Scope: Understand the state-of-the-art for pseudo prime testing (is Frobenius better than Miller-Rabin?). Implement new primitives for pseudo prime testing and "nextprime" to GMP, following given interface guidelines. The implementations need to be so fast that they can replace existing GMP code. This means that work on ultra fast trial division strategies will be needed, in addition to the pseudo prime tests.
Auxillary GMP code for needed primitives exists in the GMP development source tree.
A suitable candidate should live in Stockholm or be willing to relocate to Stockholm. He/she should have relatively good understanding of elementary number theory, and excellent programming skills.
This master thesis task is quite difficult, more difficult than is required for a 20p master thesis.
Scope: Understand FFT and in particular Martin Fürer new FFT algorithm, and implement it so well that its practical usefulness can be assessed. Ref: www.cse.psu.edu/~furer/Papers/mult.pdf.
A suitable candidate should live in Stockholm or be willing to relocate to Stockholm. He/she should have relatively good understanding of elementary number theory, and excellent programming skills.
This master thesis task is very difficult, much more difficult than is required for a 20p master thesis.