International Association
for Cryptologic Research

The linear layer of block ciphers plays an important role in their security In particular, ciphers designed following the wide-trail strategy use the branch number of the linear layer to derive bounds on the probability of linear and differential trails. At FSE 2014, the LS-design construction was introduced as a simple and regular structure to design bitsliced block ciphers. It considers the internal state as a bit matrix, and applies alternatively an identical S-Box on all the columns, and an identical L-Box on all the lines. Security bounds are derived from the branch number of the L-Box.In this paper, we focus on bitsliced linear layers inspired by the LS-design construction and the Spook AEAD algorithm. We study the construction of bitsliced linear transformations with efficient implementations using XORs and rotations (optimized for bitsliced ciphers implemented on 32-bit processors), and a high branch number. In order to increase the density of the activity patterns, the linear layer is designed on the whole state, rather than using multiple parallel copies of an L-Box. Our main result is a linear layer for 128-bit ciphers with branch number 21, improving upon the best 32-bit transformation with branch number 12, and the one of Spook with branch number 16.

Ultra-fast AES round-based software cryptographic authentication/encryption primitives have recently seen important developments, fuelled by the authenticated encryption competition CAESAR and the prospect of future high-profile applications such as post-5G telecommunication technology security standards. In particular, Universal Hash Functions (UHF) are crucial primitives used as core components in many popular modes of operation for various use-cases, such as Message Authentication Codes (MACs), authenticated encryption, wide block ciphers, etc. In this paper, we extend and improve upon existing design approaches and present a general framework for the construction of UHFs, relying only on the AES round function and 128-bit word-wide XORs. This framework, drawing inspiration from tweakable block ciphers design, allows both strong security arguments and extremely high throughput. The security with regards to differential cryptanalysis is guaranteed thanks to an optimized MILP modelling strategy, while performances are pushed to their limits with a deep study of the details of AES-NI software implementations. In particular, our framework not only takes into account the number of AES-round calls per message block, but also the very important role of XOR operations and the overall scheduling of the computations.We instantiate our findings with two concrete UHF candidates, both requiring only 2 AES rounds per 128-bit message block, and each used to construct two MACs. First, LeMac, a large-state primitive that is the fastest MAC as of today on modern Intel processors, reaching performances of 0.068 c/B on Intel Ice Lake (an improvement of 60% in throughput compared to the state-of-the-art). The second MAC construction, PetitMac, provides an interesting memory/throughput tradeoff, allowing good performances on many platforms.

In this paper we present a new representation of the AES key schedule, with some implications to the security of AES-based schemes. In particular, we show that the AES-128 key schedule can be split into four independent parallel computations operating on 32 bits chunks, up to linear transformation. Surprisingly, this property has not been described in the literature after more than 20 years of analysis of AES. We show two consequences of our new representation, improving previous cryptanalysis results of AES-based schemes. First, we observe that iterating an odd number of key schedule rounds results in a function with short cycles. This explains an observation of Khairallah on mixFeed, a second-round candidate in the NIST lightweight competition. Our analysis actually shows that his forgery attack on mixFeed succeeds with probability 0.44 (with data complexity 220GB), breaking the scheme in practice. The same observation also leads to a novel attack on ALE, another AES-based AEAD scheme. Our new representation also gives efficient ways to combine information from the first sub-keys and information from the last sub-keys, in order to reconstruct the corresponding master keys. In particular we improve previous impossible-differential attacks against AES-128.

Simon and Simeck are two lightweight block ciphers with a simple round function using only word rotations and a bit-wise AND operation. Previous work has shown a strong clustering effect for differential and linear cryptanalysis, due to the existence of many trails with the same inputs and outputs. In this paper, we explore this clustering effect by exhibiting a class of high probability differential and linear trails where the active bits stay in a fixed window of w bits. Instead of enumerating a set of good trails contributing to a differential or a linear approximation, we compute the probability distribution over this space, including all trails in the class. This results in stronger distinguishers than previously proposed, and we describe key recovery attacks against Simon and Simeck improving the previous results by up to 7 rounds. In particular, we obtain an attack against 42-round Simeck-64, leaving only two rounds of security margin, and an attack against 45-round Simon-96/144, reducing the security margin from 16 rounds to 9 rounds.