good books on Abstract Algebra and Cryptography for self-study

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.

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