Habilitation and PhD Theses and Scientific Report

• L.Budaghyan. Construction and Analysis of Cryptographic Functions. Habilitation Thesis, University of Paris 8, Sept. 2013. pdf

• L.Budaghyan. The Equivalence of Almost Bent and Almost Perfect Nonlinear Functions and Their Generalizations. PhD Thesis, Otto-von-Guericke-University Magdeburg, Dec. 2005.

• L.Budaghyan. Classification and decidability of the elementary theories of algebras with hyperidentities of Boolean algebras. Scientific Report. Yerevan State University, (in Russian) 2002.
  
  

  Books

• L.Budaghyan, C.Carlet, T.Helleseth (Edt.). Special Issue on Boolean functions and Their Applications 2018 (to appear in Cryptography and Communications).

• L.Budaghyan, C.Carlet, T.Helleseth (Edt.). Special Issue on Boolean functions and Their Applications 2017, Cryptography and Communications, 2019.

• L.Budaghyan, C.Li, M.Parker (Edt.). Special Issue on Mathematical Methods for Cryptography, Cryptography and Communications, 2019.

• L.Budaghyan, F.Radrigez-Fernandez (Edt.). Post-proceeding of WAIFI 2018 International Conference, Lecture Notes in Computer Science, 2019.

• L.Budaghyan, T.Helleseth, A.Kholosha. Special Issue on Boolean functions and Their Applications. "Cryptography and Communications: Discrete Structures, Boolean Functions and Sequences", 8(2), 2016.

• L.Budaghyan. Construction and Analysis of Cryptographic Functions. Springer Verlag, 168 pages, 2014.

• L.Budaghyan, T.Helleseth, M.Parker (Edt.). Special Issue on Coding and Cryptography. "Designs, Codes and Cryptography", 73(2), 2014.

• L.Budaghyan, T.Helleseth, M.Parker (Edt.). Preproceedings of the International Workshop on Coding and Cryptography WCC 2013, Bergen, Norway, 2013.

• L.Budaghyan. The Equivalence of AB and APN Functions and Their Generalizations. VDM verlag, (92 pages) 2008.
  
  

Papers

• L.Budaghyan, M.Calderini, C.Carlet, R.Coulter, I.Villa. Constructing APN Ffunctions Through Isotopic Shifts. Submitted to IEEE Trans. Inf. Theory.

• L.Budaghyan, N.Kaleyski, S.Kwon, C.Riera, P.Stanica. Partially APN Boolean Functions and Classes of Functions That Are Not APN Infinitely Often. Crypt. and Communications, 2019.

• L.Budaghyan, M.Calderini, I.Villa. On relations between CCZ- and EA-equivalences. Crypt. and Communications, 2019.

• L.Budaghyan, M.Calderini, C.Carlet, R.Coulter, I.Villa. On Isotopic Shift Construction for Planar Functions. Proceeding of ISIT 2019, Paris, France, July 2019.

• L.Budaghyan, M.Calderini, I.Villa. On equivalence between some families of APN functions. Preproceedings of the International Workshop on Coding and Cryptography, WCC 2019, Saint-Jacut-de-la-Mer, France, April 2019.

• L.Budaghyan, M.Calderini, C.Carlet, R.Coulter, I.Villa. Generalized Isotopic Shift of Gold Functions. Preproceedings of the International Workshop on Coding and Cryptography, WCC 2019, Saint-Jacut-de-la-Mer, France, April 2019.

• L.Budaghyan, P.Stanica. What is a cryptographic Boolean function. Notices of American Mathematical Society, 2019.

• L.Budaghyan, M.Calderini, C.Carlet, R.Coulter, I.Villa. Constructing APN functions through isotopic shifts. Proceedings of the Int. Conference on Sequences and Their Applications SETA 2018, Hong Kong, Oct. 2018.

• L.Budaghyan, N.Kaleyski, S.Kwon, C.Riera, P.Stanica. Partially APN Boolean Functions. Proceedings of the Int. Conference on Sequences and Their Applications – SETA 2018, Hong Kong, Oct. 2018.

• L.Budaghyan, C.Carlet, T.Helleseth. N.Li, B.Sun. On upper bounds for algebraic degrees of APN functions. IEEE Trans. on Inform. Theory, 2018.

• L.Budaghyan, T.Helleseth, N.Li, B.Sun: Some Results on the Known Classes of Quadratic APN Functions. C2SI 2017, LNCS, pp.3-16, 2017.

