We will discuss signature schemes, protocols for identification and basics of secure multi-party computation.

Mod­ule In­form­a­tion

  • Module III.2.2: Algorithmen II (algorithms II)
  • Module III.2.3: Komplexität und Kryptographie (complexity and cryptography)
  • Course: L.079.05830
  • V2 + Ü1 SWS (contact time)
  • 4 ECTS credits (workload)
  • Useful previous knowledge: Einführung in Kryptographie (German) or any equivalent course
  • This course will be held in english.

For further information see the corresponding section in the module handbook.


  • Important Note: the lecture will only take place during the second half of the semester. The first appointment is on Tuesday, May 31st, 2p.m. Tutorials will start on June 7th.
  • Lecture:
    • Tuesday, 11 - 13 o'clock, F1.110
    • Tuesday, 14 - 16 o'clock, F2.211
  • Tutorials:
    • Tuesday, 16 - 18 o'clock, F2.211

Lec­ture Notes

This course will make use of the literature given below. Beside this, there will be no lecture notes for this course. Extensive lecture notes in cryptography of Luca Trevisan are available online.

Title Slides
1. Introduction [PDF]
2. Signatures [PDF]
3. Identification [PDF]
4. Interactive Protocols [PDF]
5. Proofs of Knowledge [PDF]
6. Witness Indistinguishability [PDF]
7. Commitment Schemes [PDF]


The oral exams for Cryptographic Protocols have to be planned individually. Send your requests of an examination date to Claudia Jahn and the second professor of the module using the email form for the type A exam from


Here we will publish the home exercises. Note that we won't publish any solutions to these exercises. Solutions to selected exercises will be discussed in the tutorials. You can submit your solutions in the box at F2.108.  We encourage submissions of solutions by small groups of up to four students.

Handout 12016-06-03
Handout 22016-06-10
Handout 32016-06-20
Handout 42016-06-24updated 2016-06-27, corrections in Ex. 2; Presentation
Handout 52016-07-05
Handout 62016-07-08updated 2016-07-11, hints added


  • Bellare, Rogaway: Lecture Notes on "Introduction to Modern Cryptography", University of California, San Diego, 2004--2005. Lecture notes available online!
  • Goldreich: "Foundations of Cryptography, Volume 1: Basic Tools", Cambridge University Press, 2001. ISBN: 0-521-79172-3. Early draft version available online!
  • Goldreich: "Foundations of Cryptography, Volume 2: Basic Applications", Cambridge University Press, 2004. ISBN: 0-521-83084-2.
  • Goldwasser, Bellare: Lecture Notes on "Cryptography", MIT, 1996--2001. Lecture notes available online!
  • Katz, Lindell: "Introduction to Modern Cryptography", Chapman & Hall / CRC Press, 2007. ISBN: 1-5848-8551-3
  • Lindell: Lecture Notes on "Introduction to Cryptography", Bar-Ilan University, 2005. Lecture notes available online!
  • Menezes, van Oorschot, Vanstone: "Handbook of Applied Cryptography", CRC Press, 1996. ISBN: 0-8493-8523-7. Complete book available online!
  • Shoup: "A Computational Introduction to Number Theory and Algebra", Cambridge University Press, 2005. ISBN: 0-521-85154-8. Complete book available online!
  • M. Sipser: "Introduction to the Theory of Computation", 3rd edition, Cengage Learning, 2013. ISBN: 1-133-18779-X.
  • Stinson: "Cryptography: Theory and Practice", 2nd edition, Chapman & Hall / CRC Press, 2001. ISBN: 1-5848-8206-9.
  • Trappe, Washington: "Introduction to Cryptography with Coding Theory", 3rd edition, Chapman & Hall / CRC Press, 2005. ISBN: 1-5848-8508-4.
  • Berry Schoenmakers: "Lecture Notes on Cryptographic Protocols", Chapter 4: Identification Protocols, available online