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  Summary of some cryptographic criteria of functions in 8 variablesGini, Agnese  ; Meaux, Pierrick Report (2023) The purpose of this document is to collect the state of the art about criteria of WPB functions in 8 variables. Detailed reference viewed: 140 (0 UL) On the algebraic immunity of weightwise perfectly balanced functionsGini, Agnese ; Meaux, Pierrick E-print/Working paper (2023) Detailed reference viewed: 154 (2 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: 172 (11 UL)On the hardness of the hidden subset sum problem: algebraic and statistical attacksGini, Agnese Doctoral thesis (2022) Detailed reference viewed: 183 (21 UL)Provably Solving the Hidden Subset Sum Problem via Statistical LearningCoron, Jean-Sébastien ; Gini, Agnese in Mathematical Cryptology (2022, March), 1 At Crypto ’99, Nguyen and Stern described a lattice based algorithm for solving the hidden subset sum problem, a variant of the classical subset sum problem where the n weights are also hidden. As an ... [more ▼] At Crypto ’99, Nguyen and Stern described a lattice based algorithm for solving the hidden subset sum problem, a variant of the classical subset sum problem where the n weights are also hidden. As an application, they showed how to break the Boyko et al. fast generator of random pairs (x, g x(mod p)). The Nguyen-Stern algorithm works quite well in practice for moderate values of n, but its complexity is exponential in n. A polynomial-time variant was recently described at Crypto 2020, based on a multivariate technique, but the approach is heuristic only. In this paper, we describe a proven polynomial-time algorithm for solving the hidden subset-sum problem, based on statistical learning. In addition, we show that the statistical approach is also quite efficient in practice: using the FastICA algorithm, we can reach n = 250 in reasonable time. [less ▲] Detailed reference viewed: 212 (15 UL)Weightwise perfectly balanced functions and nonlinearityGini, Agnese ; Meaux, Pierrick in Codes, Cryptology and Information Security (2022) In this article we realize a general study on the nonlinearity of weightwise perfectly balanced (WPB) <br />functions. First, we derive upper and lower bounds on the nonlinearity from this class of ... [more ▼] In this article we realize a general study on the nonlinearity of weightwise perfectly balanced (WPB) <br />functions. First, we derive upper and lower bounds on the nonlinearity from this class of functions for all n. Then, <br />we give a general construction that allows us to provably provide WPB functions with nonlinearity as low as <br />2 <br />n/2−1 <br />and WPB functions with high nonlinearity, at least 2 <br />n−1 − 2 <br />n/2 <br />. We provide concrete examples in 8 and <br />16 variables with high nonlinearity given by this construction. In 8 variables we experimentally obtain functions <br />reaching a nonlinearity of 116 which corresponds to the upper bound of Dobbertin’s conjecture, and it improves <br />upon the maximal nonlinearity of WPB functions recently obtained with genetic algorithms. Finally, we study the <br />distribution of nonlinearity over the set of WPB functions. We examine the exact distribution for n = 4 and provide <br />an algorithm to estimate the distributions for n = 8 and 16, together with the results of our experimental studies for <br />n = 8 and 16. [less ▲] Detailed reference viewed: 132 (8 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: 89 (1 UL)A Polynomial-Time Algorithm for Solving the Hidden Subset Sum ProblemCoron, Jean-Sébastien ; Gini, Agnese in Advances in Cryptology -- CRYPTO 2020 (2020, August 10) At Crypto '99, Nguyen and Stern described a lattice based algorithm for solving the hidden subset sum problem, a variant of the classical subset sum problem where the n weights are also hidden. While the ... [more ▼] At Crypto '99, Nguyen and Stern described a lattice based algorithm for solving the hidden subset sum problem, a variant of the classical subset sum problem where the n weights are also hidden. While the Nguyen-Stern algorithm works quite well in practice for moderate values of n, we argue that its complexity is actually exponential in n; namely in the final step one must recover a very short basis of a n-dimensional lattice, which takes exponential-time in n, as one must apply BKZ reduction with increasingly large block-sizes. [less ▲] Detailed reference viewed: 308 (32 UL)Supersingular Isogeny-Based Designated Verifier Blind SignatureSahu, Rajeev Anand ; Gini, Agnese ; E-print/Working paper (2019) Detailed reference viewed: 155 (5 UL)Improved Cryptanalysis of the AJPS Mersenne Based CryptosystemCoron, Jean-Sébastien ; Gini, Agnese in Journal of Mathematical Cryptology (2019) At Crypto 2018, Aggarwal, Joux, Prakash and Santha (AJPS) described a new public-key encryption scheme based on Mersenne numbers. Shortly after the publication of the cryptosystem, Beunardeau et al ... [more ▼] At Crypto 2018, Aggarwal, Joux, Prakash and Santha (AJPS) described a new public-key encryption scheme based on Mersenne numbers. Shortly after the publication of the cryptosystem, Beunardeau et al. described an attack with complexity O(2^(2h)). In this paper, we describe an improvedattack with complexity O(2^(1.75h)) . [less ▲] Detailed reference viewed: 136 (17 UL)$\mathcal{S}_0$-equivalent classes, a new direction to find better weightwise perfectly balanced functions, and moreGini, Agnese ; Meaux, Pierrick E-print/Working paper (n.d.) Detailed reference viewed: 139 (0 UL) |
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