Research
Prof. Lilya Budaghyan is the leader of Boolean functions research team at the Selmer Center of the University of Bergen.
Her main research interests are in the field of Boolean functions and their applications.
She obtained her PhD degree from the University of Magdeburg (Germany, 2005) and habilitation degree from the University of Paris VIII (France, 2013).
She is the author of the book "Construction and Analysis of Cryptographic Functions", and has been awarded a few prestigious fellowships and awards among which are TMS starting grant award (2016), “Young Research Talent Grant” from Norwegian Research Council (2014), postdoctoral fellowship award from Foundation of Mathematical Sciences of Paris (2012) and Emil Artin Junior Prize in Mathematics (2011). Since 2019 she is a member of the Norwegian Academy of Technological Sciences.
Since 2007 she has been with the University of Bergen (Norway), and as head of the Selmer Center during 2017-2024. Previously, she also conducted her research at the Yerevan State University (Armenia, 1998-2003), University of Magdeburg (Germany, 2003-2005), University of Trento (Italy, 2005-2007), Telecom ParisTech (2011), Universities of Paris VIII and Paris XIII (2012-2013).
Publications
Editorial
- Budaghyan, Lilya; Carlet, Claude Michael; Helleseth, Tor et al. (2024). Editorial: Special issue on Boolean functions and their applications 2023. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor et al. (2023). Editorial: Special issue on Boolean functions and their applications, 2022. (external link)
- Budaghyan, Lilya; Carlet, Claude Michael; Ding, Cunsheng et al. (2022). Editorial: Special issue on Boolean functions and their applications 2021: This special issue is dedicated to the 50th birthday of Vincent Rijmen. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor et al. (2021). Editorial: Special issue on Boolean functions and their applications 2020. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor (2019). Special issue on Boolean functions and their applications 2018. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor (2019). Editorial: Special Issue on Boolean functions and their applications. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor (2019). Editorial: Special issue on Boolean functions and their applications 2018. (external link)
- Budaghyan, Lilya; Helleseth, Tor; Kholosa, Alexander (2016). Editorial: Special issue on Boolean functions and their applications. (external link)
- Budaghyan, Lilya; Helleseth, Tor; Parker, Matthew Geoffrey (2014). Editorial: Special issue on coding and cryptography. (external link)
Academic article
- Budaghyan, Lilya; Pal, Mohit (2024). Arithmetization-oriented APN permutations. (external link)
- Budaghyan, Lilya; Imaña, José L.; Kaleyski, Nikolay Stoyanov (2024). Low-Complexity Hardware Architecture of APN Permutations Using TU-Decomposition. (external link)
- Imaña, José L.; Kaleyski, Nikolay Stoyanov; Budaghyan, Lilya (2023). Hardware architecture of Dillon's APN permutation for different primitive polynomials. (external link)
- Piccione, Enrico; Andreoli, Samuele; Budaghyan, Lilya et al. (2023). An Optimal Universal Construction for the Threshold Implementation of Bijective S-Boxes. (external link)
- Budaghyan, Lilya; Calderini, Marco; Carlet, Claude Michael et al. (2022). On Two Fundamental Problems on APN Power Functions. (external link)
- Gorodilova, A.A.; Tokareva, N.N.; Agievich, S.V. et al. (2022). An overview of the Eight International Olympiad in Cryptography "Non-Stop University CRYPTO". (external link)
- Budaghyan, Lilya; Ivkovic, Ivana; Kaleyski, Nikolay Stoyanov (2022). Triplicate functions. (external link)
- Calderini, Marco; Budaghyan, Lilya; Carlet, Claude Michael (2021). On Known Constructions of APN and AB Functions and their Relation to Each Other. (external link)
- Davidova, Diana; Budaghyan, Lilya; Carlet, Claude Michael et al. (2021). Relation between o-equivalence and EA-equivalence for Niho bent functions. (external link)
- Budaghyan, Lilya; Kaleyski, Nikolay Stoyanov; Riera, Constanza Susana et al. (2021). On the behavior of some APN permutations under swapping points. (external link)
- Yu, Yuyin; Kaleyski, Nikolay Stoyanov; Budaghyan, Lilya et al. (2020). Classification of quadratic APN functions with coefficients in F2 for dimensions up to 9. (external link)
- Budaghyan, Lilya; Calderini, Marco; Carlet, Claude Michael et al. (2020). Generalized isotopic shift construction for APN functions. (external link)
- Budaghyan, Lilya; Calderini, Marco; Villa, Irene (2020). On equivalence between known families of quadratic APN functions. (external link)
- Budaghyan, Lilya; Carlet, Claude Michael; Helleseth, Tor et al. (2020). On the Distance Between APN Functions. (external link)
- Budaghyan, Lilya; Helleseth, Tor; Kaleyski, Nikolay Stoyanov (2020). A New Family of APN Quadrinomials. (external link)
