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  On the algebraic immunity of weightwise perfectly balanced functionsGini, Agnese  ; Meaux, Pierrick E-print/Working paper (2023) Detailed reference viewed: 34 (1 UL)  On the weightwise nonlinearity of weightwise perfectly balanced functionsGini, Agnese ; Meaux, Pierrick in Discrete Applied Mathematics (2022), 322 In this article we perform a general study on the criterion of weightwise nonlinearity for the functions which are weightwise perfectly balanced (WPB). First, we investigate the minimal value this ... [more ▼] In this article we perform a general study on the criterion of weightwise nonlinearity for the functions which are weightwise perfectly balanced (WPB). First, we investigate the minimal value this criterion can take over WPB functions, deriving theoretic bounds, and exhibiting the first values. We emphasize the link between this minimum and weightwise affine functions, and we prove that for n≥8 no n-variable WPB function can have this property. Then, we focus on the distribution and the maximum of this criterion over the set of WPB functions. We provide theoretic bounds on the latter and algorithms to either compute or estimate the former, together with the results of our experimental studies for n up to 8. Finally, we present two new constructions of WPB functions obtained by modifying the support of linear functions for each set of fixed Hamming weight. This provides a large corpus of WPB function with proven weightwise nonlinearity, and we compare the weightwise nonlinearity of these constructions to the average value, and to the parameters of former constructions in 8 and 16 variables. [less ▲] Detailed reference viewed: 64 (11 UL)Homomorphic encryption for privacy-friendly augmented democracy; ; Meaux, Pierrick in 2022 IEEE 21st Mediterranean Electrotechnical Conference (MELECON) (2022) Detailed reference viewed: 31 (0 UL)On the algebraic immunity of direct sum constructionsMeaux, Pierrick in Discrete Applied Mathematics (2022), 320 In this paper, we study sufficient conditions to improve the lower bound on the algebraic immunity of a direct sum of Boolean functions. We exhibit three properties on the component functions such that ... [more ▼] In this paper, we study sufficient conditions to improve the lower bound on the algebraic immunity of a direct sum of Boolean functions. We exhibit three properties on the component functions such that satisfying one of them is sufficient to ensure that the algebraic immunity of their direct sum exceeds the maximum of their algebraic immunities. These properties can be checked while computing the algebraic immunity and they allow to determine better the security provided by functions central in different cryptographic constructions such as stream ciphers, pseudorandom generators, and weak pseudorandom functions. We provide examples for each property and determine the exact algebraic immunity of candidate constructions. [less ▲] Detailed reference viewed: 26 (1 UL)A Complete Study of Two Classes of Boolean Functions: Direct Sums of Monomials and Threshold Functions; Meaux, Pierrick in IEEE Transactions on Information Theory (2022), 68(5), 3404--3425 In this paper, we make a comprehensive study of two classes of Boolean functions whose interest originally comes from hybrid symmetric-FHE encryption (with stream ciphers like FiLIP), but which also ... [more ▼] In this paper, we make a comprehensive study of two classes of Boolean functions whose interest originally comes from hybrid symmetric-FHE encryption (with stream ciphers like FiLIP), but which also present much interest for general stream ciphers. The functions in these two classes are cheap and easy to implement, and they allow the resistance to all classical attacks and to their guess and determine variants as well. We determine exactly all the main cryptographic parameters (algebraic degree, resiliency order, nonlinearity, algebraic immunity) for all functions in these two classes, and we give close bounds for the others (fast algebraic immunity, the dimension of the space of annihilators of minimal degree). This is the first time that this is done for all functions in large classes of cryptographic interest. [less ▲] Detailed reference viewed: 45 (2 UL)When Bad News Become Good News Towards Usable Instances of Learning with Physical Errors; ; et al in IACR Transactions on Cryptographic Hardware and Embedded Systems (2022), 2022(4), 1--24 Detailed reference viewed: 32 (2 UL)Towards Globally Optimized Hybrid Homomorphic Encryption - Featuring the Elisabeth Stream Cipher; ; Meaux, Pierrick et alReport (2022) Hybrid Homomorphic Encryption (HHE) reduces the amount of computation client-side and bandwidth usage in a Fully Homomorphic Encryption (FHE) framework. HHE requires the usage of specific symmetric ... [more ▼] Hybrid Homomorphic Encryption (HHE) reduces the amount of computation client-side and bandwidth usage in a Fully Homomorphic Encryption (FHE) framework. HHE requires the usage of specific symmetric schemes that can be evaluated homomorphically efficiently. In this paper, we introduce the paradigm of Group Filter Permutator (GFP) as a generalization of the Improved Filter Permutator paradigm introduced by Méaux et al. From this paradigm, we specify Elisabeth, a family of stream cipher and give an instance: Elisabeth. After asserting the security of this scheme, we provide a Rust implementation of it and ensure its performance is comparable to state-of-the-art HHE. The true strength of Elisabeth lies in the available operations server-side: while the best HHE applications were limited to a few multiplications server-side, we used data sent through Elisabeth to homomorphically evaluate a neural network inference. Finally, we discuss the improvement and loss between the HHE and the FHE framework and give ideas to build more efficient schemes from the Elisabeth family. [less ▲] Detailed reference viewed: 51 (0 UL)Weightwise almost perfectly balanced functions: secondary constructions for all n and better weightwise nonlinearitiesGini, Agnese ; Meaux, Pierrick E-print/Working paper (2022) Detailed reference viewed: 27 (1 UL)Weightwise perfectly balanced functions and nonlinearityGini, Agnese ; Meaux, Pierrick E-print/Working paper (2022) Detailed reference viewed: 35 (0 UL) |
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