International Association
for Cryptologic Research

The performance of higher-order masked implementations of lattice-based based key encapsulation mechanisms (KEM) is currently limited by the costly conversions between arithmetic and boolean masking. While bitslicing has been shown strongly speed up to masked implementations of symmetric primitives, it has never been used in higher-order arithmetic-to-boolean and boolean-to-arithmetic masking conversion gadgets. In this paper, we first show that bitslicing can indeed accelerate existing conversion gadgets. We then optimize these gadgets, exploiting the degrees of freedom offered by bitsliced implementations. As a result, we introduce new arbitrary-order boolean masked addition, arithmetic-to-boolean and boolean-to-arithmetic masking conversion gadgets, each in two variants: modulo \(2^k\) and modulo \(p\) (for any integers \(k\) and \(p\)). Practically, our new gadgets achieve a speedup of up to 25x over the state of the art. Turning to the KEM application, we develop the first open-source embedded (Cortex-M4) implementations of Kyber768 and Saber masked at arbitrary order. The implementations based on the new bitsliced gadgets achieve a speedup of 1.8x for Kyber and 3x for Saber, compared to the implementation based on state of the art gadgets. The bottleneck of the bitslice implementations is the masked Keccak-f[1600] permutation.

Private Set Union ($\mathsf{PSU}$) allows two players, the sender and the receiver, to compute the union of their input datasets without revealing any more information than the result. While it has found numerous applications in practice, not much research has been carried out so far, especially for large datasets.

In this work, we take shuffling technique as a key to design $\mathsf{PSU}$ protocols for the first time. By shuffling receiver's set, we put forward the first protocol, denoted as $\Pi_{\mathsf{PSU}}^{\mathsf{receiver}}$, that eliminates the expensive operations in previous works, such as additive homomorphic encryption and repeated operations on the receiver's set. It outperforms the state-of-the-art design by Kolesnikov et al. (ASIACRYPT 2019) in both efficiency and security; the unnecessary leakage in Kolesnikov et al.'s design, can be avoided in our design.

We further extend our investigation to the application scenarios in which both players may hold unbalanced input datasets. We propose our second protocol $\Pi_{\mathsf{PSU}}^{\mathsf{sender}}$, by shuffling the sender's dataset. This design can be viewed as a dual version of our first protocol, and it is suitable in the cases where the sender's input size is much smaller than the receiver's.

Finally, we implement our protocols $\Pi_{\mathsf{PSU}}^{\mathsf{receiver}}$ and $\Pi_{\mathsf{PSU}}^{\mathsf{sender}}$ in C++ on big datasets, and perform a comprehensive evaluation in terms of both scalability and parallelizability. The results demonstrate that our design can obtain a $4$-$5 \times$ improvement over the state-of-the-art by Kolesnikov et al. with a single thread in WAN/LAN settings.

We define a framework for analyzing the security of cryptographic protocols that makes minimal assumptions about what a "realistic model of computation is". In particular, whereas classical models assume that the attacker is a (perhaps non-uniform) probabilistic polynomial-time algorithm, and more recent definitional approaches also consider quantum polynomial-time algorithms, we consider an approach that is more agnostic to what computational model is physically realizable.

Our notion of cosmic security considers a reduction-based notion of security that models attackers as arbitrary unbounded stateful algorithms; we also consider a more relaxed notion of cosmic security w.r.t. weakly-restartable adversaries which makes additional restrictions on the attacker’s behavior. We present both impossibility results and general feasibility results for our notions, indicating that extended Church-Turing hypotheses may not be needed for a well-founded theory of Cryptography.

