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We explore the use of subfield arithmetic for efficient implementations of Galois Field arithmetic especially in the context of the Rijndael block cipher. Our technique involves mapping field elements to a composite field representation. We describe how to select a representation which minimizes the computation cost of the relevant arithmetic, taking into account the cost of the mapping as well. Our method results in a very compact and fast gate circuit for Rijndael encryption. In conjunction with bit-slicing techniques applied to newly proposed parallelizable modes of operation, our circuit leads to a high-performance software implementation for Rijndael encryption which offers significant speedup compared to previously reported implementations.

Efficient Rijndael Encryption Implementation with Composite Field Arithmetic