Cryptology ePrint Archive: Report 2021/1041

On the Multiplicative Complexity of Cubic Boolean Functions

Meltem Sonmez Turan and 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.

Category / Keywords: secret-key cryptography / multiplicative complexity and Boolean functions and cubic functions

Date: received 11 Aug 2021

Contact author: meltemsturan at gmail com, rene peralta at nist gov

Available format(s): PDF | BibTeX Citation

Note: The work will be presented at Boolean Functions and their Applications (BFA) 2021 workshop.

Version: 20210816:131025 (All versions of this report)

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