An idealised decentralised exchange (DEX) provides a medium in which players wishing to exchange one token for another can interact with other such players and liquidity providers at a price which reflects the true exchange rate, without the need for a trusted third-party. Unfortunately, extractable value is an inherent flaw in existing blockchain-based DEX implementations. This extractable value takes the form of monetizable opportunities that allow blockchain participants to extract money from a DEX without adding demand or liquidity to the DEX, the two functions for which DEXs are intended. This money is taken directly from the intended DEX participants. As a result, the cost of participation in existing DEXs is much larger than the upfront fees required to post a transaction on a blockchain and/or into a smart contract. We present FairTraDEX, a decentralised variant of a frequent batch auction (FBA), a DEX protocol which provides formal game-theoretic guarantees against extractable value. FBAs when run by a trusted third-party provide unique game-theoretic optimal strategies which ensure players are shown prices equal to the liquidity provider's fair price, excluding explicit, pre-determined fees. FairTraDEX replicates the key features of an FBA that provide these game-theoretic guarantees using a combination of set-membership in zero-knowledge protocols and an escrow-enforced commit-reveal protocol. We extend the results of FBAs to handle monopolistic and/or malicious liquidity providers, and provide a detailed pseudo-code implementation of FairTraDEX based on existing mainstream blockchain protocols.

Given a private string q and a remote server that holds a set of public documents D, how can one of the K most relevant documents to q in D be selected and viewed without anyone (not even the server) learning anything about q or the document? This is the oblivious document ranking and retrieval problem. In this paper, we describe Coeus, a system that solves this problem. At a high level, Coeus composes two cryptographic primitives: secure matrix-vector product for scoring document relevance using the widely-used term frequency-inverse document frequency (tf-idf) method, and private information retrieval (PIR) for obliviously retrieving documents. However, Coeus reduces the time to run these protocols, thereby improving the user-perceived latency, which is a key performance metric. Coeus first reduces the PIR overhead by separating out private metadata retrieval from document retrieval, and it then scales secure matrix-vector product to tf-idf matrices with several hundred billion elements through a series of novel cryptographic refinements. For a corpus of English Wikipedia containing 5 million documents, a keyword dictionary with 64K keywords, and on a cluster of 143 machines on AWS, Coeus enables a user to obliviously rank and retrieve a document in 3.9 seconds---a 24x improvement over a baseline system.

In SIDH and SIKE protocols, public keys are defined over quadratic extensions of prime fields. We present in this work a projective invariant property characterizing affine Montgomery curves defined over prime fields. We then force a secret 3-isogeny chain to repeatedly pass through a curve defined over a prime field in order to exploit the new property and inject zeros in the A-coefficient of an intermediate curve to successfully recover the isogeny chain one step at a time. Our results introduce a new kind of fault attacks applicable to SIDH and SIKE.

Hash-Based Signature (HBS) uses a hash function to construct a digital signature scheme, where its security is guaranteed by the collision resistance of the hash function used. To provide sufficient security in the post-quantum environment, the length of hash should be satisfied. Modern HBS can be classified into stateful and stateless schemes. Two representative stateful and stateless HBS are XMSS and SPHINCS$^+$, respectively. In this paper, we propose two HBS schemes: K-XMSS and K-SPHINCS$^+$, which replace internal hash functions of XMSS and SPHINCS$^+$ with Korean cryptography algorithms. K-XMSS is a stateful signature, while K-SPHINCS$^+$ is its stateless counterpart. We also showcase the reference implementation of K-XMSS and K-SPHINCS$^+$ employing LSH and two hash functions based on block ciphers (i.e. CHAM and LEA) as the internal hash function. The reference code is developed as a proof-of-concept, which can be optimized for better performance using advanced implementation techniques (e.g. AVX2 and NEON).

In ToSC 2021(2), Sun et al. implemented an automatic search with the Boolean satisfiability problem (SAT) method on GIFT-128 and identified a 19-round linear approximation with the expected linear potential being $2^{-117.43}$, which is utilised to launch a 24-round attack on the cipher. In this addendum, we discover a new 19-round linear approximation with a lower expected linear potential. However, in the attack, one more round can be appended after the distinguisher. As a result, we improve the previous optimal linear attack by one round and put forward a 25-round linear attack. Given that the optimal differential attack on GIFT-128, for now, covers 27-round, the resistances of the cipher against differential and linear attacks still have a 2-round gap.

