Boolean functions with multiplicative complexity 3 and 4

Çalık, Çağdaş; Turan, Meltem Sönmez; Peralta, René

doi:10.1007/s12095-020-00445-z

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2022

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“…Unfortunately, computing the multiplicative complexity is intractable [9] and for a random n-variable Boolean function f it is at least 2 n/2 − O(n) with high probability [3]. However, for several families of Boolean functions the multiplicative complexity has been analyzed, including quadratic functions [12], all functions up to 6 variables [5], all functions with a multiplicative complexity of at most 4 [6], all symmetric functions [4], and the Hamming weight function [2].…”

Section: Introductionmentioning

confidence: 99%

The multiplicative complexity of interval checking

Häner¹,

Soeken²

2022

Preprint

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Section: Introductionmentioning

confidence: 99%

The multiplicative complexity of interval checking

Häner¹,

Soeken²

2022

Preprint

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Multiplicative Complexity of XOR Based Regular Functions

Bernasconi

Cimato

Ciriani

et al. 2022

IEEE Trans. Comput.

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XOR-AND Graphs (XAGs) are an enrichment of the classical AND-Inverter Graphs (AIGs) with XOR nodes. In particular, XAGs are networks composed by ANDs, XORs, and inverters. Besides several emerging technologies applications, XAGs are often exploited in cryptography-related applications based on the multiplicative complexity of a Boolean function. The multiplicative complexity of a function is the minimum number of AND gates (i.e., multiplications) that are sufficient to represent the function over the basis {AND, XOR, NOT}. In fact, the minimization of the number of AND gates is important for high-level cryptography protocols such as secure multiparty computation, where processing AND gates is more expensive than processing XOR gates. Moreover, it is an indicator of the degree of vulnerability of the circuit, as a small number of AND gates corresponds to a high vulnerability to algebraic attacks. In this paper we study the multiplicative complexity of Boolean functions characterized by two particular regularities, called autosymmetry and D-reducibility. Moreover, we exploit these regularities for decreasing the number of AND nodes in XAGs. The experimental results validate the proposed approaches.

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Boolean functions with multiplicative complexity 3 and 4

Cited by 2 publications

References 15 publications

The multiplicative complexity of interval checking

The multiplicative complexity of interval checking

Multiplicative Complexity of XOR Based Regular Functions

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