security, assuming that a size-$n$ database is simultaneously accessed by $\text{poly}(n)$ clients. This should be contrasted with the recent breakthrough result of Lin, Mook, and Wichs (STOC 2023) on doubly efficient PIR in the standard model, which is (inherently) limited to computational security.

We consider constructions that combine outputs of a single permutation $\pi:\{0,1\}^n \rightarrow \{0,1\}^n$ using a public function. These are popular constructions for achieving security beyond the birthday bound when implementing a pseudorandom function using a block cipher (i.e., a pseudorandom permutation). One of the best-known constructions (denoted SXoP$[2,n]$) XORs the outputs of 2 domain-separated calls to $\pi$.

Modeling $\pi$ as a uniformly chosen permutation, several previous works proved a tight information-theoretic indistinguishability bound for SXoP$[2,n]$ of about $q/2^{n}$, where $q$ is the number of queries. On the other hand, tight bounds are unknown for the generalized variant (denoted SXoP$[r,n]$) which XORs the outputs of $r>2$ domain-separated calls to a uniform permutation.

In this paper, we obtain two results. Our first result improves the known bounds for SXoP$[r,n]$ for all (constant) $r \geq 3$ (assuming $q \leq O(2^n/r)$ is not too large) in both the single-user and multi-user settings. In particular, for $q=3$, our bound is about $\sqrt{u}q_{\max}/2^{2.5n}$ (where $u$ is the number of users and $q_{\max}$ is the maximal number of queries per user), improving the best-known previous result by a factor of at least $2^n$.

For odd $r$, our bounds are tight for $q > 2^{n/2}$, as they match known attacks. For even $r$, we prove that our single-user bounds are tight by providing matching attacks.

Our second and main result is divided into two parts. First, we devise a family of constructions that output $n$ bits by efficiently combining outputs of 2 calls to a permutation on $\{0,1\}^n$, and achieve multi-user security of about $\sqrt{u} q_{\max}/2^{1.5n}$. Then, inspired by the CENC construction of Iwata [FSE'06], we further extend this family to output $2n$ bits by efficiently combining outputs of 3 calls to a permutation on $\{0,1\}^n$. The extended construction has similar multi-user security of $\sqrt{u} q_{\max}/2^{1.5n}$.

The new single-user ($u=1$) bounds of $q/2^{1.5n}$ for both families should be contrasted with the previously best-known bounds of $q/2^n$, obtained by the comparable constructions of SXoP$[2,n]$ and CENC.

All of our bounds are proved by Fourier analysis, extending the provable security toolkit in this domain in multiple ways.

Message Authentication Codes (MACs) are ubiquitous primitives deployed in multiple flavors through standards such as HMAC, CMAC, GMAC, LightMAC, and many others. Its versatility makes it an essential building block in applications necessitating message authentication and integrity checks, in authentication protocols, authenticated encryption schemes, or as a pseudorandom or key derivation function. Its usage in this variety of settings makes it susceptible to a broad range of attack scenarios. The latest attack trends leverage a lack of commitment or context-discovery security in AEAD schemes and these attacks are mainly due to the weakness in the underlying MAC part. However, these new attack models have been scarcely analyzed for MACs themselves. This paper provides a thorough treatment of MACs committing and context-discovery security. We reveal that commitment and context-discovery security of MACs have their own interest by highlighting real-world vulnerable scenarios. We formalize the required security notions for MACs, and analyze the security of standardized MACs for these notions. Additionally, as a constructive application, we analyze generic AEAD composition and provide simple and efficient ways to build committing and context-discovery secure AEADs.

he current cryptographic frameworks like RSA, ECC, and AES are potentially under quantum threat. Quantum cryptographic and post-quantum cryptography are being extensively researched for securing future information. The quantum computer and quantum algorithms are still in the early developmental stage and thus lack scalability for practical application. As a result of these challenges, most researched PQC methods are lattice-based, code-based, ECC isogeny, hash-based, and multivariate crypto schemes. In this paper, we explore other mathematical topics such as stereographic projection, Mobius transformation, change of basis, Apollonian circle, Binary Quadratic form equivalence, Gauss composition law, and its conjunctions. It fulfills preliminary conditions like bijection, primality, and np-hard problems, and the feasibility of one-way functions along with its interconnection. Thus allowing the exploration of new realms of mathematics for the development of secure protocols for future communication

