Cryptology ePrint Archive: Report 2020/1562

A complete study of two classes of Boolean functions for homomorphic-friendly stream ciphers

Claude Carlet and Pierrick Méaux

Abstract: In this paper, we completely study two classes of Boolean functions that are suited for hybrid symmetric-FHE encryption with stream ciphers like FiLIP. These functions (which we call homomorphic-friendly) need to satisfy contradictory constraints: 1) allow a fast homomorphic evaluation, and have then necessarily a very elementary structure, 2) be secure, that is, allow the cipher to resist all classical attacks (and even more, since guess and determine attacks are facilitated in such framework). Because of constraint 2, these functions need to have a large number of variables (often more than 1000), and this makes even more difficult to satisfy constraint 1 (hence the interest of these two classes). 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, dimension of the space of annihilators of minimal degree). This is the first time that this is done for all functions in classes of a sufficient cryptographic interest.

Category / Keywords: secret-key cryptography / Boolean Functions, (Improved) Filter Permutator, Homomorphic Encryption

Date: received 14 Dec 2020

Contact author: pierrick meaux at uclouvain be,claude carlet@gmail com

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Version: 20201217:094058 (All versions of this report)

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