On the Multiplicative Complexity of Cubic Boolean Functions

Meltem Sonmez Turan; Rene Peralta

Paper 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.

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

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint. MINOR revision.
Contact author(s): meltemsturan @ gmail com
rene peralta @ nist gov
History: 2021-08-16: received
Short URL: https://ia.cr/2021/1041
License: CC BY

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}
}