Title

Mathematics In Cryptography And Communication

Date of Award

1982

Availability

Article

Degree Name

Doctor of Arts (D.A.)

Department

Mathematics

Abstract

This paper is an introduction to the use of mathematics in two important aspects of electronic communication: reliability and security of cryptographic systems.Chapter I deals with the problem of reliability viewed as that of designing error correcting codes in which an efficient procedure for decoding can be determined. The search for codes, with an algebraic structure that facilitates their implementation, leads through the study of linear and cyclic codes, and culminates on a decoding algorithm for BCH codes.Chapter II deals with the problem of security. The use of maximal length shift register sequences to imitate the unconditionally secure one-time tape system and the use of nonlinear operations to increase the complexity of such sequences are discussed. Some results on sequences generated by shift registers with nonlinear logic are also given. Finally, trapdoor one-way functions are presented as bases for computationally secure public key systems; authentication and signatures are briefly discussed in connection with the RSA public key cryptosystem.

Keywords

Mathematics

Link to Full Text

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