Isogeny-based cryptography is one of the main candidates of post-quantum cryptography. To realize efficient computations, one usually uses formulas of scalar multiplications and isogeny computations on elliptic curves using only one coordinate in isogeny-based cryptography. The $x$-coordinate of Montgomery curves is the most standard, and we sometimes use the $x$-coordinate of Montgomery$^-$ curves, the $w$-coordinate of Edwards curves, and the $w$-coordinate of Huff's curves.

In this paper, we define a novel function on elliptic curves called the generalized Montgomery coordinate that has the four coordinates described above as special cases. For a generalized Montgomery coordinate, we construct an explicit formula of scalar multiplication which includes the division polynomial, and both a formula of an image point under an isogeny and that of a coefficient of the codomain curve.

Finally, we expect numerous applications for the generalized Montgomery coefficient. As an experimental study, we present two applications of the theory of a generalized Montgomery coordinate. The first one is to construct a new efficient formula to compute isogenies on Montgomery curves. This formula is more efficient than the previous one for high degree isogenies as the $\sqrt{\vphantom{2}}$\'{e}lu's formula in our implementation. The second one is to construct a new generalized Montgomery coordinate for Montgomery$^-$ curves used for CSURF.

In this work, we first propose a new functional bootstrapping with TFHE for evaluating any function of domain and codomain the real torus T by using a small number of bootstrappings. This result improves some aspects of previous approaches: like them, we allow for evaluating any functions, but with better precision. In addition, we develop more efficient multiplication and addition over ciphertexts building on the digit-decomposition approach. As a practical application, our results lead to an efficient implementation of ReLU, one of the most used activation functions in deep learning. The paper is concluded by extensive experimental results comparing each building block as well as their practical relevance and trade-offs.

Firekite is a synchronous stream cipher using a pseudo-random number generator (PRNG) whose security relies on the hardness of the \textit{Learning Parity with Noise} (LPN) problem. It is one of a few LPN-based symmetric encryption schemes and it can be very efficiently implemented on a low-end SoC FPGA. The designers, Bogos, Korolija, Locher, and Vaudenay, demonstrated appealing properties of Firekite such as requiring only one source of cryptographically strong bits, small key size, high attainable throughput, and a concrete measurement for the bit level security depending on the selected practical parameters. We propose distinguishing and key-recovery attacks on Firekite by exploiting the structural properties of its PRNG. We adopt several \textit{birthday-paradox} techniques to show that a particular sum of Firekite's output has a low Hamming weight with higher probability than the random case. We achieve the best distinguishing attacks with complexities $2^{66.75}$ and $2^{106.75}$ for Firekite's parameters corresponding to $80$-bit and $128$-bit security, respectively. By applying the distinguishing attacks and an additionally suggested algorithm, one can also recover the secret matrix used in the Firekite PRNG, which is built from the secret key bits. This key recovery attack works on most large parameter sets and has slightly larger complexity, for example $2^{69.87}$ on the $80$-bit security parameters $n=16384, m = 216, k = 216$.

