International Association
for Cryptologic Research

The existence of finite maps from hyperelliptic curves to elliptic curves has been studied for more than a century and their existence has been related to isogenies between a product of elliptic curves and their Jacobian surface. Such finite covers, sometimes named gluing maps have recently appeared in cryptography in the context of genus 2 isogenies and more spectacularly, in the work of Castryck and Decru about the cryptanalysis of SIKE. Computation methods include the use of algebraic theta functions or correspondences such as Richelot isogenies or degree 3 analogues. This article aims at giving geometric meaning to the gluing morphism from a product of elliptic curves $E_1 \times E_2$ to a genus 2 Jacobian when it is a degree (3, 3) isogeny. An explicit (uni)versal family and an algorithm were previously provided in the literature (Bröker-Howe-Lauter-Stevenhagen) and a similar special case was studied by Kuwata. We provide an alternative construction of the universal family using concepts from classical algebraic and projective geometry. The family of genus 2 curves which are triple covers of 2 elliptic curves with a level 3 structure arises as a correspondence given by a polarity relation. The construction does not provide closed formulas for the final curves equations and morphisms. However, an alternative algorithm based on the geometric construction is proposed for computation on finite fields. It relies only on elementary operations and a limited number of square roots and computes the equation of the genus 2 curves and morphisms in all cases.

\par Topology-hiding computation (THC) enables $n$ parties to perform a secure multiparty computation (MPC) protocol in an incomplete communication graph while keeping the communication graph hidden. The work of Akavia et al. (CRYPTO 2017 and JoC 2020) shown that THC is feasible for any graph. In this work, we focus on the efficiency of THC and give improvements for various tasks including broadcast, sum and general computation. We mainly consider THC on undirected cycles, but we also give two results for THC on general graphs. All of our results are derived in the presence of a passive adversary statically corrupting any number of parties.

\par In the undirected cycles, the state-of-the-art topology-hiding broadcast (THB) protocol is the Akavia-Moran (AM) protocol of Akavia et al. (EUROCRYPT 2017). We give an optimization for the AM protocol such that the communication cost of broadcasting $O(\kappa)$ bits is reduced from $O(n^2\kappa^2)$ bits to $O(n^2\kappa)$ bits. We also consider the sum and general computation functionalities. Previous to our work, the only THC protocols realizing the sum and general computation functionalities are constructed by using THB to simulate point-to-point channels in an MPC protocol realizing the sum and general computation functionalities, respectively. By allowing the parties to know the exact value of the number of the parties (the AM protocol and our optimization only assume the parties know an upper bound of the number of the parties), we can derive more efficient THC protocols realizing these two functionalities. As a result, comparing with previous works, we reduce the communication cost by a factor of $O(n\kappa)$ for both the sum and general computation functionalities.

\par As we have mentioned, we also get two results for THC on general graphs. The state-of-the-art THB protocol for general graphs is the Akavia-LaVigne-Moran (ALM) protocol of Akavia et al. (CRYPTO 2017 and JoC 2020). Our result is that our optimization for the AM protocol also applies to the ALM protocol and can reduce its communication cost by a factor of $O(\kappa)$. Moreover, we optimize the fully-homomorphic encryption (FHE) based GTHC protocol of LaVigne et al. (TCC 2018) and reduce its communication cost from $O(n^8\kappa^2)$ FHE ciphertexts and $O(n^5\kappa)$ FHE public keys to $O(n^6\kappa)$ FHE ciphertexts and $O(n^5\kappa)$ FHE public keys.

Previously [4], Orbis Labs presented a method for compiling (“arithmetizing”) relations, expressed as Σ¹₁ formulas in the language of rings, into Halo 2 [1, 2, 3] arithmetic circuits. In this research, we extend this method to support polynomial quantifier bounds, in addition to constant quantifier bounds. This allows for more efficient usage of rows in the resulting circuit.

