Photo:
Randi Heggernes Eilertsen
- E-mailnikolay.kaleyski@uib.no
- Visitor AddressHIB - Thormøhlens gate 555006 Bergen
- Postal AddressPostboks 78035020 Bergen
My research focuses on the analysis and construction of Boolean functions and other functions over finite fields and vector spaces with optimal cryptographic properties (APN functions, planar functions, and others). I am also interested in the design of algorithms for testing properties of such functions, and in efficient implementations of algorithms and search procedures.
Academic article
- (2024). Two New Infinite Families of APN Functions in Trivariate Form. IEEE Transactions on Information Theory. 1436-1452.
- (2023). Hardware architecture of Dillon's APN permutation for different primitive polynomials. Microprocessors and Microsystems: Embedded Hardware Design (MICPRO). 10 pages.
- (2023). An infinite family of 0-APN monomials with two parameters. Cryptography and Communications. 1139-1169.
- (2022). Triplicate functions. Cryptography and Communications. 35-83.
- (2022). On Two Fundamental Problems on APN Power Functions. IEEE Transactions on Information Theory. 3389-3403.
- (2021). On the behavior of some APN permutations under swapping points. Cryptography and Communications. 319-345.
- (2021). Invariants for EA- and CCZ-equivalence of APN and AB functions. Cryptography and Communications. 995-1023.
- (2021). Generalization of a class of APN binomials to Gold-like functions. Lecture Notes in Computer Science (LNCS). 195-206.
- (2021). Deciding EA-equivalence via invariants. Cryptography and Communications. 20 pages.
- (2020). Partially APN functions with APN-like polynomial representations. Designs, Codes and Cryptography. 1159-1177.
- (2020). On the Distance Between APN Functions. IEEE Transactions on Information Theory. 5742-5753.
- (2020). Classification of quadratic APN functions with coefficients in F2 for dimensions up to 9. Finite Fields and Their Applications. 16 pages.
- (2020). A New Family of APN Quadrinomials. IEEE Transactions on Information Theory. 7081-7087.
- (2019). Partially APN Boolean functions and classes of functions that are not APN infinitely often. Cryptography and Communications. 1-19.
- (2019). Changing APN functions at two points. Cryptography and Communications. 1165-1184.
Academic lecture
- (2020). On the sensitivity of some permutation APN functions to swapping points.
- (2018). Partially APN Boolean functions.
Doctoral dissertation
- (2021). Towards a deeper understanding of APN functions and related longstanding problems.
More information in national current research information system (CRIStin)
I can offer master projects on topics related to cryptographic Boolean functions, which may involve implementation/experimental work, mathematical studies, or any combination thereof.
I have supervised the following master projects to their completion:
- On self-equivalences of APN functions, Vegard Jensløkken, 2023
- Computational searches for quadratic APN functions with subfield coefficients, Simon Berg, 2023
- Computational search for isotopic semifields and planar functions in characteristic 3, Markus Bergmann, 2023 (co-supervisor, with L. Budaghyan as main supervisor)
- Classification and computational search for planar functions in characteristic 3, Alise Haukenes, 2022 (co-supervisor, with L. Budaghyan as main supervisor)
- An efficient implementation of a test for EA-equivalence, Marie Heggebakk, 2022 (co-supervisor, with L. Budaghyan as main supervisor)
- Experimental construction of optimal cryptographic functions by expansion, Maren Aleksandersen, 2021 (co-supervisor, with L. Budaghyan as main supervisor)
- Computational investigation of 0-APN monomials, Kjetil Nesheim, 2021 (co-supervisor, with L. Budaghyan as main supervisor)
Fields of competence