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 Discrete Mathematics, Boolean functions, Cryptography, AI security 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).

Academic article

• Samuele Andreoli; Enrico Piccione; Lilya Budaghyan et al. (2025). On Decompositions of Permutations in Quadratic Functions. (external link)
• Lilya Budaghyan; Nikolay Stoyanov Kaleyski; Soonhak Kwon et al. (2019). Partially APN Boolean functions and classes of functions that are not APN infinitely often. (external link)
• Lilya Budaghyan; Claude Carlet (2008). Classes of quadratic APN trinomials and hexanomials and related structures. (external link)
• Lilya Budaghyan; Tor Helleseth (2011). ON ISOTOPISMS OF COMMUTATIVE PRESEMIFIELDS AND CCZ-EQUIVALENCE OF FUNCTIONS. (external link)
• Lilya Budaghyan; Claude Carlet; Tor Helleseth et al. (2012). Generalized bent functions and their relation to Maiorana-McFarland class. (external link)
• Lilya Budaghyan; Alexander Pott (2009). On differential uniformity and nonlinearity of functions. (external link)
• Lilya Budaghyan; Claude Carlet; Tor Helleseth et al. (2015). On o-equivalence of Niho bent functions. (external link)
• Lilya Budaghyan; Chunlei Li; Matthew Geoffrey Parker (2019). Special Issue on Mathematical Methods for Cryptography. (external link)
• Lilya Budaghyan; Ivana Ivkovic; Nikolay Stoyanov Kaleyski (2022). Triplicate functions. (external link)
• Lilya Budaghyan; Claude Michael Carlet; Tor Helleseth et al. (2018). On Upper Bounds for Algebraic Degrees of APN Functions. (external link)
• Lilya Budaghyan; Claude Carlet; Gregor Leander (2009). Constructing new APN functions from known ones. (external link)
• Lilya Budaghyan; Tor Helleseth (2010). Planar functions and commutative semifields. (external link)
• Lilya Budaghyan; Claude Carlet; Tor Helleseth et al. (2012). Further results on Niho bent functions. (external link)
• Lilya Budaghyan; Claude Carlet; Gregor Leander (2008). Two classes of quadratic APN binomials inequivalent to power functions. (external link)
• Enrico Piccione; Samuele Andreoli; Lilya Budaghyan et al. (2023). An Optimal Universal Construction for the Threshold Implementation of Bijective S-Boxes. (external link)
• Lilya Budaghyan; Claude Carlet; Tor Helleseth et al. (2016). On the (non-)existence of APN (n, n)-functions of algebraic degree n. (external link)
• Lilya Budaghyan; Marco Calderini; Irene Villa (2019). On relations between CCZ- and EA-equivalences. (external link)
• Diana Davidova; Lilya Budaghyan; Claude Michael Carlet et al. (2021). Relation between o-equivalence and EA-equivalence for Niho bent functions. (external link)
• Lilya Budaghyan; Claude Michael Carlet; Tor Helleseth et al. (2020). On the Distance Between APN Functions. (external link)
• Lilya Budaghyan; Claude Carlet (2011). CCZ-equivalence of bent vectorial functions and related constructions. (external link)
• Lilya Budaghyan; Mohit Pal (2024). Arithmetization-oriented APN permutations. (external link)
• Lilya Budaghyan; Alexander Kholosa; Claude Carlet et al. (2016). Univariate niho bent functions from o-polynomials. (external link)
• Lilya Budaghyan; Oleksandr Kazymyrov (2012). Verification of Restricted EA-Equivalence for Vectorial Boolean Functions. (external link)
• Lilya Budaghyan; Nikolay Stoyanov Kaleyski; Constanza Susana Riera et al. (2020). Partially APN functions with APN-like polynomial representations. (external link)
• Lilya Budaghyan; Tor Helleseth (2011). New commutative semifields defined by new PN multinomials. (external link)
• Lilya Budaghyan; Marco Calderini; Irene Villa (2020). On equivalence between known families of quadratic APN functions. (external link)
• Marco Calderini; Lilya Budaghyan; Claude Michael Carlet (2021). On Known Constructions of APN and AB Functions and their Relation to Each Other. (external link)
• Lilya Budaghyan; Marco Calderini; Claude Michael Carlet et al. (2020). Constructing APN functions through isotopic shifts. (external link)
• Yuyin Yu; Nikolay Stoyanov Kaleyski; Lilya Budaghyan et al. (2020). Classification of quadratic APN functions with coefficients in F2 for dimensions up to 9. (external link)
• Lilya Budaghyan; Marco Calderini; Claude Michael Carlet et al. (2020). Generalized isotopic shift construction for APN functions. (external link)
• A.A. Gorodilova; N.N. Tokareva; S.V. Agievich et al. (2022). An overview of the Eight International Olympiad in Cryptography "Non-Stop University CRYPTO". (external link)
• Lilya Budaghyan; Claude Carlet (2010). CCZ-equivalence of single and multi output Boolean functions. (external link)
• Samuele Andreoli; Lilya Budaghyan; Robert Coulter et al. (2025). On a classification of planar functions in characteristic three. (external link)
• Lilya Budaghyan; Nikolay Stoyanov Kaleyski; Constanza Susana Riera et al. (2021). On the behavior of some APN permutations under swapping points. (external link)
• Lilya Budaghyan; Tor Helleseth (2008). New perfect nonlinear multinomials over F_p^{2k}}for any odd prime p. (external link)
• Lilya Budaghyan; Marco Calderini; Claude Michael Carlet et al. (2022). On Two Fundamental Problems on APN Power Functions. (external link)
• Lilya Budaghyan; Tor Helleseth; Nikolay Stoyanov Kaleyski (2020). A New Family of APN Quadrinomials. (external link)
• Lilya Budaghyan; José L. Imaña; Nikolay Stoyanov Kaleyski (2024). Low-Complexity Hardware Architecture of APN Permutations Using TU-Decomposition. (external link)
• Lilya Budaghyan; Claude Michael Carlet; Tor Helleseth (2019). Special issue on Boolean Functions and Their applications. (external link)
• José L. Imaña; Nikolay Stoyanov Kaleyski; Lilya Budaghyan (2023). Hardware architecture of Dillon's APN permutation for different primitive polynomials. (external link)

