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

2024-08-21

AI Summary

Lightweight cryptographic hardware demands both high security and low computational overhead, yet existing Boolean function constructions struggle to simultaneously optimize nonlinearity, algebraic immunity, and implementation efficiency. Method: This paper proposes a novel construction framework that uniquely integrates integer arithmetic (addition and bit-shift operations) with polynomial operations over the binary field GF(2), enabling synergistic optimization of nonlinearity and algebraic immunity. Contribution/Results: For input sizes (n leq 20), the proposed functions achieve optimal trade-offs among implementation complexity, nonlinearity, and algebraic immunity. All constructed functions significantly outperform state-of-the-art efficient designs while requiring only basic arithmetic operations—addition, subtraction, multiplication, division, and bit-shifts—thus ensuring low hardware cost. Crucially, they exhibit strong resistance against fast algebraic attacks and high unpredictability, satisfying stringent security requirements. The approach is particularly suited for designing lightweight distinguishers and predicate functions in resource-constrained environments.

Technology Category

• Machine Learning: Hardware-aware ML
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 $nleq 20$, 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.

Problem

• Resistant Function
• Efficient Truth Judgment
• Cryptography

Innovation

• Boolean functions
• attack resistance
• efficient computation