Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography

Algorithmic Number Theory provides a systematic exploration of computational methods in number theory and their applications to cryptography and computer science. The book covers fundamental topics including lattices, number fields, curves, and primality testing. The text progresses from basic concepts to advanced algorithms, presenting both theoretical foundations and practical implementations. Each chapter includes detailed proofs, concrete examples, and exercises to reinforce key concepts. The book serves as both a reference work for researchers and a textbook for graduate students in mathematics and computer science. Extensive citations and historical notes place the material in broader mathematical context. This comprehensive treatment connects classical number theory with modern computational techniques, demonstrating the evolving relationship between pure mathematics and practical applications in cryptography and computing.

There are not enough internet reviews to create a summary of this book. Instead, here is a summary of reviews of Jeffrey Shallit's overall work: Jeffrey Shallit's works receive attention primarily from mathematics and computer science academics. His most-cited book "Automatic Sequences: Theory, Applications, Generalizations" (co-authored with Jean-Paul Allouche) has become a technical reference text. Readers praise: - Clear explanations of complex mathematical concepts - Comprehensive coverage of automatic sequences - Detailed examples and proofs - Useful as both a reference and learning tool Common criticisms: - High barrier to entry for non-specialists - Dense technical writing style - Limited introductory material for newcomers to the field The book has a 4.5/5 rating on Google Books (based on 4 reviews) and similar ratings on academic citation platforms. Reader reviews are limited on commercial platforms like Amazon and Goodreads, reflecting its specialized academic audience. One mathematics professor noted: "The text provides a thorough treatment of the subject, though students may need additional background reading to fully grasp the concepts."

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🔢 Jeffrey Shallit is not only a mathematician but also a well-known figure in computer science, serving as a professor at the University of Waterloo since 1990. 🔍 The book bridges pure mathematics with practical applications, particularly in cryptography, making complex number theory concepts accessible to computer scientists and engineers. ⚡ Algorithmic number theory emerged as a distinct field in the 1970s, largely driven by the development of public-key cryptography and the RSA algorithm. 🎯 The lattice-based algorithms discussed in the book have gained renewed importance due to their potential resistance to quantum computing attacks, unlike many current cryptographic methods. 💡 The text includes contributions from multiple experts in the field, making it a collaborative work that brings together various perspectives on algorithmic number theory.