Efficient Rijndael Encryption Implementation with Composite Field Arithmetic

Abstract. We explore the use of subfield arithmetic for efficient imple-mentations 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 represen-tation 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 par-allelizable modes of operation, our circuit leads to a high-performance software implementation for Rijndael encryption which offers significant speedup compared to previously reported implementations