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Galois Field arithmetic blocks are the key components in many securityapplications, such as Elliptic Curve Cryptography (ECC) and the S-Boxes of theAdvanced Encryption Standard (AES) cipher. This paper introduces a novelhardware intellectual property (IP) protection technique by obfuscatingarithmetic functions over Galois Field (GF), specifically, focusing onobfuscation of GF multiplication that underpins complex GF arithmetic andelliptic curve point arithmetic functions. Obfuscating GF multiplicationcircuits is important because the choice of irreducible polynomials in GFmultiplication has the great impact on the performance of the hardware designs,and because the significant effort is spent on finding an optimum irreduciblepolynomial for a given field, which can provide one company a competitiveadvantage over another.

Algorithmic Obfuscation over GF($2^m$)