Centre for Information Security and Cryptography
The efficiency of many public key cryptosystems relies on the speed of the arithmetic in various algebraic structures, such as exponentiation in a finite field or adding points on an elliptic curve. Thus, in addition to investigating efficiency improvements to cryptographic schemes themselves, it is important to work towards improving the speed of the underlying arithmetic operations. Furthermore, the same arithmetic is used in algorithms for solving problems arising in computational number theory, including discrete logarithm problems.
At CISaC, our focus is on algorithms for fast arithmetic of divisors on algebraic curves and ideals in global fields, finding invariants of global fields (e.g., regulators, class numbers) and extracting discrete logarithms in various number theoretic settings. This research includes theoretical foundations, algorithm design and analysis, and computer implementation. Much of our work in this area focuses on algorithmic improvements that are verified using highly-optimized software simulations. CISaC's Advanced Cryptography Laboratory includes a Beowulf cluster which we are using to implement and test our algorithms and produce large-scale numerical data. In addition, we partner with the University of Calgary's Advanced Technology Information Processing Systems Laboratory (ATIPS), whose members are involved in designing and building cryptographic custom hardware platforms.