Zero Knowledge Set Membership Proofs (zkSMPs) allow efficiently, i.e. sublinearly in the size of the set, proving membership of a value in a set in zero knowledge with respect to the value. They have been used to construct anonymous cryptocurrencies such as ZCash, which uses a zero knowledge Merkle proof to show that the inputs of a transaction belong to the Transaction Output (TXO) set. Using a Merkle tree instantiated with a pair of Pedersen hash functions between an amicable cycle of elliptic curves, similarly to Curve Trees, and the Weil Elliptic Curve Inner Product (ECIPs) proofs, I design a set membership protocol with substantially smaller witness sizes than other Merkle zkSMPs. This protocol uses a pair of communicating Bulletproofs, one over each curve, whose total proof size I am able to reduce by proving portions of each verifier inside the other proof. Using these techniques, along with an adaptation of the Bulletproofs++ confidential transaction protocol, I design an anonymous transaction protocol for a decentralized cryptocurrency, whose security argument is reducible to the discrete log problem over a pair of elliptic curves and that does not require a trusted setup. Over a $256$ bit field, these transactions are $1349 + 64n + 32 \lceil \log_2 c \rceil$ bytes for $n$ inputs, $m$ outputs, $d$ depth, and $c$ proof capacity, which is bounded by a linear function of $n d$, $n$, and $m$ and is equal to $1$ for up to $m < 1000$ or $n < 37$ when $d = 48$. Proving complexity is quasilinear and verifier complexity is linear in both $n d$ and $m$, and in practice verification will be dominated by the cost of two Bulletproof verifications of length $1536$ and $1744$ for $c=1$. $\mu$Cash support efficient batch verification, user defined assets and multi-asset confidential transactions, privacy preserving multi-party proving, adaptor signatures, absolute and relative time locks, and a multiphase transaction structure to support scriptless scripts for private atomic swaps and payment channels. This protocol is likely compatible with the Halo accumulation scheme, although I do not investigate this.

Although the supersingular isogeny Diffie-Hellman (SIDH) protocol is one of the most promising post-quantum cryptosystems, it is significantly slower than its main counterparts due to the underlying large smooth-degree isogeny computation. In this work, we address the problem of evaluating and constructing a strategy for computing the large smooth-degree isogeny in the multi-processor setting by formulating them as scheduling problems with dependencies. The contribution of this work is two-fold. For the strategy evaluation, we transform strategies into task dependency graphs and apply precedence-constrained scheduling algorithms to them in order to find their costs. For the strategy construction, we construct strategies from smaller parts that are optimal solutions of integer programming representing the problem. We show via experiments that the proposed two techniques together offer more than 13% reduction in the strategy costs compared to the best current results by Hutchinson and Karabina presented at Indocrypt 2018.

Assume that Alice can do only classical probabilistic polynomial-time computing while Bob can do quantum polynomial-time computing. Alice and Bob communicate over only classical channels, and finally Bob gets a state $|x_0\rangle+|x_1\rangle$ with some bit strings $x_0$ and $x_1$. Is it possible that Alice can know $\{x_0,x_1\}$ but Bob cannot? Such a task, called {\it remote state preparations}, is indeed possible under some complexity assumptions, and is bases of many quantum cryptographic primitives such as proofs of quantumness, (classical-client) blind quantum computing, (classical) verifications of quantum computing, and quantum money. A typical technique to realize remote state preparations is to use 2-to-1 trapdoor collision resistant hash functions: Alice sends a 2-to-1 trapdoor collision resistant hash function $f$ to Bob, and Bob evaluates it coherently, i.e., Bob generates $\sum_x|x\rangle|f(x)\rangle$. Bob measures the second register to get the measurement result $y$, and sends $y$ to Alice. Bob's post-measurement state is $|x_0\rangle+|x_1\rangle$, where $f(x_0)=f(x_1)=y$. With the trapdoor, Alice can learn $\{x_0,x_1\}$ from $y$, but due to the collision resistance, Bob cannot. This Alice's advantage can be leveraged to realize the quantum cryptographic primitives listed above. It seems that the collision resistance is essential here. In this paper, surprisingly, we show that the collision resistance is not necessary for a restricted case: we show that (non-verifiable) remote state preparations of $|x_0\rangle+|x_1\rangle$ secure against {\it classical} probabilistic polynomial-time Bob can be constructed from classically-secure (full-domain) trapdoor permutations. Trapdoor permutations are not likely to imply the collision resistance, because black-box reductions from collision-resistant hash functions to trapdoor permutations are known to be impossible. As an application of our result, we construct proofs of quantumness from classically-secure (full-domain) trapdoor permutations.

