International Association
for Cryptologic Research

<p>In recent years, there has been a growing interest in low-latency ciphers. Since the first low-latency block cipher PRINCE was proposed at ASIACRYPT 2012, many low-latency primitives sprung up, such as Midori, MANTIS, QARMA and SPEEDY. Some ciphers, like SPEEDY and Orthros, introduce bit permutations to achieve reduced delay. However, this approach poses a challenge in evaluating the resistance against some cryptanalysis, especially differential and linear attacks. SPEEDY-7-192, was fully broken by Boura et.al. using differential attack, for example. In this paper, we manage to propose a novel low-latency block cipher, which guarantees security against differential and linear attacks. Revisiting the permutation technique used in Orthros, we investigate the selection of nibble permutations and propose a method for selecting them systematically rather than relying on random search. Our new nibble permutation method ensures the existence of impossible differential and differential trails for up to 8 rounds, while the nibble permutations for both branches of Orthros may lead to a 9-round impossible differential trail. Furthermore, we introduce a new approach for constructing low-latency coordinate functions for 4-bit S-boxes, which involves a more precise delay computation compared to traditional methods based solely on circuit depth. The new low-latency primitive uLBC we propose, is a family of 128-bit block ciphers, with three different versions of key length, respectively 128-bit and 256-bit key, as well as a 384-bit tweakey version with variable-length key. According to the key length, named uLBC-128, uLBC-256 and uLBC-384t. Our analysis shows that uLBC-128 exhibits lower latency and area requirements compared to ciphers such as QARMA9-128 and Midori128. On performance, uLBC-128 has excellent AT performance, the best performance except SPEEDY-6, and even the best performance in UMC 55nm in our experiments. </p>

Cryptographic group actions have attracted growing attention as a useful tool for constructing cryptographic schemes. Among their applications, commitment schemes are particularly interesting as fundamental primitives, playing a crucial role in protocols such as zero-knowledge proofs, multi-party computation, and more. In this paper, we introduce a novel framework for constructing commitment schemes based on cryptographic group actions. Specifically, we propose two key techniques for general group actions: re-randomization and randomness extraction. Roughly speaking, a re-randomization algorithm introduces randomness within an orbit for any input element, while a randomness extractor maps this randomness to uniformity over the message space. We demonstrate that these techniques can significantly facilitate the construction of commitment schemes, providing a flexible framework for constructing either perfectly hiding or perfectly binding commitments, depending on the type of extractor involved. Moreover, we extend our framework to support the construction of commitments with additional desirable properties beyond hiding and binding, such as dual-mode commitments and enhanced linkable commitments. These extensions are achieved by further adapting the extractor to satisfy trapdoor or homomorphic properties. Finally, we instantiate all our proposed commitment schemes using lattices, specifically leveraging the lattice isomorphism problem (LIP) and the lattice automorphism problem (LAP) as underlying cryptographic assumptions. To the best of our knowledge, this is the first commitment scheme construction based on LIP/LAP. Additionally, we use LIP to provide a repair and improvement to the tensor isomorphism-based non-interactive commitment scheme proposed by D'Alconzo, Flamini, and Gangemi (ASIACRYPT 2023), which was recently shown to be insecure by an attack from Gilchrist, Marco, Petit, and Tang (CRYPTO 2024).

The MPC-in-the-head with preprocessing (MPCitH-PP) paradigm presents a novel approach for constructing post-quantum digital signatures like Picnic3. This paper revisits the MPCitH-PP construction, analyzing both its offline and online phases and proposing a reformulation of the protocol. By identifying redundant computations in these phases, we optimize them into a single phase, thereby enhancing the efficiency of MPCitH-PP. Furthermore, we explore the independence of the mask, demonstrating that it can be calculated in parallel, which also enables the optimization of the masked witness calculation.Our optimized implementation of Picnic3 shows significant improvements. At the L1 security level, the optimal software implementation reduces MPCitH-PP calculation time to about 30% of the previous implementation. The optimal signature implementation costs about 78% of the previous implementation time. At the L5 security level, MPCitH-PP with parallelism optimal is reduced to about 26% of the previous solution’s time, and the optimal signature implementation runs at about 53% of the previous solution’s time. For the hardware implementation, our optimizations reduce the clock cycles of MPCitH-PP from r sequential rounds to a single parallel round, where r denotes the number of rounds in the LowMC algorithm, with little change in hardware usage, and perform better in AT product, especially for parallel computing.

