Cryptography

Corresponding entry in Aachen Campus, Bonn University (Lecture, Tutorial).

Lecture

Prof. Joachim von zur Gathen

Tutorial

Konstantin Ziegler

Time & Place

Tuesday, 14⁴⁵-16¹⁵, b-it bitmax
Wednesday, 13⁴⁵-15¹⁵, b-it bitmax
Tutorial 1: Wednesday, 15³⁰-17⁰⁰, b-it bitmax
Tutorial 2: Tuesday, 13⁰⁰-14³⁰, b-it 2.1

First meeting: Tuesday, 28 October 2008, b-it Rheinsaal

No class on Tuesday before Christmas, 23 December 2008

Allocation

4+2 SWS, 8 credits. Optionally, 3+2 SWS, 6 credits.

Successful completion of the course yields 8 credit points. For students who only want 6 credit points, a breakpoint at about 3/4 of the teaching time will be defined, and only the course material up to that point will be relevant for their exams and grades.

Media Informatics: Computer and Communication Technology.
Recommendation for University of Bonn - Computer Science: A or A1, respectively.

Final Exam

The final exam took place

on Tuesday, 17 Febuary 2009, 14.00-17.00
at the bitmax, b-it.

Results at b-it 1.22.

Certificates available at b-it 1.26.

Students who took, but failed the final exam may take the make-up exam

on Tuesday, 11 August 2009, 13.00-16.00
at the bitmax, b-it.

Results at b-it 1.22.

Certificates available at b-it 1.26.

Prerequisites

None.

Cryptography deals with methods for secure data transfer. In earlier times this was the domain of military and intelligence agencies, but today modern cryptography has grown into a key technology, enabling e-commerce and secure internet communications. Its many applications range from credit and debit cards, mobile phones, tv decoders, and electronic money to unforgeable electronic signatures under orders and contracts in the internet. In the course, we first discuss two of the current standard tools, namely AES and RSA. Further topics are key exchange, including group cryptography and discrete logarithm, digital signatures and identification, and cryptographic hash functions.

Lecture notes

are available here regularly.

Assignments

Assignment 1: Arithmetic in F_2⁸ (due November 4th) pdf
Assignment 2: Arithmetic in F_2⁸[y] and Repeated Squaring (due November 12th) pdf
Assignment 3: Carmichael numbers and the Chinese Remainder Theorem (due November 19th) pdf
Assignment 4: Pollard's rho method and polynomial-time reductions (due November 26th) pdf
Assignment 5: RSA, DH and more on orders (due December 4th) pdf
Assignment 6: CRT and Pohlig-Hellman for discrete logarithms (due December 10th) pdf and the 1024-bit prime or exercise 6.2 txt
Assignment 7: Index calculus and hash functions (due December 17th) pdf
Assignment 8: algorithms for the discrete logarithm (due January 07th) pdf
Assignment 9: Identification via Schnorr's identification scheme (due January 20th) pdf
Assignment 10: The ElGamal Signature Scheme (due January 21th) pdf
Assignment 11: Security Reductions (due January 28th) pdf
Assignment 12: Cryptography on Elliptic Curves (due Febuary 4th) pdf

Literature

Mihir Bellare & Shafi Goldwasser (2001). Lecture Notes on Cryptography. PDF.
Johannes A. Buchmann (2004). Introduction to Cryptography. Birkhäuser Verlag, 2nd edition. ISBN 0-387-21156-X (hardcover), 0-387-20756-2. Erratum.
Alfred J. Menezes, Paul C. van Oorschot & Scott A. Vanstone (1997). Handbook of Applied Cryptography. CRC Press, Boca Raton FL. ISBN 0-8493-8523-7. Its homepage includes all chapteres available for free download.
Douglas R. Stinson (2005). Cryptography - Theory and Practice. Discrete Mathematics and its Applications. Chapman \& Hall / CRC Press, Boca Raton FL, 3rd edition. ISBN 1584885084, 600pp. Erratum.
Nigel Smart (2002), Cryptography: An Introduction. McGraw-Hill. ISBN 0-077-09987-7. This first edition is out of print, but a second edition is available online.