  Topological Coding consists of two different kinds of mathematics:
topological structure and mathematical relation. The colorings and labelings of
graph theory are main techniques in topological coding applied in asymmetric
encryption system. Topsnut-gpws (also, colored graphs) have the following
advantages: (1) Run fast in communication networks because they are saved in
computer by popular matrices rather than pictures. (2) Produce easily
text-based (number-based) strings for encrypt files. (3) Diversity of
asymmetric ciphers, one public-key corresponds to more private-keys, or more
public-keys correspond more private-keys. (4) Irreversibility, Topsnut-gpws can
generate quickly text-based (number-based) strings with bytes as long as
desired, but these strings can not reconstruct the original Topsnut-gpws. (5)
Computational security, since there are many non-polynomial (NP-complete,
NP-hard) algorithms in creating Topsnut-gpws. (6) Provable security, since
there are many mathematical conjectures (open problems) in graph labelings and
graph colorings. We are committed to create more kinds of new Topsnut-gpws to
approximate practical applications and antiquantum computation, and try to use
algebraic method and Topsnut-gpws to establish graphic group, graphic lattice,
graph homomorphism etc.
