Biography
Hello, I am Koen de Boer, and I love mathematics. I am currently doing a post-doc at the Mathematical Institute of Universiteit Leiden in the field of post-quantum cryptography. Next to mathematics, I have a passion for music as well.
Interests
- Lattices & Cryptography
- Algebraic and Arithmetic Number Theory
- Quantum Algorithms
Education
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PhD in Cryptography, 2022
CWI, Amsterdam
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MSc in Mathematics, 2016
Radboud Universiteit Nijmegen
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BSc in Mathematics, 2013
Radboud Universiteit Nijmegen
Recent Publications
PhD Thesis: Random Walks on Arakelov Class Groups
The main topic of this PhD thesis is the Arakelov ray class group of a number field, an algebraic object that contains both the ideal class group structure and the unit group structure. The main result consists of the fact that certain specific random walks on the Arakelov ray class group result in a target point that is uniformly distributed on this group, under the assumption of an extended version of the Riemann Hypothesis. Almost all other results of this work are consequences of this fact. (Errata)
Random Self-reducibility of Ideal-SVP via Arakelov Random Walks
We prove a worst-case to average-case reduction for Hermite-SVP on ideal lattices by using random-walk techniques over the Arakelov class group. This group can be seen as the group of all ideal lattices associated to a fixed number field, up to isometry.
On the Quantum Complexity of the Continuous Hidden Subgroup Problem
We rigorously prove and bound the complexity of (a variant of) the quantum algorithm solving the Continuous Hidden Subgroup Problem by Eisenträger et al.
Attacks on the AJPS Mersenne-Based Cryptosystem
We introduce and analyze a Meet-in-the-Middle (quantum) attack on the AJPS cryptosystem of Aggarwal et al., based on Mersenne numbers. Next to that we elaborately analyze another attack, proposed by Beunardeau et al., on the same cryptosystem.
Calculating the power residue symbol and ibeta
We show that computations within the unit group of local fields leads to two new algorithms in number theory. One of them is an algorithm computing ‘ibeta’, an object characterizing local fields. The other one is an algorithm computing the power residue symbol.
Recent & Upcoming Talks
Other Projects
My music project TOMB together with Thomas Bronzwaer.
Contact
- Niels Bohrweg 1, Leiden, Zuid-Holland 2333CA