Parallel computing of eigenvalue of doubly stochastic matrix

The transition probability matrix of the Markov cipher is doubly stochastic. The eigenvalue of the matrix with maximum magnitude less than one plays an important role in designing the Markov cipher. This paper provides a parallel algorithm for computing the eigenvalue of the doubly stochastic matrix A of size 65535/spl times/65535, which comes from a Markov cipher shrunken model with both 16 bit plaintext and ciphertext. An analysis of the complexity of the parallel algorithm is also considered.