Invariant bilinear forms and its application in information security

The invariant bilinear form is an important tool in the representation theory of algebras. Constructing representation for some algebra groups is desirable for study of the properties of the underlying group. This representation is also very useful for some applications, e.g. the application of cyclic group in information security (cryptographic protocol). In this paper we construct the invariant bilinear forms on the modules of the simple-pointed Hopf algebra R(q,α). In addition, we discuss its application in information security. This construction provides a new group for cryptographic protocol design. It is motivated by the current wide applications of multi-bilinear mappings to information security, especially for the design of multivariable cryptographic protocols, signature schemes, and public key encryptions.