Some recent research articles [23, 24] addressed an explicit specification of indicators that specify bent functions in the so-called $\mathcal{C}$ and $\mathcal{D}$ classes, derived from the Maiorana- McFarland ($\mathcal{M}$) class by C. Carlet in 1994 [5]. Many of these bent functions that belong to $\mathcal{C}$ or $\mathcal{D}$ are provably outside the completed $\mathcal{M}$ class. Nevertheless, these modifications are performed on affine subspaces, whereas modifying bent functions on suitable subsets may provide us with further classes of bent functions. In this article, we exactly specify new families of bent functions obtained by adding together indicators typical for the $\mathcal{C}$ and $\mathcal{D}$ class, thus essentially modifying bent functions in $\mathcal{M}$ on suitable subsets instead of subspaces. It is shown that the modification of certain bent functions in $\mathcal{M}$ gives rise to new bent functions which are provably outside the completed $\mathcal{M}$ class. Moreover, we consider the so-called 4-bent concatenation (using four different bent functions on the same variable space) of the (non)modified bent functions in $\mathcal{M}$ and show that we can generate new bent functions in this way which do not belong to the completed $\mathcal{M}$ class either. This result is obtained by specifying explicitly the duals of four constituent bent functions used in the concatenation. The question whether these bent functions are also excluded from the completed versions of $\mathcal{PS}$, $\mathcal{C}$ or $\mathcal{D}$ remains open and is considered difficult due to the lack of membership indicators for these classes.

We address the problem of learning a machine learning model from training data that originates at multiple data owners, while providing formal privacy guarantees regarding the protection of each owner's data. Existing solutions based on Differential Privacy (DP) achieve this at the cost of a drop in accuracy. Solutions based on Secure Multiparty Computation (MPC) do not incur such accuracy loss but leak information when the trained model is made publicly available. We propose an MPC solution for training DP models. Our solution relies on an MPC protocol for model training, and an MPC protocol for perturbing the trained model coefficients with Laplace noise in a privacy-preserving manner. The resulting MPC+DP approach achieves higher accuracy than a pure DP approach, while providing the same formal privacy guarantees. Our work obtained first place in the iDASH2021 Track III competition on confidential computing for secure genome analysis.

QR-UOV is a variant of UOV with smaller keys proposed at Asiacrypt 2021. In this paper, we show that QR-UOV can be constructed by a smaller UOV over an extension field.

We extend a previous framework for designing differentially private (DP) mechanisms via randomized graph colorings that was restricted to binary functions, corresponding to colorings in a graph, to multi-valued functions. As before, datasets are nodes in the graph and any two neighboring datasets are connected by an edge. In our setting, we assume each dataset has a preferential ordering for the possible outputs of the mechanism, which we refer to as a rainbow. Different rainbows partition the graph of datasets into different regions. We show that when the DP mechanism is pre-specified at the boundary of such regions, at most one optimal mechanism can exist. Moreover, if the mechanism is to behave identically for all same-rainbow boundary datasets, the problem can be greatly simplified and solved by means of a morphism to a line graph. We then show closed form expressions for the line graph in the case of ternary functions. Treatment of ternary queries in this paper displays enough richness to be extended to higher-dimensional query spaces with preferential query ordering, but the optimality proof does not seem to follow directly from the ternary proof.

Bent functions are optimal combinatorial objects and have been studied over the last four decades. Secondary construction plays a central role in constructing bent functions since it may generate bent functions outside the primary classes of bent functions. In this study, we improve a theoretical framework of the secondary construction of bent functions in terms of the composition of Boolean functions. Based on this framework, we propose several constructions of bent functions through the composition of a balanced Boolean function and dually isomorphic (DI) bent functions defined herein. In addition, we present a construction of self-dual bent functions.

We introduce verifiable partially-decryptable commitments (VPDC), as a building block for constructing efficient privacy-preserving protocols supporting auditability by a trusted party. A VPDC is an extension of a commitment along with an accompanying proof, convincing a verifier that (i) the given commitment is well-formed and (ii) a certain part of the committed message can be decrypted using a (secret) trapdoor known to a trusted party.

We first formalize VPDCs and then introduce a general decryption feasibility result that overcomes the challenges in relaxed proofs arising in the lattice setting. Our general result can be applied to a wide class of Fiat-Shamir based protocols and may be of independent interest.

Next, we show how to extend the commonly used lattice-based `Hashed-Message Commitment' (HMC) scheme into a succinct and efficient VPDC. In particular, we devise a novel `gadget'-based Regev-style (partial) decryption method, compatible with efficient relaxed lattice-based zero-knowledge proofs. We prove the soundness of our VPDC in the setting of adversarial proofs, where a prover tries to create a valid VPDC output that fails in decryption.

