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On the Multiplicative Complexity of Cubic Boolean Functions



Meltem Sonmez Turan, Rene Peralta


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.
Cryptology ePrint Archive


secret-key cryptography, Multiplicative Complexity, Cubic Boolean Function


Sonmez Turan, M. and Peralta, R. (2021), On the Multiplicative Complexity of Cubic Boolean Functions, Cryptology ePrint Archive, [online],, (Accessed July 19, 2024)


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Created August 11, 2021, Updated November 29, 2022