Fast bit-level, word-level and parallel arithmetic in finite fields for elliptic curve cryptosystems

Graduation date: 1999Computer and network security has recently become a popular subject due to\ud the explosive growth of the Internet and the migration of commerce practices to the\ud electronic medium. Thus the authenticity and privacy of the information transmitted\ud and the data stored on networked computers is of utmost importance.\ud The deployment of network security procedures requires the implementation of\ud cryptographic functions. More specifically, these include encryption, decryption, authentication,\ud digital signature algorithms and message-digest functions. Performance\ud has always been the most critical characteristic of a cryptographic function, which\ud determines its effectiveness.\ud In this thesis, we concentrate on developing high-speed algorithms and architectures\ud for number theoretic cryptosystems. Our work is mainly focused on implementing\ud elliptic curve cryptosystems efficiently, which requires space- and time-efficient\ud implementations of arithmetic operations over finite fields.\ud We introduce new methods for arithmetic operations over finite fields. Methodologies\ud such as precomputation, residue number system representation, and parallel\ud computation are adopted to obtain efficient algorithms that are applicable on a variety\ud of cryptographic systems and subsystems.\ud Since arithmetic operations in finite fields also have applications in coding theory\ud and computer algebra, the methods proposed in this thesis are applicable to these\ud applications as well