An introduction to mathematical cryptography

Name: An introduction to mathematical cryptography
ISBN: 0387779930

by Jeffrey Hoffstein · first published 2008

6mentions

5recommended by

5HN commenters

2014–2025first – last mentioned

100% recommend

Why HN recommends it

Rigorous yet approachable introduction to the number theory and lattice math behind modern cryptography. It serves as a standard text for learning the mathematics beyond the basics.

Summarised by Claude from recommending comments

Security & Privacy

This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: * classical cryptograp

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What Hacker News says

tptacek · May 27, 2022 · Recommends

…Engineering_: https://www.amazon.com/Cryptography-Engineering-Principles-P... --- dated, a little wrong about some things, but not insane (like _Applied Cryptography_ is). Hoffman, Pipher, and Silverman's _Introduction to Mathematical Cryptography_: https://www.amazon.com/Introduction-Mathematical-Cryptograph... --- a good first step into theoretical cryptography.
on “Ask HN: Best book on modern cryptography?” ↗
tptacek · Jul 25, 2017 · Recommends

…blog post of the year. LLL comes up a lot in attacks on asymmetric cryptography. If you're interested in crypto or linear algebra but don't know what a lattice is, a great starting point is Hoffstein's _Introduction to Mathematical Cryptography_: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.182... (If you know what a vector space is, you know what a lattice is; it's a vector space where only integers are allowed as coefficients…
on “Building lattice reduction (LLL) intuition” ↗
gradschool · Jun 25, 2021 · Recommends

some "out there" suggestions: - "Extremal Combinatorics" by Staysys Jukna - "Convex Optimization" by Boyd and Vandenberghe - "Delay Insensitive Circuits" [1] - "An Introduction to Mathematical Cryptography" by Hoffstein, Pipher, and Silverman - "Quantum Computing since Democritus" by Scott AAronson [1] https://www.delayinsensitive.com disclosure: I'm the author.
on “Ask HN: Technical Summer Reading List” ↗
ReidZB · May 25, 2014 · Recommends

Mmm, certainly. Hoffstein et al.'s An Introduction to Mathematical Cryptography is a wonderful text, highly thought of, that really is a better choice than the above link for this sort of thing. Another shorter text is Koblitz's A Course in Number Theory and Cryptography, but I think…
on “Mathematical Cryptology [pdf]” ↗
semigroupoid · Aug 27, 2015 · Recommends

…(http://abstract.pugetsound.edu/sage-aata.html) on Abstract Algebra which includes Sage exercises. The most prominent application of number theory in computer science is probably cryptography. I can highly recommend "An Introduction to Mathematical Cryptography" by Hoffstein, Pipher and Silverman in that area.
on “A Computational Introduction to Number Theory and Algebra” ↗
xoa · Oct 6, 2025 · Recommends

…best present path on it. In terms of books, JP Aumasson's "Serious Cryptography" got a 2nd edition not too long ago and the first edition was good. Katz & Lindell's "Modern Cryptography" and Hoffstein's "Introduction to Mathematical Cryptography" are both standard texts that I think a lot of courses still get started with. Finally I've heard good things about Esslinger's "Learning and Experiencing Cryptography with CrypTool and SageMath" from…