- Budaghyan, Lilya; Calderini, Marco; Carlet, Claude Michael et al. (2020). Constructing APN functions through isotopic shifts. (external link)
- Budaghyan, Lilya; Kaleyski, Nikolay Stoyanov; Riera, Constanza Susana et al. (2020). Partially APN functions with APN-like polynomial representations. (external link)
- Budaghyan, Lilya; Carlet, Claude Michael; Helleseth, Tor (2019). Special issue on Boolean Functions and Their applications. (external link)
- Budaghyan, Lilya; Li, Chunlei; Parker, Matthew Geoffrey (2019). Special Issue on Mathematical Methods for Cryptography. (external link)
- Budaghyan, Lilya; Calderini, Marco; Villa, Irene (2019). On relations between CCZ- and EA-equivalences. (external link)
- Budaghyan, Lilya; Kaleyski, Nikolay Stoyanov; Kwon, Soonhak et al. (2019). Partially APN Boolean functions and classes of functions that are not APN infinitely often. (external link)
- Budaghyan, Lilya; Carlet, Claude Michael; Helleseth, Tor et al. (2018). On Upper Bounds for Algebraic Degrees of APN Functions. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor et al. (2016). On the (non-)existence of APN (n, n)-functions of algebraic degree n. (external link)
- Budaghyan, Lilya; Kholosa, Alexander; Carlet, Claude et al. (2016). Univariate niho bent functions from o-polynomials. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor et al. (2015). On o-equivalence of Niho bent functions. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor et al. (2012). Generalized bent functions and their relation to Maiorana-McFarland class. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor et al. (2012). Further results on Niho bent functions. (external link)
- Budaghyan, Lilya; Kazymyrov, Oleksandr (2012). Verification of Restricted EA-Equivalence for Vectorial Boolean Functions. (external link)
- Budaghyan, Lilya; Helleseth, Tor (2011). ON ISOTOPISMS OF COMMUTATIVE PRESEMIFIELDS AND CCZ-EQUIVALENCE OF FUNCTIONS. (external link)
- Budaghyan, Lilya; Helleseth, Tor (2011). New commutative semifields defined by new PN multinomials. (external link)
- Budaghyan, Lilya; Carlet, Claude (2011). CCZ-equivalence of bent vectorial functions and related constructions. (external link)
- Budaghyan, Lilya; Carlet, Claude (2010). CCZ-equivalence of single and multi output Boolean functions. (external link)
- Budaghyan, Lilya; Helleseth, Tor (2010). Planar functions and commutative semifields. (external link)
- Budaghyan, Lilya; Carlet, Claude; Leander, Gregor (2009). Constructing new APN functions from known ones. (external link)
- Budaghyan, Lilya; Pott, Alexander (2009). On differential uniformity and nonlinearity of functions. (external link)
- Budaghyan, Lilya; Helleseth, Tor (2008). New perfect nonlinear multinomials over F_p^{2k}}for any odd prime p. (external link)
- Budaghyan, Lilya; Carlet, Claude; Leander, Gregor (2008). Two classes of quadratic APN binomials inequivalent to power functions. (external link)
- Budaghyan, Lilya; Carlet, Claude (2008). Classes of quadratic APN trinomials and hexanomials and related structures. (external link)
Doctoral dissertation
Academic lecture
Academic chapter/article/Conference paper
- Budaghyan, Lilya; Calderini, Marco; Carlet, Claude et al. (2019). On Isotopic Shift Construction for Planar Functions. (external link)
- Budaghyan, Lilya; Helleseth, Tor; Li, Nian et al. (2017). Some Results on the Known Classes of Quadratic APN Functions. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor et al. (2012). Generalized bent functions and their relation to Maiorana-McFarland class. (external link)
- Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor (2011). On bent functions associated to AB functions. (external link)
Academic monograph
Academic anthology/Conference proceedings
Projects
- BoolTI: Cryptographic Boolean Functions for Threshold Implementations (10.5 MNOK), 2021-2025 (Principal Investigator: Lilya Budaghyan; other key members: Claude Carlet, George Petrides and Vincent Rijmen)
- Project of Russia Program at Norwegian Center for International Cooperation in Education “Development of a new joint educational program in Information Security and Cryptography at the UiB and Novosibirsk State University” with N.Tokareva for period 02.2019 - 02.2021 (0.3M NOK).
- Eurasia 2017 Project Development Funding Grant for “Development of Education in Computer Science and Applied Mathematics in Armenia” with Yu.Movsisyan and G.Khachatrian for period 10.2017 - 12.2017 (50K NOK).
- Trond Mohn Foundation Recruitment Program Grant for “Optimal Boolean Functions” project for period 05.2017 - 04.2021 (23.5M NOK).
- "Young research talent grant" from Norwegian Research Council for “Discrete Functions and There Applications in Cryptography and Mathematics” for period 09.2014 - 09.2018 (7 M NOK)