I am taking a number theory course this semester which includes a brief intro to the field of cryptology including only :
Applications to Cryptology, Character Ciphers,Block and stream Ciphers,Exponentiation Ciphers,public key cryptography.

My syllabus does not recommend any good books, just one or two which treat the subject matter very formally from the beginning .

So, can anyone recommend some good books or lecture notes available or video lectures or anything that can help me to make good foundations in this subject apart from covering what is in my syllabus.

Any sort of help is appreciated,

Thanks in advance.

P.S.: I have introduction to mathematical cryptography by Hoffstein, Pipher and Silverman. I havem't checked it out but is it suitable for a beginner?


Unfortunately, there is not ever going to be a single source for this as it covers too many areas. We are dealing with several classes of items here from symmetric, asymmetric, stream, hash functions and random number generators, for example. Each has a different approach to attack. As new ciphers are being generated, they are designed to withstand the currently known attack approaches.

There have been some attempts to write books and here are some examples (listed from easier to harder)

  • Cryptanalysis: A Study of Ciphers and Their Solution, by Helen F. Gaines
  • Elementary Cryptanalysis: A Mathematical Approach, Elementary Cryptanalysis, Abraham Sinkov
  • Cryptanalysis of RSA and Its Variants, by M. Jason Hinek
  • Differential Cryptanalysis of the Data Encryption Standard, by Eli Biham, Adi Shamir
  • Cryptanalysis of Number Theoretic Ciphers (Computational Mathematics), Samuel S. Wagstaff Jr.
  • Algorithmic Cryptanalysis Series, Antoine Joux
  • Modern Cryptanalysis: Techniques for Advanced Code Breaking, Christopher Swenson
  • Algebraic Cryptanalysis, Gregory Bard

If you have the mathematical and creative ability, you need to learn this by seeing what others are doing. You can see the examples that were done for the AES and Secure Hash Algorithm (SHA) competition on the web. There are also the proof side for things like symmetric cipher modes of operation you can review. You should also read and understand the Handbook of Applied Cryptography and its Elliptic Curve partner.

Also, Bruce Schneier has written some very nice items on this very topic and these include:

Here are some of the military examples:

There are probably some Opencourseware items on this topic too that you might want to explore.

  • $\begingroup$ What a nice list here! +1 $\endgroup$
    – amWhy
    Oct 16 '13 at 0:37
  • $\begingroup$ This is a very interesting and challenging area and is always a moving target. Thanks $\endgroup$
    – Amzoti
    Oct 16 '13 at 0:37
  • $\begingroup$ Good morning, Amzoti! I'm hopin' to hit $90$K today. I'll need another "accept" for that, though. I would like to surpass $100$K by the end of the year. We need a woman in those ranks! Once that's done, whenever that happens (if ever) I'll rest comfortably, and make much wiser use of my time!! ;-) $\endgroup$
    – amWhy
    Oct 16 '13 at 13:30
  • $\begingroup$ @amWhy: You deserve it and it is possible! I am reviewing a book a DEQ that was written by a male and female author. It is beautifully written and I know she had a lot to do with that. So yes, we need women in those ranks! I will help all I can! :-) Also, I have been asked to give two talks and want to research some things too, so I love the idea of less MSE so we can get to things that enrich us! $\endgroup$
    – Amzoti
    Oct 16 '13 at 13:32
  • $\begingroup$ the link is now schneier.com/wp-content/uploads/2016/02/paper-self-study.pdf $\endgroup$
    – athos
    Sep 24 '20 at 16:36

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