IT-Security is a topic of highest relevance in today’s web applications. However, users will only accept the use of protecting tools if they do not slow down efficiency of their system. Most actual cryptographic protocols make use of mathematical developments and algorithms from number theory. Efficient implementation of these is therefore of utmost importance.

Cryptographic protocols like Diffie-Hellman key exchange, RSA, El-Gamal (either on Galois fields or elliptic curves) all require large numbers of arithmetic operations. Efficient use of these protocols thus hinges on efficient implementation of basic arithmetic operations, starting with addition, multiplication, exponentiation, etc., but also the efficient use of these operations as basic building blocks.

The goal of this project is the study of the computational complexity of so called arithmetic circuits, i.e., circuits that have multiplication and addition gates or any other ring operation instead of the usual Boolean gates.

Results of this project will lead to efficient implementations of arithmetic algorithms involved in cryptographic protocols, but also point out efficient hardware solutions (cryptography on a chip).

For more information contact Anselm Haak, +49 511 762 19774 .