Mixed-Integer Linear Programming (MILP) modeling has become an important tool for both the analysis and the design of symmetric cryptographic primitives. The bit-wise modeling of their nonlinear components, especially the S-boxes, is of particular interest since it allows more informative analysis compared to word-oriented models focusing on counting active S-boxes. At the same time, the size of these models, especially in terms of the number of required inequalities, tends to significantly influence and ultimately limit the applicability of this method to real-world ciphers, especially for larger number of rounds.

It is therefore of great cryptographic significance to study optimal linear inequality descriptions for Boolean functions. The pioneering works of Abdelkhalek et al. (FSE 2017), Boura and Coggia (FSE 2020) and Li and Sun (FSE 2023) provided various heuristic techniques for this computationally hard problem, decomposing it into two algorithmic steps, coined Problem 1 and Problem 2, with the latter being identical to the well-known NP-hard set cover problem, for which there are many heuristic and exact algorithms in the literature.

In this paper, we introduce a novel and efficient branch-and-bound algorithm for generating all minimal, non-redundant candidate inequalities that satisfy a given Boolean function, therefore solving Problem 1 in an optimal manner without relying on heuristics. We furthermore prove that our algorithm correctly computes optimal solutions. Using a number of dedicated optimizations, it provides significantly improved runtimes compared to previous approaches and allows the optimal modeling of the difference distribution tables (DDT) and linear approximation tables (LAT) of many practically used S-boxes. The source code for our algorithm is publicly available as a tool for researchers and practitioners in symmetric cryptography.

Raccoon is a lattice-based scheme submitted to the NIST 2022 call for additional post-quantum signatures. One of its main selling points is that its design is intrinsically easy to mask against side-channel attacks. So far, Raccoon's physical security guarantees were only stated in the abstract probing model. In this paper, we discuss how these probing security results translate into guarantees in more realistic leakage models. We also highlight that this translation differs from what is usually observed (e.g., in symmetric cryptography), due to the algebraic structure of Raccoon's operations. For this purpose, we perform an in-depth information theoretic evaluation of Raccoon's most innovative part, namely the AddRepNoise function which allows generating its arithmetic shares on-the-fly. Our results are twofold. First, we show that the resulting shares do not enforce a statistical security order (i.e., the need for the side-channel adversary to estimate higher-order moments of the leakage distribution), as usually expected when masking. Second, we observe that the first-order leakage on the (large) random coefficients manipulated by Raccoon cannot be efficiently turned into leakage on the (smaller) coefficients of its long-term secret. Concretely, our information theoretic evaluations for relevant leakage functions also suggest that Raccoon's masked implementations can ensure high security with less shares than suggested by a conservative analysis in the probing model.

The adversary model of white-box cryptography includes an extreme case where the adversary, sitting at the endpoint, has full access to a cryptographic scheme. Motivating by the fact that most existing white-box implementations focus on symmetric encryption, we present implementations for hash-based signatures so that the security against white-box attackers (who have read-only access to data with a size bounded by a space-hardness parameter M) depends on the availability of a white-box secure cipher (in addition to a general one-way function). We also introduce parameters and key-generation complexity results for white-box secure instantiation of stateless hash-based signature scheme SPHINCS+, one of the NIST selections for quantum-resistant digital signature algorithms, and its older version SPHINCS. We also present a hash tree-based solution for one-time passwords secure in a white-box attacker context. We implement the proposed solutions and share our performance results.

The problem of Broadcast Encryption (BE) consists in broadcasting an encrypted message to a large number of users or receiving devices in such a way that the emitter of the message can control which of the users can or cannot decrypt it.

Since the early 1990s, the design of BE schemes has received significant interest and many different concepts were proposed. A major breakthrough was achieved by Naor, Naor and Lotspiech (CRYPTO 2001) by partitioning cleverly the set of authorized users and associating a symmetric key to each subset. Since then, while there have been many advances in public-key based BE schemes, mostly based on bilinear maps, little was made on symmetric cryptography.

In this paper, we design a new symmetric-based BE scheme, named $\Sigma\Pi$BE, that relies on logic optimization and consensual security assumptions. It is competitive with the work of Naor et al. and provides a different tradeoff: the bandwidth requirement is significantly lowered at the cost of an increase in the key storage.