Most common public key cryptosystems and public key exchange protocols presently in use, such as the RSA algorithm, Diffie-Hellman, and elliptic curve methods are number theory based and hence dependâ€¦ (More)

There are certain families of words and word sequences (words in the generators of a two-generator group) that arise frequently in the TeichmÃ¼ller theory of hyperbolic three-manifolds and Kleinianâ€¦ (More)

It is proven that the Freiheitssatz holds for all one-relator products of cyclic groups if the relator is cyclically reduced and a proper power. The method of proof involves representing such groupsâ€¦ (More)

The ways in which a nontrivial commutator can be a proper power in a free product of groups are identified. It is well known that in a free group, a nontrivial commutator cannot be a proper power.â€¦ (More)

The prime number theorem, describing the aymptotic density of the prime numbers, has often been touted as the most surprising result in mathematics. The statement and development of the theorem byâ€¦ (More)

We explain and perform the steps for an .n; t/ secret sharing scheme based on the closest vector theorem. We then compare this scheme and its complexity to the secret sharing schemes of both Shamirâ€¦ (More)