Vote-by-mail is increasingly used in Europe and worldwide for government elections. Nevertheless, very few attempts have been made towards the design of verifiable vote-by-mail, and none of them come with a rigorous security analysis. Furthermore, the ballot privacy of the currently deployed (non-verifiable) vote-by-mail systems relies on procedural means that a single malicious operator can bypass.

We propose a verifiable vote-by-mail system that can accommodate the constraints of many of the large ballots that are common in Europe. Verifiability and privacy hold unless multiple system components collude to cheat on top of the postal channel. These security notions are expressed and analyzed in the simplified UC security framework.

Our vote-by-mail system only makes limited requirements on the voters: voters can verify their vote by copying and comparing short strings and verifying the computation of a single hash on a short input, and they can vote normally if they want to ignore the verification steps completely. Our system also relies on common cryptographic components, all available in the ElectionGuard verifiable voting SDK for instance, which limits the risks of errors in the implementation of the cryptographic aspects of the system.

We present a novel approach to small area and low-latency first-order masking in hardware. The core idea is to separate the processing of shares in time in order to achieve non-completeness. Resulting circuits are proven first-order glitch-extended PINI secure. This means the method can be straightforwardly applied to mask arbitrary functions without constraints which the designer must take care of. Furthermore we show that an implementation can benefit from optimization through EDA tools without sacrificing security. We provide concrete results of several case studies. Our low-latency implementation of a complete PRINCE core shows a 32% area improvement (44% with optimization) over the state-of-the-art. Our PRINCE S-Box passes formal verification with a tool and the complete core on FPGA shows no first-order leakage in TVLA with 100 million traces. Our low-latency implementation of the AES S-Box costs roughly one third (one quarter with optimization) of the area of state-of-the-art implementations. It shows no first-order leakage in TVLA with 250 million traces.

We revisit the question of relating the elliptic curve discrete logarithm problem (ECDLP) between ordinary elliptic curves over finite fields with the same number of points. This problem was considered in 1999 by Galbraith and in 2005 by Jao, Miller, and Venkatesan. We apply recent results from isogeny cryptography and cryptanalysis, especially the Kani construction, to this problem. We improve the worst case bound in Galbraith's 1999 paper from $\tilde{O}( q^{1.5} )$ to (heuristically) $\tilde{O}( q^{0.4} )$ operations.

The two cases of main interest for discrete logarithm cryptography are random curves (flat volcanoes) and pairing-based crypto (tall volcanoes with crater of constant or polynomial size). In both cases we show a rigorous $\tO( q^{1/4})$ algorithm to compute an isogeny between any two curves in the isogeny class. We stress that this paper is motivated by pre-quantum elliptic curve cryptography using ordinary elliptic curves, which is not yet obsolete.

This paper introduces and develops the concept of ``ticketing'', through which atomic broadcasts are orchestrated by nodes in a distributed system. The paper studies different ticketing regimes that allow parallelism, yet prevent slow nodes from hampering overall progress. It introduces a hybrid scheme which combines managed and unmanaged ticketing regimes, striking a balance between adaptivity and resilience. The performance evaluation demonstrates how managed and unmanaged ticketing regimes benefit throughput in systems with heterogeneous resources both in static and dynamic scenarios, with the managed ticketing regime performing better among the two as it adapts better. Finally, it demonstrates how using the hybrid ticketing regime performance can enjoy both the adaptivity of the managed regime and the liveness guarantees of the unmanaged regime.

