Cryptography WS 2013/2014

News | Dates | Grading | Content | Exercises | Material

Password for the slides (new "feature")

As I hopefully have some time now to update this somewhat regularly, from now on you will have to solve some little exercises to access the slides.

The answers to the exercises will give you the current password then.

The user is always "crypto13" (all lower case).

Note that the password is case-sensitive in general.

• Password "quiz" (17.01.2014):

  Implement the missing code in here.

  You should only (need to) edit main.cpp. The comments will tell you what you have to do.

  (There might be some bugs in the code -- but as long as you don't fix them and add no new bugs it should work; the keccak implementation is taken from [here].)

• Password "quiz" (10.12.2013) (old):

  The password pw to the slides is constructed as follows pw = k1||k2||k3||k4||k5 ("||" denotes the concatenation of strings)

  where k1,k2,k3,k4,k5 are written in decimal and defined as follows:

  • 0<= k1 < 106 is the (unique) solution to 26^k1 ≡₁₀₇ 23 34^(k1) = 101 (mod 107) (34 is only a generator of QR₁₀₇ and thus has only order 53.).
  • 0<= k2 < k3 < k4 < k5 < 55 are the (only) solutions to the equation X² ≡₅₅ 34
  The numbers are small enough to solve the problems using brute force and standard 32bit integers (as long as you do not simply first compute 34^x in its "full glory").

Slides (updated on 03.02.2014)

[PDF]

Annotated slides

No guarantee whatsoever, in particular regarding spelling, read at your own risk!

• 15.10.2013: [PDF]
• 16.10.2013: [PDF]
• 22.10.2013: [PDF]
• 23.10.2013: [PDF]
• 30.10.2013: [PDF]
• 06.11.2013: [PDF]
• 12.11.2013: [PDF]
• 13.11.2013: [PDF]
• 26.11.2013: [PDF]
• 27.11.2013: [PDF] (same set of slides as 26.11.)
• 04.12.2013: [PDF]
• 10.12.2013: [PDF]
• 11.12.2013: [PDF]
• 17.12.2013: [PDF]
• 18.12.2013: [PDF]
• 08.01.2014: [PDF]
• 14.01.2014: [PDF]
• 15.01.2014: [PDF]
• 22.01.2014: [PDF]

References, Further Reading, Tools

• The lecture is mostly based on
  • the Lecture notes by M. Bellare and S. Goldwasser, resp. P. Rogaway, and
  • Introduction to modern cryptography by J. Katz and Y. Lindell, Chapman & Hall/CRC, 2007 (see the library).
• A very comprehensive book on algebra, number theory and their computational aspects is
  • A Computational Introduction to Number Theory and Algebra by Victor Shoup (click the link for the free online version).
  • If you want to toy around with some groups, you might be interested in the "number theory library" by Victor Shoup.
• On Oded Goldreich's homepage you can find several draft versions of books by him on the more theoretical aspects of cryptography, in particular, on the study of cryptographic primitives:
  • Modern Cryptography, Probabilistic Proofs and Pseudorandomness (draft)
  • Foundations of Cryptography (drafts)
• A nice wiki for cryptography: CRYPTUTOR.
• If you want to see, how the cryptographic schemes discussed in the lecture are implemented in practice, have a look at the crypto++ library by Wei Dai.
• Further references
  
  regarding cryptography in general:
  • Lecture notes by Yevgeniy Dodis.
  • Kryptologie, Ch. Karpfinger, H. Kiechle, Vieweg+Teubner 2010
  • Einführung in die Kryptographie, Johannes Buchmann, Springer Verlag, 2010
  • Handbook of applied cryptography, A. Menezes, P. van Oorschot, S. Vanstone, CRC, 2001
    • Free online version
  • Cryptool
  regarding computational complexity:
  • Computational Complexity, S. Arora, B. Barak, Cambridge University Press, 2009
  • Computational Complexity, C. Papadimitriou, Addison Wesley, 1995
  regarding elliptic curves:
  • Elliptic Cruves - Number Theory and Cryptography (2n edition), L. Washington, Chapman & Hall/CRC, 2008
  • Elliptic Curve Public Key Cryptosystems, A. Menezes, Kluwer Academic Publishers, 1993)
  • Elliptische Kurven in der Kryptographie, A. Werner, Springer, 2002