Algebraic Analysis of Variants of Multi-State k-out-of-n Systems

We apply the algebraic reliability method to the analysis of several variants of multi-state k-out-of-n systems. We describe and use the reliability ideals of multi-state consecutive k-out-of-n systems with and without sparse, and show the results of computer experiments on these kinds of systems. We also give an algebraic analysis of weighted multi-state k-out-of-n systems and show that this provides an efficient algorithms for the computation of their reliability.

A White-Box Implementation of IDEA

IDEA is a classic symmetric encryption algorithm proposed in 1991 and widely used in many applications. However, there is little research into white-box IDEA. In traditional white-box implementations of existing block ciphers, S-boxes are always converted into encoded lookup tables. However, the algebraic operations of IDEA without S-boxes, make the implementation not straight forward and challenging. We propose a white-box implementation of IDEA by applying a splitting symmetric encryption method, and verify its security against algebraic analysis and BGE-like attacks. Our white-box implementation requires an average of about 2800 ms to encrypt a 64-bit plaintext, about 60 times more than the original algorithm would take, which is acceptable for practical applications. Its storage requirements are only about 10 MB. To our knowledge, this is the first public white-box IDEA solution, and its design by splitting can be applied to similar algebraic encryption structures.

Ideals in residuated lattices

"The notion of ideal in residuated lattices is introduced in [Kengne, P. C., Koguep, B. B., Akume, D. and Lele, C., L-fuzzy ideals of residuated lattices, Discuss. Math. Gen. Algebra Appl., 39 (2019), No. 2, 181–201] and [Liu, Y., Qin, Y., Qin, X. and Xu, Y., Ideals and fuzzy ideals in residuated lattices, Int. J. Math. Learn & Cyber., 8 (2017), 239–253] as a natural generalization of that of ideal in MV algebras (see [Cignoli, R., D’Ottaviano, I. M. L. and Mundici, D., Algebraic Foundations of many-valued Reasoning, Trends in Logic-Studia Logica Library 7, Dordrecht: Kluwer Academic Publishers, 2000] and [Chang, C. C., Algebraic analysis of many-valued logic, Trans. Amer. Math. Soc., 88 (1958), 467–490]). If A is an MV algebra and I is an ideal on A then the binary relation x ∼I y iff x^{*}Ꙩ y; x Ꙩy^{*} ∈ I , for x; y ∈ A; is a congruence relation on A. In this paper we find classes of residuated lattices for which the relation ∼ I (defined for MV algebras) is a congruence relation and we give new characterizations for i-ideals and prime i-ideals in residuated lattices. As a generalization of the case of BL algebras (see [Lele, C. and Nganou, J. B., MV-algebras derived from ideals in BL-algebras, Fuzzy Sets and Systems, 218 (2013), 103–113]), we investigate the relationship between i-ideals and deductive systems in residuated lattices."

Total Differentiability and Monogenicity for Functions in Algebras of Order 4

In this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.