Robust eigenvalue solvers
Researchers
Description
Cryptography is the study of mathematical techniques used to make codes for information security. Conventional cryptography is generally focussed on encryption and decryption to ensure the security of digitally transferred information. It provides confidentiality, user-authentication, data integrity and non-repudiation for many practical applications, from credit card purchases to wireless transactions.
Elliptic curves as algebraic/geometric entities have been studied extensively for the past 150 years, and from these studies has emerged a rich and deep theory. Elliptic curve public key cryptosystems were first proposed in 1985. These systems are based on the discrete logarithm problem in the (additive) group on an elliptic curve over a finite field. This problem is believed to be much more complex than the discrete logarithm problem in a finite field or than integer factorisation, on which other cryptosystems are built. Therefore, smaller block sizes and keys can be used to provide the same security as other cryptosystems. (e.g. RSA)
The research focusses on the mathematical background of the discrete logarithm problem in order to understand and investigate the feasibility of some algorithms to solve this problem on elliptic curves.
A world record "counting points on an elliptic curve" was established by one of our master theses students: Frederic Vercauteren. Here is a newspaper article in Dutch from "Campuskrant", or see the pdf file. Also Veto article (In Dutch) or here.