Weak coin flipping is an important cryptographic primitive, as it is the strongest known secure two-party computation primitive, that classically becomes secure only when certain assumptions are made (e.g. computational hardness), while quantumly there exist protocols that achieve arbitrarily close to perfect security. This breakthrough result was established by C. Mochon in 2007 [arXiv:0711.4114], however, his proof of existence was partially non-constructive, thus, setting back the proposal of explicit protocols. In this work, we report three different solutions to the quantum weak coin flipping problem. In particular, we propose different methods that result---either analytically or numerically---in the operators needed to construct weak coin flipping protocols with different levels of security, including nearly perfect security. In order to develop these methods, we study the quantum weak coin flipping problem from both an algebraic and a geometric perspective. We also analytically construct illustrative examples of weak coin flipping protocols achieving different levels of security.

We construct non-malleable codes in the split-state model with codeword length $m + 3\lambda$ or $m+5\lambda$, where $m$ is the message size and $\lambda$ is the security parameter, depending on how conservative one is. Our scheme is very simple and involves a single call to a block cipher meeting a new security notion which we dub entropic fixed-related-key security, which essentially means that the block cipher behaves like a pseudorandom permutation when queried upon inputs sampled from a distribution with sufficient min-entropy, even under related-key attacks with respect to an arbitrary but fixed key relation. Importantly, indistinguishability only holds with respect to the original secret key (and not with respect to the tampered secret key).

In a previous work, Fehr, Karpman, and Mennink (ToSC 2018) used a related assumption (where the block cipher inputs can be chosen by the adversary, and where indistinguishability holds even with respect to the tampered key) to construct a non-malleable code in the split-state model with codeword length $m + 2\lambda$. Unfortunately, no block cipher (even an ideal one) satisfies their assumption when the tampering function is allowed to be cipher-dependent. In contrast, we are able to show that entropic fixed-related-key security holds in the ideal cipher model with respect to a large class of cipher-dependent tampering attacks (including those which break the assumption of Fehr, Karpman, and Mennink).

Arithmetic to Boolean masking (A2B) conversion is a crucial technique in the masking of lattice-based post-quantum cryptography. It is also a crucial part of building a masked comparison which is one of the hardest to mask building blocks for active secure lattice-based encryption. We first present a new method, called one-hot conversion, to efficiently convert from higher-order arithmetic masking to Boolean masking using a variant of the higher-order table-based conversion of Coron et al. Secondly, we specialize our method to perform arithmetic to 1-bit Boolean functions. Our one-hot function can be applied to masking lattice-based encryption building blocks such as masked comparison or to determine the most significant bit of an arithmetically masked variable. In our benchmarks, a speedup of 40 to 66 times is achieved over state-of-the-art table-based A2B conversions, bringing table-based A2B conversions in the performance range of the Boolean circuit-based A2B conversions by only a slowdown of factor 1.2 to 2.

Cryptanalysis of block ciphers is an active and important research area with an extensive volume of literature. For this work, we focus on SBox-based ciphers, as they are widely used and cover a large class of block ciphers. While there have been prior works that have consolidated attacks on block ciphers, they usually focus on describing and listing the attacks. Moreover, the methods for evaluating a cipher's security are often ad hoc, differing from cipher to cipher, as attacks and evaluation techniques are developed along the way. As such, we aim to organise the attack literature, as well as the work on security evaluation.

In this work, we present a systematization of cryptanalysis of SBox-based block ciphers focusing on three main areas: (1) Evaluation of block ciphers against standard cryptanalytic attacks; (2) Organisation and relationships between various attacks; (3) Comparison of the evaluation and attacks on existing ciphers.

