Studies in Cryptological Combinatorics

The key-agreement problem (finding a private key to use for secret messages, otherwise referred to as the public-key distribution problem), was introduced by Diffie and Hellman in 1976. An approach to structuring key-agreement protocols via the use of one-way associative functions was proposed in 1993 by Rabi and Sherman. We propose here a provably strong associative one-way function based upon knot composition (answering an open problem proposed by Rabi and Sherman whether any such associative one-way functions exist). We also introduce and solve a game, exploring its relation to problems in graph and braid theory and develop a new technique for computing whether a graph is n-colorable. En route we look at estimator and prediction problems raised in Classical Probability Theory using Urn problems.