  Two recent Hill cipher modifications which iteratively use interweaving and
interlacing are considered. We show that strength of these ciphers is due to
non-linear transformation used in them (bit-level permutations). Impact of
number of iterations on the avalanche effect is investigated. We propose two
Hill cipher modifications using column swapping and arbitrary permutation with
significantly less computational complexity (2 iterations are used versus 16).
The proposed modifications decrease encryption time while keeping the strength
of the ciphers. Numerical experiments for two proposed ciphers indicate that
they can provide a substantial avalanche effect.