The FX construction provides a way to increase the effective key length of a block cipher E. We prove security of a tweakable version of the FX construction in the post-quantum setting, i.e., against a quantum attacker given only classical access to the secretly keyed construction while retaining quantum access to E, a setting that seems to be the most relevant one for real-world applications. We then use our results to prove post-quantum security—in the same model—of the (plain) FX construction, Elephant (a finalist of NIST's lightweight cryptography standardization effort), and Chaskey (an ISO-standardized lightweight MAC).

Searchable Symmetric Encryption (SSE) supports efficient yet secure query processing over outsourced symmetrically encrypted databases without the need for decryption. A longstanding open question has been the following: can we design a fast, scalable, linear storage and low-leakage SSE scheme that efficiently supports arbitrary Boolean queries over encrypted databases? In this paper, we present the design, analysis and prototype implementation of the first SSE scheme that efficiently supports conjunctive, disjunctive and more general Boolean queries (in both the conjunctive and disjunctive normal forms) while scaling smoothly to extremely large encrypted databases, and while incurring linear storage overheads and supporting extremely fast query processing in practice. We quantify the leakage of our proposal via a rigorous cryptographic analysis and argue that it achieves security against a well-known class of leakage-abuse and volume analysis attacks. Finally, we demonstrate the storage-efficiency and scalability of our proposed scheme by presenting experimental results of a prototype implementation of our scheme over large real-world databases.

Shor's algorithm solves Elliptic Curve Discrete Logarithm Problem(ECDLP) in polynomial time. To optimize Shor's algorithm for binary elliptic curve, reducing the cost for binary field multiplication is essential because it is most cost-critical basic arithmetic. In this paper, we propose Toffoli gate count optimized space-efficient quantum circuits for binary field $(\mathbb{F}_{2^{n}})$ multiplication. To do so, we take advantage of Karatsuba-like formula and show that its application can be provided without ancillary qubits and optimized them in terms of CNOT gate and depth. Based on the Karatsuba-like formula, we drive a space-efficient CRT-based multiplication with two types of out-of-place multiplication algorithm to reduce CNOT gate cost. Our quantum circuits do not use ancillary qubits and have extremely low TOF gates count $O(n2^{\log_{2}^{\ast}n})$ where $\log_{2}^{\ast}$ is a function named iterative logarithm that grows very slowly. Compared to recent Karatsuba-based space-efficient quantum circuit, our circuit requires only $(12 \sim 24 \% )$ of Toffoli gate count with comparable depth for cryptographic field sizes $(n = 233 \sim 571)$. To the best of our knowledge, this is the first result that utilizes Karatsuba-like formula and CRT-based multiplication in quantum circuits.

This work considers the problem of mitigating information leakage between communication and sensing in systems jointly performing both operations. Specifically, a discrete memoryless state-dependent broadcast channel model is studied in which (i) the presence of feedback enables a transmitter to convey information, while simultaneously performing channel state estimation; (ii) one of the receivers is treated as an eavesdropper whose state should be estimated but which should remain oblivious to part of the transmitted information. The model abstracts the challenges behind security for joint communication and sensing if one views the channel state as a sensitive attribute, e.g., location. For independent and identically distributed states, perfect output feedback, and when part of the transmitted message should be kept secret, a partial characterization of the secrecy-distortion region is developed. The characterization is exact when the broadcast channel is either physically-degraded or reversely-physically-degraded. The partial characterization is also extended to the situation in which the entire transmitted message should be kept secret. The benefits of a joint approach compared to separation-based secure communication and state-sensing methods are illustrated with binary joint communication and sensing models.

This work explores several architectural optimizations to report a fast and area-time (AT) product efficient hardware accelerator for a lattice based Key Encapsulation Mechanism (KEM) scheme called the CRYSTALS-KYBER. Kyber was recently chosen as the first quantum resistant KEM scheme for standardisation, after three rounds of the National Institute of Standards and Technology (NIST) initiated NIST PQC competition for the search of the best quantum resistant KEMs and digital signatures (started in 2016). Kyber is based on Module-Learning with Errors (M-LWE) class of Lattice-based Cryptography, that is known to manifest efficiently on FPGAs. The architectural optimizations include inter-module and intra-module pipelining, that is designed and balanced via FIFO based buffering to ensure maximum parallelisation. The implementation results show that compared to the state-of-the-art, the proposed architecture delivers 23.8-43.8% speedups at three different security levels on Artix-7 and Zynq UltraScale+ devices, 50-75% reduction in DSPs and no BRAM resources at comparable security level. Consequently, the AT product efficiency is reported to be 45.8-51.9% higher in comparison with the state-of-the-art designs.

