Algorithmic Obfuscation over GF($2^m$)

TL;DR

This paper presents a new hardware obfuscation technique for Galois Field arithmetic, especially GF multiplication, to protect intellectual property in cryptographic hardware by complicating the choice of irreducible polynomials.

Contribution

It introduces a novel obfuscation method for GF multiplication circuits, enhancing IP protection by making the selection of irreducible polynomials more challenging.

Findings

Obfuscation increases circuit complexity and security.

The technique complicates the process of identifying the irreducible polynomial used.

Potential to deter IP theft in cryptographic hardware implementations.

Abstract

Galois Field arithmetic blocks are the key components in many security applications, such as Elliptic Curve Cryptography (ECC) and the S-Boxes of the Advanced Encryption Standard (AES) cipher. This paper introduces a novel hardware intellectual property (IP) protection technique by obfuscating arithmetic functions over Galois Field (GF), specifically, focusing on obfuscation of GF multiplication that underpins complex GF arithmetic and elliptic curve point arithmetic functions. Obfuscating GF multiplication circuits is important because the choice of irreducible polynomials in GF multiplication has the great impact on the performance of the hardware designs, and because the significant effort is spent on finding an optimum irreducible polynomial for a given field, which can provide one company a competitive advantage over another.