Picnic is a post-quantum digital signature, the security of which relies solely on symmetric-key primitives such as block ciphers and hash functions instead of number theoretic assumptions. One of the main concerns of Picnic is the large signature size. Although Katz et al.’s protocol (MPCitH-PP) significantly reduces the size of Picnic, the involvement of more parties in MPCitH-PP leads to longer signing/verification times and more hardware resources. This poses new challenges for implementing high-performance Picnic on resource-constrained FPGAs. So far as we know, current works on the hardware implementation of MPCitH-based signatures are compatible with 3 parties only. In this work, we investigate the optimization of the implementation of MPCitH-PP and successfully deploying MPCitH-PP with more than three parties on resource-constrained FPGAs, e.g., Xilinx Artix-7 and Kintex-7, for the first time. In particular, we propose a series of optimizations, which include pipelining and parallel optimization for MPCitH-PP and the optimization of the underlying symmetric primitives. Besides, we make a slight modification to the computation of the offline commitment, which can further reduce the number of computations of Keccak. These optimizations significantly improve the hardware performance of Picnic3. Signing messages on our FPGA takes 0.047 ms for the L1 security level, outperforming Picnic1 with hardware by a factor of about 5.3, which is the fastest implementation of post-quantum signatures as far as we know. Our FPGA implementation for the L5 security level takes 0.146 ms beating Picnic1 by a factor of 8.5, and outperforming Sphincs by a factor of 17.3.

The circulant twin column parity mixer (TCPM) is a type of mixing layer for the round function of cryptographic permutations designed by Hirch et al. at CRYPTO 2023. It has a bitwise differential branch number of 12 and a bitwise linear branch number of 4, which makes it competitive in applications where differential security is required. Hirch et al. gave a concrete instantiation of a permutation using such a mixing layer, named Gaston, and showed the best 3-round differential and linear trails of Gaston have much higher weights than those of Ascon. In this paper, we first prove why the TCPM has linear branch number 4 and then show that Gaston’s linear behavior is worse than Ascon for more than 3 rounds. Motivated by these facts, we aim to enhance the linear security of the TCPM. We show that adding a specific set of row cyclic shifts to the TCPM can make its differential and linear branch numbers both 12. Notably, by setting a special relationship between the row shift parameters of the modified TCPM, we obtain a special kind of mixlayer called the symmetric circulant twin column parity mixer. The symmetric TCPM has a unique design property that its differential and linear branch histograms are the same, which makes the parameter selection process and the security analysis convenient. Using the symmetric TCPM, we present two new 320-bit cryptographic permutations, namely (1) Gaston-S where we replace the mixing layer in Gaston with the symmetric TCPM and (2) SBD which uses a low-latency degree-4 S-box as the non-linear layer and the symmetric TCPM as the mixing layer. We evaluate the security of these permutations considering differential, linear and algebraic analysis, and then provide the performance comparison with Gaston in both hardware and software. Our results indicate that Gaston-S and SBD are competitive with Gaston in both security and performance.

$\mathbb{Z}^n$ is one of the simplest types of lattices, but the computational problems on its rotations, such as $\mathbb{Z}$SVP and $\mathbb{Z}$LIP, have been of great interest in cryptography. Recent advances have been made in building cryptographic primitives based on these problems, as well as in developing new algorithms for solving them. However, the theoretical complexity of $\mathbb{Z}$SVP and $\mathbb{Z}$LIP are still not well understood. In this work, we study the problems on rotations of $\mathbb{Z}^n$ by exploiting the symmetry property. We introduce a randomization framework that can be roughly viewed as `applying random automorphisms’ to the output of an oracle, without accessing the automorphism group. Using this framework, we obtain new reduction results for rotations of $\mathbb{Z}^n$. First, we present a reduction from $\mathbb{Z}$LIP to $\mathbb{Z}$SCVP. Here $\mathbb{Z}$SCVP is the problem of finding the shortest characteristic vectors, which is a special case of CVP where the target vector is a deep hole of the lattice. Moreover, we prove a reduction from $\mathbb{Z}$SVP to $\gamma$-$\mathbb{Z}$SVP for any constant $\gamma = O(1)$ in the same dimension, which implies that $\mathbb{Z}$SVP is as hard as its approximate version for any constant approximation factor. Second, we investigate the problem of finding a nontrivial automorphism for a given lattice, which is called LAP. Specifically, we use the randomization framework to show that $\mathbb{Z}$LAP is as hard as $\mathbb{Z}$LIP. We note that our result can be viewed as a $\mathbb{Z}^n$-analogue of Lenstra and Silverberg's result in [JoC2017], but with a different assumption: they assume the $G$-lattice structure, while we assume the access to an oracle that outputs a nontrivial automorphism.