Can anyone suggest me some good books on cryptography? I have just starting studying cryptography but I know elementary number theory, abstract algebra and algorithms. Also please mention the difficulty level of the book.
"Introduction to Modern Cryptography", Jonathan Katz and Yehuda Lindell. This is a great book for learning about provable security.
And for actual crypto protocols and algorithms, there's always the classic: "Handbook of Applied Crypto" by Paul van Oorschot, A. J. Menezes, and Scott Vanstone. This is more a reference book than a textbook. And its available free of cost on one of the authors web-pages.
It depends on what the purpose is, I personally read the A very short introduction to Cryptography which was a perfect guide to someone knowing nothing about this subject. If your purpose is to begin applying readily available algorithms this is a good book. If you want to get in deap and look at the functioning of algorithms you will need something more thorough
I'd recommend "Understanding Cryptography", Christof Paar & Jan Pelzl, if you are self teaching some cryptography. Why? Since it can be really hard to just follow a textbook by yourself, professor Christof Paar uploaded his lectures on youtube (Introduction to Cryptography by Christof Paar) so you can have a more complete experience.
I would have to say that Applied Cryptography by Bruce Schneier is the best I have come across. It's a good introduction, but at the same time have a detailed level.
IMHO a very good book for you may be: J. Hoffstein, J.Pipher, J. H. Silverman, An Introduction to Mathematical Cryptography. ISBN 976-1-4419-2674-6. It is published 2010 in the Springer series Undergraduate Texts in Mathematics.