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The art of cryptography: lattices and cryptography

This course is listed in Aachen Campus as The art of cryptography: lattices and cryptography and in Bonn Basis as MA-INF 1312 The art of cryptography: lattices and cryptography.


Prof. Dr. Joachim von zur Gathen


Dr. Daniel Loebenberger

Time & Place

First meeting: Thursday, 11 April 2013.


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Exam: 19 July 2013, 11:00, b-it

2nd Exam: 28 August 2013, 11:00, b-it


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.


Lattices are of great importance in the design and the analysis of cryptographic algorithms. The most important algorithm is the so called lattice basis reduction, which was invented by Lenstra, Lenstra and Lovasz in 1982 and revolutionized computational aspects of "the geometry of numbers", leading to breakthroughs in fields like computer algebra, cryptography and algorithmic number theory.

The Ajtai-Dwork cryptosystem and NTRU are two examples of lattice-based protocols. The knapsack cryptosystem and the linear congruential pseudo-random generator were completely broken with the help of lattices. They also provide an attack on RSA when partial information about the prime factors or the exponents is known, or when one of the exponents is small.

The course will start with an introduction to lattices. After having explored the main tool of basis reduction, we will delve into the various applications.



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Basic knowledge in cryptography is needed, as for example the course Cryptography held in the previous winter. Compare our programme.



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