NTRU-ν-um is a fully homomorphic encryption schemes making use of NTRU as a building block. NTRU-ν-um comes in two versions: a first instantiation working with polynomials modulo XN − 1 with N a prime [cyclic version] and a second instantiation working with polynomials modulo XN + 1 with N a power of two [negacyclic version].

This report shows that the cyclic version of NTRU-ν-um is not secure. Specifically, it does not provide indistinguishability of encryptions. More critically, the scheme leaks the underlying private LWE keys. Source code for mounting the attacks is provided. The attacks were practically validated on the given parameter sets.

Event date: 19 August to 24 August 2023
Submission deadline: 16 February 2023
Notification: 5 May 2023

It has been forty years since the TCP/IP protocol blueprint, which is the core of modern worldwide Internet, was published. Over this long period, technology has made rapid progress. These advancements are slowly putting pressure and placing new demands on the underlying network architecture design. Therefore, there was a need for innovations that can handle the increasing demands of new technologies like IoT while ensuring secrecy and privacy. It is how Named Data Networking (NDN) came into the picture. NDN enables robust data distribution with interest-based content retrieval and leave-copy-everywhere caching policy. Even though NDN has surfaced as a future envisioned and decisive machinery for data distribution in IoT, it suffers from new data security challenges like content poisoning attacks. In this attack, an attacker attempts to introduce poisoned content with an invalid signature into the network. Given the circumstances, there is a need for a cost-effective signature scheme, requiring inexpensive computing resources and fast when implemented. An identity-based signature scheme (IBS) seems to be the natural choice to address this problem. Herein, we present an IBS, namely Mul-IBS relying on multivariate public key cryptography (MPKC), which leads the race among the post-quantum cryptography contenders. A 5-pass identification scheme accompanying a safe and secure signature scheme based on MPKC works as key ingredients of our design. Our Mul-IBS attains optimal master public key size, master secret key size, and user’s secret key size in the context of multivariate identity-based signatures. The proposed scheme Mul-IBS is proven to be secure in the model “existential unforgeability under chosen-message and chosen identity attack (uf-cma)” contingent upon the fact that Multivariate Quadratic (MQ) problem is NP-hard. The proposed design Mul-IBS can be utilized as a crucial cryptographic building block to build a robust and resilient IoT-based NDN architecture.

Post-Compromise Security (PCS) is a property of secure-channel establishment schemes, which limits the security breach of an adversary that has compromised one of the endpoint to a certain number of messages, after which the channel heals. An attractive property, especially in view of Snowden's revelation of mass-surveillance, PCS was pioneered by the Signal messaging protocol, and is present in OTR. In this paper, we introduce a framework for quantifying and comparing PCS security, with respect to a broad taxonomy of adversaries. The generality and flexibility of our approach allows us to model the healing speed of a broad class of protocols, including Signal, but also an identity-based messaging protocol named SAID, and even a composition of 5G handover protocols.

Databases often require the flexibility to control which entities can access specific database records. Such access control is absent in works that provide private access to databases, namely private information retrieval (PIR) systems. In this paper, we show how to address this shortcoming by introducing Pirmission, the first practical single-server PIR system that allows the enforcement of access control policies. Pirmission’s mechanism does not even reveal whether the client passed or failed the access control check—instead the client receives random data if they are not authorized to access a database record. To demonstrate the usefulness and practicality of Pirmission, we use it to build a private contact discovery platform that allows users to only be discoverable by their friends (who have permission). Compared to state-of- the-art single-server PIR protocols that do not provide access control, Pirmission increases the server’s response time by around 2.8X (much less for databases with large records), and requires only one additional ciphertext to be sent by the client.