  The cryptographic protocol based on topological knot theory,recently proposed
by the authors, is improved for what concerns the efficiency of the encoding of
knot diagrams and its error robustness. The standard Dowker-Thistlethwaite
code, based on the ordered assignment of two numbers to each crossing of a knot
diagram and not unique for some classes of knots, is replaced by a system of
eight prototiles (knot mosaics) which, once assembled according to a set of
combinatorial rules, reproduces unambiguously any unoriented knot diagram. A
Reed-Muller scheme is used to encode with redundancy the eight prototiles into
blocks and, once the blank tile is added and suitably encoded, the knot diagram
is turned into an N X N mosaic, uniquely associated with a string of length 4
N^2 bits. The complexity of the knot, measured topologically by the number of
crossings, is in turn polynomially related to the number of tiles of the
associated mosaic, and for knot diagrams of higher complexity the mosaic
encoding provides a design of the knot-based protocol which is fault-tolerant
under random 1-bit flips. It is also argued that the knot mosaic alphabet might
be used in other applications which require high-capacity data transmission.
