Computational Cryptography
Algorithmic Aspects of Cryptology

A guide to cryptanalysis and the implementation of cryptosystems, written for students and security engineers by leading experts.

Joppe Bos (Edited by), Martijn Stam (Edited by)

9781108795937, Cambridge University Press

Paperback / softback, published 2 December 2021

398 pages
22.9 x 15.3 x 2.1 cm, 0.58 kg

'With highly accessible surveys by leading cryptographers, this book hits all pins with a single strike: framing the important area of "computational cryptography" through its fascinating history, peeking into its (no less prominent) future, and celebrating the impactful research career of one of its principal architects, Arjen Lenstra.' Ronald Cramer, CWI Amsterdam and Leiden University

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.

1. Introduction Joppe Bos and Martijn Stam
Part I. Crytanalysis: 2. Lattice attacks on NTRU and LWE – a history of refinements Martin Albrecht and Léo Ducas
3. History of integer factorization Samuel Wagstaff, Jr.
4. Lattice-based integer factorization – an introduction to Coppersmith's Method Alexander May
5. Computing discrete logarithms Rob Granger and Antoine Joux
6. RSA, DH, and DSA in the wild Nadia Heninger
7. A survey of chosen-prefix collisions attacks Marc Stevens
Part II. Implementations: 8. Efficient modular arithmetic Joppe Bos, Thorsten Kleinjung and Daniel Page
9. Arithmetic software libraries Victor Shoup
10. XTR and Tori Martijn Stam
11. History of cryptographic key sizes Nigel Smart and Emmanuel Thomé.

Subject Areas: Number theory [PBH], Mathematics [PB], Coding theory & cryptology [GPJ]