Vectorial Resilient $PC(l)$ of Order $k$ Boolean Functions from AG-Codes

TL;DR

This paper introduces a novel method for constructing vectorial Boolean functions with specific cryptographic properties using algebraic-geometric codes over GF(2^m), enhancing prior constructions based on linear or nonlinear codes.

Contribution

It extends existing Boolean function constructions by utilizing algebraic-geometric codes to achieve desired propagation and resiliency properties.

Findings

Constructs vectorial Boolean functions satisfying $PC(l)$ of order $k$.

Demonstrates improved cryptographic properties over previous methods.

Provides comparative analysis with existing constructions.

Abstract

Propagation criterion of degree $l$ and order $k$ ($PC(l)$ of order $k$) and resiliency of vectorial Boolean functions are important for cryptographic purpose (see [1, 2, 3,6, 7,8,10,11,16]. Kurosawa, Stoh [8] and Carlet [1] gave a construction of Boolean functions satisfying $PC(l)$ of order $k$ from binary linear or nonlinear codes in. In this paper, algebraic-geometric codes over $GF(2^m)$ are used to modify Carlet and Kurosawa-Satoh's construction for giving vectorial resilient Boolean functions satisfying $PC(l)$ of order $k$. The new construction is compared with previously known results.