A study of polynomial residue number systems over binary Galois fields GF(2m) for cryptography

This thesis is concerned with GF(2m) Polynomial Residue Number Systems (PRNS)
and their application in cryptography to provide resistance against side-channel-
analysis and protection against fault attacks.
PRNS operations over GF(2m) required in a number of cryptography primitives are
investigated. A partial-conversion method is introduced to simplify the costly
conversion operation and this is then combined with a partial modular reduction
technique and applied to design and implement a PRNS based GF(2m) multiplier with
improved performance.
The Advanced Encryption Standard (AES) is used as vehicle to analyse and quantify
the PRNS overhead where different AES architectures are proposed and implemented.
The PRNS based AES is shown to achieve excellent multiple error coverage with a
reasonable overhead. It is also argued in the thesis, that PRNS AES designs provide
an intrinsic resistance against probing attacks and, due to the introduction of
redundant information and the residue representation replacing the original
representation, exhibit increased confusion and hence enhanced design security.