  In this work, we present an algorithm for the design of $n\times n$-bits
substitution boxes (S-boxes) based on time series of a discrete dynamical
system with chaotic behavior. The elements of a $n\times n$-bits substitution
box are given by binary sequences generated by time series with uniform
distribution. Particularly, time series with uniform distribution are generated
via two lag time chaotic series of the logistic map. The aim of using these two
lag time sequences is to hide the map used, and thus U-shape distribution of
the logistic map is avoided and uncorrelated S-box elements are obtained. The
algorithm proposed is simple and guarantees the generation of S-boxes, which
are the main component in block cipher, fulfill the strong S-box criteria:
bijective; nonlinearity; strict avalanche criterion; output bits independence
criterion; criterion of equiprobable input/output XOR distribution and; maximum
expected linear probability. The S-boxes that fulfill these criteria are
commonly known as "good S-boxes". Finally, an application based on
polyalphabetic ciphers principle is developed to obtain uniform distribution of
the plaintext via dynamical S-boxes.
