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I want to self-study some abstract algebra and cryptography during the summer, so what are some of books that are suitable for self-study? I have very limited background in algebra and none in cryptography, and like to learn by examples. Also, please let me know if there are any books on these subjects with solutions to most of the exercises, so I can check on myself. (I saw yunone's post about good algebra books, but I would like to focus more on those with good exercises and detailed solutions.)

All suggestions are welcome! Thank you!!

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up vote 3 down vote accepted

Try An Introduction to Mathematical Cryptography by Hoffstein, Pipher, and Silverman.

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+1 This was the first textbook I read on cryptography. Good level of depth for a first course and it contains all the algebra necessary. – Brandon Carter May 4 '11 at 11:59

Stinson's book is very readable and clear, and develops the algebra needed by itself.

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The book handbook of applied cryptography explains the topic step by step with concrete algorithms, the necessary background in algebra is either explained in full or to the extend that enables the reader to understand what he/she needs to learn from a math book about algebra.

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