Use of Simple Arithmetic Operations to Construct Efficiently Implementable Boolean functions Possessing High Nonlinearity and Good Resistance to Algebraic Attacks

Claude Carlet; Palash Sarkar

Paper 2024/1305

Use of Simple Arithmetic Operations to Construct Efficiently Implementable Boolean functions Possessing High Nonlinearity and Good Resistance to Algebraic Attacks

Claude Carlet, University of Paris, University of Bergen

Palash Sarkar

, Indian Statistical Institute

Abstract

We describe a new class of Boolean functions which provide the presently best known trade-off between low computational complexity, nonlinearity and (fast) algebraic immunity. In particular, for $n\leq 20$, we show that there are functions in the family achieving a combination of nonlinearity and (fast) algebraic immunity which is superior to what is achieved by any other efficiently implementable function. The main novelty of our approach is to apply a judicious combination of simple integer and binary field arithmetic to Boolean function construction.

Note: A major revision.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint.
Keywords: Boolean function nonlinearity algebraic immunity efficient implementation
Contact author(s): claude carlet @ gmail com
palash @ isical ac in
History: 2025-01-12: revised; 2024-08-21: received; See all versions
Short URL: https://ia.cr/2024/1305
License: CC BY-NC-SA

BibTeX

@misc{cryptoeprint:2024/1305,
      author = {Claude Carlet and Palash Sarkar},
      title = {Use of Simple Arithmetic Operations to Construct Efficiently Implementable Boolean functions Possessing High Nonlinearity and Good Resistance to Algebraic Attacks},
      howpublished = {Cryptology {ePrint} Archive, Paper 2024/1305},
      year = {2024},
      url = {https://eprint.iacr.org/2024/1305}
}