Number-Theoretic Algorithms

on Number - Theoretic Algorithms

Most of the algorithms described in these notes take as input a few, typically two, integers, and are required to do simple arithmetic operations over them. In the rest of this course, we assumed that arithmetic operations over two integers could be done in unit time, and that an arbitrary input could fit into one register of memory. Such a model was justified for applications where the input i...

Number Theoretic Algorithms and Cryptology

Elliptic Curves and Number-Theoretic Algorithms

Derandomizing Some Number-theoretic and Algebraic Algorithms

Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms

Over the past five years a number of algorithms decoding some well-studied error-correcting codes far beyond their “error-correcting radii” have been developed. These algorithms, usually termed as listdecoding algorithms, originated with a list-decoder for Reed-Solomon codes [36, 17], and were soon extended to decoders for Algebraic Geometry codes [33, 17] and as also some number-theoretic code...