Math 511A/512A: Cryptography and Error-Correcting Codes
Neal Koblitz
Autumn/Winter 1999-2000, MWF 10:30-11:20
During the first quarter we will study the theory of error-correcting
codes. I will use a textbook by Vanstone and van Oorschot, supplemented
by a survey of Algebraic Geometry Codes by Høholdt, van Lint, and
Pellikaan. We will cover cyclic and BCH codes, with emphasis on practical
error-correcting. Then in a more theoretical vein we will examine
the role of the Riemann-Roch theorem and other concepts of algebraic geometry
in the construction of codes with good parameters.
The second quarter will be devoted to cryptography. We will use
my book Algebraic Aspects of Cryptography, supplemented with papers
on the NTRU system and lattice-basis reduction.
Prerequisite: the graduate algebra sequence, or some other strong
introduction to algebra.