A Course in Number Theory and Cryptography (Graduate Texts in Mathematics, 114) Second Edition

I won't be sharing too many textbooks but this one needs attention. Written by Neal Koblitz, one of my favorite mathematicians and the inventor of elliptic curve cryptography. I love two of his books. This is one of them. I'll keep the other book secret until the next part of the series. I love Neal's book because he gets straight to the point and uses a smaller font in his books to pack more information on one page.This is one of the first books I ever read on mathematical foundations of cryptography. It says graduate on the cover but don't listen to that. It's really an undergraduate level book. All you need to know is a bit of algebra. Book starts with a review of several key number theory topics, moves to finite fields, then to the public key cryptography, RSA, zero-knowledge proofs, then primality testing, factoring and finally elliptic curves.This book follows definition-theorem-proof-example style that I like and it has many exercises with answers. If you like math but don't have experience with fundamentals of cryptography then this is the book to get to quickly get yourself up to speed. Fundamentals don't change and once you master what's in this book (shouldn't take more than a week or two if you're smart and dedicated), you'll be able to read any crypto text.I've placed this book #17 in my Top 100 Programming, Computer and Science books list:[...](If this link gets removed, google for >>catonmat top 100 programming computer science books<< to find my article.).

Good

I was a little leery of this book as I'm certainly no William Friedman or Alan Turing. But I was surprised to find the topic not as daunting as I thought although people who lock up when they see formulas may be intimidated at first glance. This book deals with number theory, dealing with some fundamental properties of numbers with application to cryptographic uses. Each section takes you slowly through the theory and provides exercises at the end of each chapter you can work through. (The answers are in the back of the book.) This is a particularly useful book if you are conversant in programming and want to play with certain aspects of number theory and cryptography to 'see how it really works.' It's like a course in tumblers and pins for someone who is fascinated by locks.

This is a great read on the topic from a mathematical perspective. Still, if you believe that cryptography is the only point of this book, you're doing it wrong.

Very useful for understanding cryptography.

on time and as described

Chapters 1 and 2 give some elementary background material on number theory and finite fields. Chapter 3 discusses some old and naive cryptosystems. Chapter 4 discusses public key cryptosystems. In the RSA system, the receiver chooses two large primes p,q and makes public their product pq=n and some integer e relatively prime to phi(n). The sender then sends his message to the power e reduced mod n. To invert this operation one must know phi(n), i.e. one must know the factorisation n=pq. Since factoring big numbers is hard, only the intended receiver will be able to decipher the message instantly. RSA thus uses the fact that multiplying is easy but inverting it is hard; similarly, one can employ other such "trapdoor functions", such as exponentiation in Z/nZ, to create other public key cryptosystems. In chapter 5 we look at various algorithms and tricks for factorisation and primality testing. As for the cryptosystems, classical number theory that is hundreds of years old still provides the best tools (modulo arithmetic, quadratic residues, continued fractions, etc.), and in chapter 6 we see how another classical theory--elliptic curves--also proves to be fruitful in cryptography. The points of an elliptic curve over a finite field form a finite group, which we can use as the basis for new cryptosystems, analogous to how we made cryptosystems out of Z/nZ for instance. And starting with an integer and constructing corresponding finite field elliptic curves we can employ these groups and elliptic curve techniques to give improved algorithms for primality testing and factorisation.

The item is in great conditions!

最初に書いてあるのが、プログラミングの教科書にいつも出てくる、大きなＯ（オー）記法で計算時間を見積もることですが、具体的なプログラミングの方法の話は出てきません、有限時間で答えが出せるかどうかが念頭にある、ということだと思います。A～Zの26文字を26進法の0～25に対応させて、HAPPY÷SADを計算するとか、この26進数では円周率はD.DRS…になるとか、ちょっと自分で計算してみたくなる、面白い例題から話が始まります。紙と鉛筆でもできますが、計算機でやりたい、でもExcelでささっとやるには難しそうだしプログラミングも時間がかかりそうで、「プログラムはここからダウンロードできます」ってどこかに書いてないの？と言いたくなります（書いてません＾＾）。続いて数論の基本事項から有限体と平方剰余、文字の置き換えなどの単純な暗号とその復号、公開鍵暗号の考え方とRSA、素数性（Primality）と素因数分解、最後が楕円曲線です。GTMですが！高校の数学と数論の知識が少しあれば読めるレベルです。ほとんどすべての問題に答も載っているので、一人でこの本で公開鍵暗号について勉強することができると思いますが、練習問題を眺めているだけで楽しくなる本です。ニールコブリッツは楕円曲線暗号の発明者だそうです。

Niveau maths supsBeaucoup d'exercices avec correction. Traite de tous les aspects de la cryptographie avec temps de calcul. Cryptographie symétrique et asymétrique.Le livre de christophe paar sur la cryptographie est plus clair.

I found this to be very thorough, yet interesting to read. It appears, that the author managed to keep the subject interesting, without sacrificing any rigor. The book is self contained, and I did not feel, that the prerequisite in math is that much ( Except for the last chapter on ellliptic curves). If you are interested in how cryptology works, and if you are not simply looking for a cook book, but you really want to know why it works, read this book. For those who want to really become proficient, there are many excercises with complete answers!The book seems to be nearly typo-free, not that usual these days.

Somewhat useful , if u prefer or do masters in mathematics

Quality as expected, took a bit too long.