good books on Abstract Algebra and Cryptography for self-study

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!!

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

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.

Introduction to Modern Cryptography by J.Katz and Y.Lindell provides a more formal yet lucid approach, thereby facilitating self-study.

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