Paper 2021/1041 Original: eprint.iacr.org/2021/1041 ↗
On the Multiplicative Complexity of Cubic Boolean Functions
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.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2021-08-16: last updated
- 2021-08-16: published
- Short URL
- https://ia.cr/2021/1041
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2021/1041,
author = {Meltem Sonmez Turan and Rene Peralta},
title = {On the Multiplicative Complexity of Cubic Boolean Functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/1041},
year = {2021},
url = {https://eprint.iacr.org/2021/1041}
}