Instructor : Dr. Ben Arazi
Professor of CECS
Phone : (502) 852 – 6304
E-mail : arazi@louisville.edu
Computer arithmetic methods in cryptography : Various modular exponentiation methods. Various hardware implementations of modular multipliers. Implementations over integers and over fields of characteristic 2. The use of shift registers and Linear Feedback Shift Registers. Montgomery arithmetic in the bit level and character level, over various fields. Euclid and Extended Euclid in software and hardware, over various fields. ECC implementations. Point doubling and point halving. Smartcard architectures.
References : Articles from the open literature.
Information reliability and error correcting codes : Parity equations, parity checks and the parity check matrix of a linear code. The error detection and error correction capability of a code. Hamming codes. Cyclic codes. Maximal length sequences. Reed-Solomon codes. BCH codes. Burst error detection and correction. Fire codes. Convolutional codes. Diffuse error correction convolutional codes. Turbo codes. Hardware and software considerations.
Textbook : Richard E. Blahut, Algebraic Codes for Data Transmission, Cambridge University Press, 2002, ISBN: 0521553741
