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Lilya Budaghyan

Researcher
  • 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.

 

Books
  • Budaghyan, Lilya; Helleseth, Tor; Parker, Matthew Geoffrey. 2013. Preproceedings, The International Workshop on Coding and Cryptography WCC 2013. Universitetet i Bergen. 576 pages. ISBN: 978-82-308-2269-2.
Journal articles
  • Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor; Li, Nian. 2016. On the (non-)existence of APN (n, n)-functions of algebraic degree n. IEEE International Symposium on Information Theory. Proceedings. 2016-August: 480-484. doi: 10.1109/ISIT.2016.7541345
  • Budaghyan, Lilya; Helleseth, Tor; Kholosa, Alexander. 2016. Editorial: Special issue on Boolean functions and their applications. Cryptography and Communications. 8: 173-174. doi: 10.1007/s12095-015-0171-4
  • Budaghyan, Lilya; Kholosa, Alexander; Carlet, Claude; Helleseth, Tor. 2016. Univariate niho bent functions from o-polynomials. IEEE Transactions on Information Theory. 62: 2254-2265. doi: 10.1109/TIT.2016.2530083
  • Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor; Kholosa, Alexander. 2015. On o-equivalence of Niho bent functions. Lecture Notes in Computer Science. 9061: 155-168. doi: 10.1007/978-3-319-16277-5_9
  • Budaghyan, Lilya; Helleseth, Tor; Parker, Matthew Geoffrey. 2014. Editorial: Special issue on coding and cryptography. Designs, Codes and Cryptography. 73: 269. doi: 10.1007/s10623-014-9995-8
  • Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor; Kholosa, Alexander. 2012. Generalized bent functions and their relation to Maiorana-McFarland class. IEEE International Symposium on Information Theory. Proceedings. 4 pages.
  • Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor; Kholosa, Alexander; Mesnager, Sihem. 2012. Further results on Niho bent functions. IEEE Transactions on Information Theory. 58: 6979-6985. doi: 10.1109/TIT.2012.2206557
  • Budaghyan, Lilya; Kazymyrov, Oleksandr. 2012. Verification of Restricted EA-Equivalence for Vectorial Boolean Functions. Lecture Notes in Computer Science. 7369. 108-118. doi: 10.1007/978-3-642-31662-3_8
  • Budaghyan, Lilya; Carlet, Claude. 2011. CCZ-equivalence of bent vectorial functions and related constructions. Designs, Codes and Cryptography. 59: 69-87. doi: 10.1007/s10623-010-9466-9
  • Budaghyan, Lilya; Helleseth, Tor. 2011. New commutative semifields defined by new PN multinomials. Cryptography and Communications. 3: 1-16.
  • Budaghyan, Lilya; Helleseth, Tor. 2011. ON ISOTOPISMS OF COMMUTATIVE PRESEMIFIELDS AND CCZ-EQUIVALENCE OF FUNCTIONS. International Journal of Foundations of Computer Science. 22: 1243-1258. doi: 10.1142/S0129054111008684
  • Budaghyan, Lilya; Carlet, Claude. 2010. CCZ-equivalence of single and multi output Boolean functions. Contemporary Mathematics. 518: 43-54.
  • Budaghyan, Lilya; Helleseth, Tor. 2010. Planar functions and commutative semifields. Tatra Mountains Mathematical Publications. 45: 15-25.
  • Budaghyan, Lilya; Carlet, Claude; Leander, Gregor. 2009. Constructing new APN functions from known ones. Finite Fields and Their Applications. 15: 150-159. doi: 10.1016/j.ffa.2008.10.001
  • Budaghyan, Lilya; Pott, Alexander. 2009. On differential uniformity and nonlinearity of functions. Discrete Mathematics. 309: 371-384. doi: 10.1016/j.disc.2007.12.025
  • Budaghyan, Lilya; Carlet, Claude. 2008. Classes of quadratic APN trinomials and hexanomials and related structures. IEEE Transactions on Information Theory. 54: 2354-2357. doi: 10.1109/TIT.2008.920246
  • Budaghyan, Lilya; Carlet, Claude; Leander, Gregor. 2008. Two classes of quadratic APN binomials inequivalent to power functions. IEEE Transactions on Information Theory. 54: 4218-4229. doi: 10.1109/TIT.2008.928275
  • Budaghyan, Lilya; Helleseth, Tor. 2008. New perfect nonlinear multinomials over F_p^{2k}}for any odd prime p. Lecture Notes in Computer Science. 5203: 403-414.
Book sections
  • Budaghyan, Lilya; Helleseth, Tor; Li, Nian; Sun, Bo. 2017. Some Results on the Known Classes of Quadratic APN Functions. Chapter 1, pages 3-16. In:
    • El Hajji, Said; Abderrahmane, Nitaj; Souidi, El Mamoun. 2017. Codes, Cryptology and Information Security. Springer. 384 pages. ISBN: 978-3-319-55589-8.
  • Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor; Kholosa, Alexander. 2012. Generalized bent functions and their relation to Maiorana-McFarland class. Artikkel, pages 1217-1220. In:
    • Caire, Giuseppe; Effros, Michelle; Loeliger, Hans-Andrea; Vardy, Alexander. 2012. Proceedings of 2012 IEEE International Symposium on Information Theory. IEEE conference proceedings. 3175 pages. ISBN: 978-1-4673-2578-3.
  • Budaghyan, Lilya; Carlet, Claude; Helleseth, Tor. 2011. On bent functions associated to AB functions. Artikkel, pages 150-154. In:
    • Joao, Barros; Max, Costa; Jaime, Portugheis. 2011. Proceedings of IEEE Information Theory Workshop 2011. IEEE Press. 726 pages. ISBN: 978-1-4577-0438-3.

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>