Cryptography - Sage

PrefaceWhen embarking on a project to write a book in a subject saturated with such books,the natural question to ask is: what niche does this book fill not satisfied by other bookson the subject? The subject of cryptography attracts participants from many academicdisciplines, from mathematics to computer science and engineering. The goal of this bookis to provide an introduction which emphasizes the mathematical and algorithmic componentsand building blocks suitable for mathematics students, while liberally illustrating thetheory with examples. Most textbooks for a mathematics audience limit themselves to penand paper calculations, which fails to give the student a sense of either the asymptotic complexityfor the algorithms or access to a practical range for cryptographic study. Textbookswhich take a computational view usually miss the conceptual framework of the mathematics,and are either tied to a particular commercial software package or emphasize low-levelcomputations in C or Java which requires a stronger computer science background. Wechoose to use the computer algebra system SAGE for experimental exploration, since thispackage is both freely available and designed for intuitive interactive use. We hope thatthis book will fill a niche by emphasizing a mathematical presentation of structures incryptography, without sacrificing the explicit exploration of the field.1