
{"publication_number": "US-6493449-B2", "abstract": "the present invention is a method and apparatus for providing cryptographically secure algebraic key establishment protocols that use monoids and groups possessing certain algorithmic properties . special fast algorithms associated with certain monoids and groups are used to optimize both key agreement and key transport protocols . the cryptographic security of the algorithms is based on the difficulty of solving the conjugacy problem in groups and other known hard algebraic problems . braid groups and their associated algorithms are the basis for highly rapid key agreement and key transport protocols which employ modest computational resources .", "application_number": "US-3093598-A", "description": "a preferred embodiment of an apparatus which performs an algebraic key agreement protocol based on keas will now be described in detail . the algebraic key - agreement protocol requires an apparatus which can perform monoid multiplication . a preferred exemplary embodiment of such an apparatus is depicted with block diagrams in fig1 and is described as follows . let ( u , \u03b8 u ) denote a monoid whose generating set { u 1 , u 2 , . . . 