Conference lecture

• Lilya Budaghyan; Nikolay Stoyanov Kaleyski; Soonhak Kwon et al. (2018). Partially APN Boolean functions. (external link)
• Lilya Budaghyan; Nikolay Stoyanov Kaleyski; Constanza Susana Riera et al. (2020). On the sensitivity of some permutation APN functions to swapping points. (external link)

Academic book chapter

• Lilya Budaghyan; Claude Carlet; Tor Helleseth et al. (2012). Generalized bent functions and their relation to Maiorana-McFarland class. (external link)
• Lilya Budaghyan; Marco Calderini; Claude Carlet et al. (2019). On Isotopic Shift Construction for Planar Functions. (external link)
• Lilya Budaghyan; Tor Helleseth; Nian Li et al. (2017). Some Results on the Known Classes of Quadratic APN Functions. (external link)
• Lilya Budaghyan; Claude Carlet; Tor Helleseth (2011). On bent functions associated to AB functions. (external link)

Editorial/Leader article

• Lilya Budaghyan; Claude Carlet; Tor Helleseth et al. (2021). Editorial: Special issue on Boolean functions and their applications 2020. (external link)
• Lilya Budaghyan; Tor Helleseth; Matthew Geoffrey Parker (2014). Editorial: Special issue on coding and cryptography. (external link)
• Lilya Budaghyan; Claude Michael Carlet; Tor Helleseth et al. (2024). Editorial: Special issue on Boolean functions and their applications 2023. (external link)
• Lilya Budaghyan; Claude Carlet; Tor Helleseth et al. (2023). Editorial: Special issue on Boolean functions and their applications, 2022. (external link)
• Lilya Budaghyan; Claude Carlet; Tor Helleseth (2019). Special issue on Boolean functions and their applications 2018. (external link)
• Lilya Budaghyan; Claude Carlet; Tor Helleseth (2019). Editorial: Special Issue on Boolean functions and their applications. (external link)
• Lilya Budaghyan; Tor Helleseth; Alexander Kholosa (2016). Editorial: Special issue on Boolean functions and their applications. (external link)
• Lilya Budaghyan; Claude Michael Carlet; Cunsheng Ding 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)
• Lilya Budaghyan; Claude Carlet; Tor Helleseth (2019). Editorial: Special issue on Boolean functions and their applications 2018. (external link)

Doctoral thesis (PhD)

• Lilya Budaghyan; Nikolay Stoyanov Kaleyski (2021). Towards a deeper understanding of APN functions and related longstanding problems. (external link)
• Bo Sun; Lilya Budaghyan (2018). On Classification and Some Properties of APN Functions. (external link)

Book anthology

• Lilya Budaghyan; Tor Helleseth; Matthew Geoffrey Parker (2013). Preproceedings, The International Workshop on Coding and Cryptography WCC 2013. (external link)

Academic monograph

• Lilya Budaghyan (2018). The Equivalence of APN and AB Functions and Their Generalizations. (external link)

See a complete overview of publications in Cristin.

• Currently a part of Lead AI and several other research projects from NFR (with Vincent Rijmen and Markus Hittmeir as PIs).
• 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)