Cosine transforms over fields of characteristic 2: Fast computation and application to image encryption

In this paper, we introduce a fast algorithm for computing cosine transforms over fields of characteristic 2 (FFCT). Such transforms, which were recently proposed in the literature, are analogous to real-valued discrete cosine transforms in the same sense in which the finite field Fourier transform (FFFT) is analogous to the discrete Fourier transform. The referred algorithm is based on fast algorithms for computing cyclic convolutions over fields of characteristic 2. In particular, we present an algorithm for an 8-point FFCT over GF(28) and show how such a transform can be used as the basis of an image encryption scheme. We highlight the advantages of this scheme compared to that based on cosine transforms over fields of odd characteristic and perform computer simulations to demonstrate its resistance against the main cryptographic attacks.