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
Recommended Citation
Shershin, Carmen Baytan, "Mathematics In Cryptography And Communication" (1982). Dissertations from ProQuest. 1297.
https://scholarlyrepository.miami.edu/dissertations/1297
Link to Full Text
http://access.library.miami.edu/login?url=http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:8227786