A Course in Mathematical Cryptography

11 Platform Groups and Braid Group Cryptography

11.1 Cryptographic Platforms and Platform Groups

If a cryptographic protocol is based on an algebraic object, e.g., group, ring, lattice, or finite field, then this object is called the cryptographic platform or platform. In group-based cryptography this is then a platform group for the cryptographic protocol. The security of the cryptographic protocol is then dependent upon the difficulty, computational or theoretic, of solving a group theoretic problem within the platform group.

To be a reasonable platform group for a group based cryptographic protocol, a group G must possess certain properties that make the protocol both efficient to implement and secure.

We assume that the group G has a finite ...