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I'm looking for a good reference, possibly a survey, on the different types of cryptography methods. As far as I understand, the security of a cryptographic method depends on some hardness assumptions, and I've heard of methods based on the hardness of factorization, discrete logarithm, NP-complete problems (such as the Knapsack problem) and problems on lattices.

Is there any good text addressing the different existing paradigms?

In particular, I would be interested on open problems and questions on less studied methods.

Answers for this question may include both references to a text giving an overview of the area but also to specific methods.

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    $\begingroup$ Note that your question covers a huge amount of ground! If you could be more precise in the kinds of applications you are looking for. For example, your question suggests you are more interested in public key methods. $\endgroup$
    – cody
    Commented Jan 24, 2015 at 20:38
  • $\begingroup$ I guess that's a sign of my ignorance on the subject. But yes, I'm mostly interested in public key methods. $\endgroup$
    – Vinicius dos Santos
    Commented Jan 25, 2015 at 2:01
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    $\begingroup$ Have you looked at a textbook like Goldreich's Foundations of Cryptography? $\endgroup$
    – András Salamon
    Commented Feb 10, 2015 at 14:26

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A good start would be Katz and Lindell's Introduction to Modern Cryptography.

Alternatively, you might want to take one of the crypto courses on Coursera: I recommend the ones taught by Jonathan Katz and by Dan Boneh (search for "cryptography" on Coursera). They are both free.

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    $\begingroup$ The courses by Boneh and Katz on Coursera are different. The Boneh course is excellent. $\endgroup$
    – Martin Berger
    Commented Feb 6, 2015 at 21:06
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You might like to look at Bernstein, Buchmann, Dahmen (editors): Post-Quantum Cryptography. The idea of the book is to study what will be available when current methods will become insecure. The book arose via a discussion at an IPAM/UCLA workshop.

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