To demonstrate the effectiveness of our results, we extend a private blockchain payment protocol, MatRiCT, by Esgin et al. (ACM CCS '19) into a formally auditable construction, which we call MatRiCT-Au, with very low communication and computation overheads over MatRiCT.

In this work, we study hybrid exact/relaxed zero-knowledge proofs from lattices, where the proved relation is exact in one part and relaxed in the other. Such proofs arise in important real-life applications such as those requiring verifiable PRF evaluation and have so far not received significant attention as a standalone problem.

We first introduce a general framework, LANES+, for realizing such hybrid proofs efficiently by combining standard relaxed proofs of knowledge RPoK and the LANES framework (due to a series of works in Crypto'20, Asiacrypt'20, ACM CCS'20). The latter framework is a powerful lattice-based proof system that can prove exact linear and multiplicative relations. The advantage of LANES+ is its ability to realize hybrid proofs more efficiently by exploiting RPoK for the high-dimensional part of the secret witness while leaving a low-dimensional secret witness part for the exact proof that is proven at a significantly lower cost via LANES.

We apply our LANES+ framework to construct substantially shorter proofs of rounding, which is a central tool for verifiable deterministic lattice-based cryptography. Based on our rounding proof, we then design an efficient long-term verifiable random function (VRF), named LaV. LaV leads to the shortest VRF outputs among the proposals of standard (i.e., long-term and stateless) VRFs based on quantum-safe assumptions. Of independent interest, we also present a general framework for the construction of efficient VRFs (in the random oracle model) and generalized results for challenge difference invertibility, a fundamental soundness security requirement for many proof systems.

Related-key attacks (RKA) are powerful cryptanalytic attacks, where the adversary can tamper with the secret key of a cryptographic scheme. Since their invention, RKA security has been an important design goal in cryptography, and various works aim at designing cryptographic primitives that offer protection against related-key attacks. At EUROCRYPT'03, Bellare and Kohno introduced the first formal treatment of related-key attacks focusing on pseudorandom functions and permutations. This was later extended to cover other primitives such as signatures and public key encryption schemes, but until now, a comprehensive formal security analysis of authenticated encryption schemes with associated data (AEAD) in the RKA setting has been missing. The main contribution of our work is to close this gap for the relevant class of nonce-based AEAD schemes. To this end, we revisit the common approach to construct AEAD from encryption and message authentication. We extend the traditional security notion of AEAD to the RKA setting and consider an adversary that can tamper with the key $K_e$ and $K_m$ of the underlying encryption and MAC, respectively. We study two security models. In our weak setting, we require that tampering will change both $K_e$ and $K_m$, while in our strong setting, tampering can be arbitrary, i.e., only one key might be affected. We then study the security of the standard composition methods by analysing the nonce-based AEAD schemes N1 (Encrypt-and-MAC), N2 (Encrypt-then-MAC), and N3 (MAC-then-Encrypt) due to Namprempre, Rogaway, and Shrimpton (EUROCRYPT'03). We show that these schemes are weakly RKA secure, while they can be broken under a strong related-key attack. Finally, based on the N3 construction, we give a novel AEAD scheme that achieves our stronger notion.

In this work, we study the security of sponge-based authenticated encryption schemes against quantum attackers. In particular, we analyse the sponge-based authenticated encryption scheme SLAE as put forward by Degabriele et al. (ASIACRYPT'19). We show that the scheme achieves security in the post-quantum (QS1) setting in the quantum random oracle model by using the one-way to hiding lemma. Furthermore, we analyse the scheme in a fully-quantum (QS2) setting. There we provide a set of attacks showing that SLAE does not achieve ciphertext indistinguishability and hence overall does not provide the desired level of security.