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Lilya Budaghyan

Professor
  • E-mailLilya.Budaghyan@uib.no
  • Phone+47 55 58 42 87+47 930 71 879
  • Visitor Address
    HIB - Thormøhlensgt. 55
    Room 
    5165
  • Postal Address
    Postboks 7803
    5020 Bergen

Characterization, construction and general study of optimal cryptographic functions:

                         Perfect nonlinear (PN) functions

                         Almost perfect nonlinear (APN) functions

                         Bent functions

                         Almost bent (AB) functions

Equivalence realtions for cryptographic functions.

Commutative semifields.

 

Academic article
  • 2020. On equivalence between known families of quadratic APN functions. Finite Fields and Their Applications.
  • 2019. Special issue on Boolean Functions and Their applications. Cryptography and Communications. 1145-1146.
  • 2019. Special Issue on Mathematical Methods for Cryptography. Cryptography and Communications. 363-365.
  • 2019. Partially APN Boolean functions and classes of functions that are not APN infinitely often. Cryptography and Communications. 1-19.
  • 2019. On relations between CCZ- and EA-equivalences. Cryptography and Communications. 85-100.
  • 2018. On Upper Bounds for Algebraic Degrees of APN Functions. IEEE Transactions on Information Theory. 4399-4411.
  • 2016. Univariate niho bent functions from o-polynomials. IEEE Transactions on Information Theory. 2254-2265.
  • 2016. On the (non-)existence of APN (n, n)-functions of algebraic degree n. IEEE International Symposium on Information Theory. Proceedings. 480-484.
  • 2015. On o-equivalence of Niho bent functions. Lecture Notes in Computer Science (LNCS). 155-168.
  • 2012. Verification of Restricted EA-Equivalence for Vectorial Boolean Functions. Lecture Notes in Computer Science (LNCS). 108-118.
  • 2012. Generalized bent functions and their relation to Maiorana-McFarland class. IEEE International Symposium on Information Theory. Proceedings. 4 pages.
  • 2012. Further results on Niho bent functions. IEEE Transactions on Information Theory. 6979-6985.
  • 2011. ON ISOTOPISMS OF COMMUTATIVE PRESEMIFIELDS AND CCZ-EQUIVALENCE OF FUNCTIONS. International Journal of Foundations of Computer Science. 1243-1258.
  • 2011. New commutative semifields defined by new PN multinomials. Cryptography and Communications. 1-16.
  • 2011. CCZ-equivalence of bent vectorial functions and related constructions. Designs, Codes and Cryptography. 69-87.
  • 2010. Planar functions and commutative semifields. Tatra Mountains Mathematical Publications. 15-25.
  • 2010. CCZ-equivalence of single and multi output Boolean functions. Contemporary Mathematics. 43-54.
  • 2009. On differential uniformity and nonlinearity of functions. Discrete Mathematics. 371-384.
  • 2009. Constructing new APN functions from known ones. Finite Fields and Their Applications. 150-159.
  • 2008. Two classes of quadratic APN binomials inequivalent to power functions. IEEE Transactions on Information Theory. 4218-4229.
  • 2008. New perfect nonlinear multinomials over F_p^{2k}}for any odd prime p. Lecture Notes in Computer Science (LNCS). 403-414.
  • 2008. Classes of quadratic APN trinomials and hexanomials and related structures. IEEE Transactions on Information Theory. 2354-2357.
Academic lecture
  • 2018. Partially APN Boolean functions.
Editorial
  • 2019. Special issue on Boolean functions and their applications 2018. Cryptography and Communications.
  • 2019. Editorial: Special issue on Boolean functions and their applications 2018. Cryptography and Communications.
  • 2016. Editorial: Special issue on Boolean functions and their applications. Cryptography and Communications. 173-174.
  • 2014. Editorial: Special issue on coding and cryptography. Designs, Codes and Cryptography. 269.
Academic anthology/Conference proceedings
  • 2013. Preproceedings, The International Workshop on Coding and Cryptography WCC 2013. Universitetet i Bergen.
Academic monograph
  • 2018. The Equivalence of APN and AB Functions and Their Generalizations.
Doctoral dissertation
  • 2018. On Classification and Some Properties of APN Functions.
Academic chapter/article/Conference paper
  • 2019. On Isotopic Shift Construction for Planar Functions. 5 pages.
  • 2017. Some Results on the Known Classes of Quadratic APN Functions. 14 pages.
  • 2012. Generalized bent functions and their relation to Maiorana-McFarland class. 4 pages.
  • 2011. On bent functions associated to AB functions. 5 pages.

More information in national current research information system (CRIStin)

<ul><li>Discrete Functions and Their Application in Cryptography and Mathematics. Yang Research Talant Grant, Norwegian Recearch Council. 2014/2018</li><li>Modern Methods and Tools for Theoretical and Applied Cryptology. FRINATEK, Norwegian Recearch Council. 2015/2020</li><li>Cryptography brings security and freedom. EEA Scholarship Programme Slovakia. 2014/2015</li></ul>