Private Set Union (PSU) protocol allows parties, each holding an input set, to jointly compute the union of the sets without revealing anything else. In the literature, scalable PSU protocols follow the “split-execute-assemble” paradigm (Kolesnikov et al., ASIACRYPT 2019); in addition, those fast protocols often use Oblivious Transfer as building blocks. Kolesnikov et al. (ASIACRYPT 2019) and Jia et al. (USENIX Security 2022), pointed out that certain security issues can be introduced in the “split-execute-assemble” paradigm. In this work, surprisingly, we observe that the typical way of invoking Oblivious Transfer also causes unnecessary leakage, and only the PSU protocols based on additively homomorphic encryption (AHE) can avoid the leakage. However, the AHE-based PSU protocols are far from being practical.

To bridge the gap, we also design a new PSU protocol that can avoid the unnecessary leakage. Unlike the AHE-based PSU protocols, our new construction only relies on symmetric-key operations other than base OTs, thereby being much more scalable. The experimental results demonstrate that our protocol can obtain at least 873.74× speedup over the best-performing AHE-based scheme. Moreover, our performance is comparable to that of the state-of-the-art PSU protocol (Chen et al., USENIX Security 2023), which also suffers from the unnecessary leakage.

A number of existing cryptosystems use the well-known LSAG signature and its extensions. This article presents a simple logarithmic-size signature scheme LS-LSAG which, despite a radical reduction in size, retains the basic code block of the LSAG signature. Therefore, substituting LS-LSAG for LSAG requires minimal changes to almost any existing coded LSAG extension, making it logarithmic instead of linear.

We show that the smallness of message spaces can be used as a checksum allowing to hedge against CCA1 attacks in additively homomorphic encryption schemes. We first show that the additively homomorphic variant of Damgård's Elgamal provides IND-CCA1 security under the standard DDH assumption. Earlier proofs either required non-standard assumptions or only applied to hybrid versions of Damgård's Elgamal, which are not additively homomorphic. Our security proof builds on hash proof systems and exploits the fact that encrypted messages must be contained in a polynomial-size interval in order to enable decryption. With $3$ group elements per ciphertext, this positions Damgård's Elgamal as the most efficient/compact DDH-based additively homomorphic CCA1 cryptosystem. Under the same assumption, the best candidate so far was the lite Cramer-Shoup cryptosystem, where ciphertexts consist of $4$ group elements. We extend this observation to build an IND-CCA1 variant of the Boneh-Goh-Nissim encryption scheme, which allows evaluating 2-DNF formulas on encrypted data. By computing tensor products of Damgård's Elgamal ciphertexts, we obtain product ciphertexts consisting of $9$ group elements (instead of $16$ elements if we were tensoring lite Cramer-Shoup ciphertexts) in the target group of a bilinear map. Using similar ideas, we also obtain a CCA1 variant of the Elgamal-Paillier cryptosystem by forcing $\lambda$ plaintext bits to be zeroes, which yields CCA1 security almost for free. In particular, the message space remains exponentially large and ciphertexts are as short as in the IND-CPA scheme. We finally adapt the technique to the Castagnos-Laguillaumie system.

In this work, we propose a construction for $ Multi~Input~Inner ~Product ~Encryption$ (MIPFE) that can handle vectors of variable length in different encryption slots. This construction is the first of its kind, as all existing MIPFE schemes allow only equal length vectors. The scheme is constructed in the private key setting, providing privacy for both message as well as the function, thereby achieving the so-called $full-hiding$ security. Our MIPFE scheme uses bilinear groups of prime order and achieves security under well studied cryptographic assumptions, namely, the symmetric external Diffie-Hellman assumption.

We analyse the cryptographic protocols underlying Delta Chat, a decentralised messaging application which uses e-mail infrastructure for message delivery. It provides end-to-end encryption by implementing the Autocrypt standard and the SecureJoin protocols, both making use of the OpenPGP standard. Delta Chat's adoption by categories of high-risk users such as journalists and activists, but also more generally users in regions affected by Internet censorship, makes it a target for powerful adversaries. Yet, the security of its protocols has not been studied to date. We describe five new attacks on Delta Chat in its own threat model, exploiting cross-protocol interactions between its implementation of SecureJoin and Autocrypt, as well as bugs in rPGP, its OpenPGP library. The findings have been disclosed to the Delta Chat team, who implemented fixes.