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On the Multiplicative Complexity of Cubic Boolean Functions

Published

Author(s)

Meltem Sonmez Turan, Rene Peralta

Abstract

Multiplicative complexity is a relevant complexity measure for many advanced cryptographic protocols such as multi-party computation, fully homomorphic encryption, and zero-knowledge proofs, where processing AND gates is more expensive than processing XOR gates. For Boolean functions, multiplicative complexity is defined as the minimum number of AND gates that are sufficient to implement a function with a circuit over the basis (AND, XOR, NOT). In this paper, we study the multiplicative complexity of cubic Boolean functions. We propose a method to implement a cubic Boolean function with a small number of AND gates and provide upper bounds on the multiplicative complexity that are better than the known generic bounds.
Citation
Cryptology ePrint Archive
Volume
2021

Keywords

secret-key cryptography, Multiplicative Complexity, Cubic Boolean Function

Citation

Sonmez Turan, M. and Peralta, R. (2021), On the Multiplicative Complexity of Cubic Boolean Functions, Cryptology ePrint Archive, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=932391, https://eprint.iacr.org/2021/1041 (Accessed July 19, 2024)

Issues

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Created August 11, 2021, Updated November 29, 2022