Computational Cryptography: Algorithmic Aspects of Cryptology

The area of computational cryptography is dedicated to the development  of effective methods in algorithmic number theory that improve  implementation of cryptosystems or further their cryptanalysis. This  book is a tribute to Arjen K. Lenstra, one of the key contributors to  the field, on the occasion of his 65th birthday, covering his best-known  scientific achievements in the field. Students and security engineers  will appreciate this no-nonsense introduction to the hard mathematical  problems used in cryptography and on which cybersecurity is built, as  well as the overview of recent advances on how to solve these problems  from both theoretical and practical applied perspectives. Beginning with  polynomials, the book moves on to the celebrated Lenstra–Lenstra–Lovász  lattice reduction algorithm, and then progresses to integer  factorization and the impact of these methods to the selection of strong  cryptographic keys for usage in widely used standards.