• L.Budaghyan, C.Carlet, T.Helleseth. N.Li. On the (non-)existence of APN (n,n)-functions of algebraic degree n. Proceedings of IEEE Int. Symp. on Inform. Theory, ISIT 2016.

• L.Budaghyan, A.Kholosha, C.Carlet, T.Helleseth. Univariate Niho bent functions from o-polynomials. IEEE Trans. on Inform. Theory 62 (4), pp. 2254-2265, 2016.

• L.Budaghyan, C. Carlet, T. Helleseth, A. Kholosha. On o-equivalence of Niho bent functions. Arithmetics of Finite Fields, WAIFI 2014, Lecture Notes in Comp. Sci. 9061, pp. 155-168, 2015

• L.Budaghyan, C.Carlet, T.Helleseth, A.Kholosha, T.Penttila. Projective equivalence of ovals and EA-equivalence of Niho bent functions, Book of Abstracts of "Finite geometries fourth Irsee conference", 2014.pdf

• L.Budaghyan, C.Carlet, T.Helleseth, A.Kholosha, On o-Equivalence of Niho Bent Functions, Arithmetic of Finite Fields - 5th International Workshop, WAIFI 2014, Revised Selected Papers, Lecture Notes in Computer Science 9061, pp. 155-168, Gebze, Turkey, Sept. 27-28, 2014.

• L.Budaghyan, C.Carlet, T.Helleseth, A.Kholosha. Niho Bent Functions from Quadratic o- Monomials. Proceedings of the IEEE International Symposium on Information Theory, ISIT 2014, Honolulu, HI, USA, July 2014. 

• L.Budaghyan, C.Carlet, T.Helleseth, A.Kholosha, S.Mesnager. Further Results on Niho Bent Functions. IEEE Trans. Inform. Theory, 58(11), pp. 6979-6985, 2012.

• L.Budaghyan, C.Carlet, T.Helleseth, A.Kholosha. Generalized Bent Functions and Their Relation to Maiorana-McFarland Class. Proceedings of the IEEE International Symposium on Information Theory, ISIT 2012, Cambridge, MA, USA, 1-6 July 2012.

• L.Budaghyan, O.Kazymyrov. Verification of Restricted EA-Equivalence for Vectorial Boolean Functions. Proceedings of the International Workshop on the Arithmetic of Finite Fields, WAIFI 2012, Lecture Notes in Computer Science, pp. 108-118, Bochum, Germany, 16-19 July, 2012. 

• L. Budaghyan, C. Carlet, T. Helleseth. On bent functions associated to AB functions. Proceedings of IEEE Information Theory Workshop, ITW'11, Paraty, Brazil, Oct. 2011.

• L. Budaghyan and T. Helleseth. On isotopisms of commutative semifields and CCZ-equivalence of functions. Special Issue on Cryptography of International Journal of Foundations of Computer Science, v. 22(6), pp. 1243-1258 , 2011.

• L. Budaghyan and C. Carlet. CCZ-equivalence of bent vectorial functions and related constructions. Dec. Codes and Cryptogr., v. 59(1-3), pp. 69-87, 2011.

• L. Budaghyan and T. Helleseth. New commutative semifields defined by new PN multinomials. Cryptography and Communications: Discrete Structures, Boolean Functions and Sequences, v. 3(1), pp. 1-16, 2011. 

• L.Budaghyan and T.Helleseth. Planar functions and commutative semifields. "Nilcrypt'10", Tatra Mountains Math. Publication, v. 45, pp. 15-26, 2010.

• L.Budaghyan and C.Carlet. CCZ-equivalence of single and multi output Boolean functions. Post-proceedings of the 9-th International Conference on Finite Fields and Their Applications Fq'09, Contemporary Math., AMS, v. 518, pp. 43-54, 2010.

• L.Budaghyan, C.Carlet, G.Leander. On a construction of quadratic APN functions. Proceedings of IEEE Information Theory Workshop, ITW'09, pp. 374-378, Taormina, Sicily, Oct. 2009.

• L.Budaghyan and T.Helleseth. On commutative semifields of a family of planar functions. Proceedings of International Conference on Computer Science and Information Technologies, CSIT 2009, pp. 129-132, Yerevan, Armenia, Sept. 2009.

• L.Budaghyan and C.Carlet. CCZ-equivalence and Boolean functions. Book of Abstracts of the 9-th International Conference on Finite Fields and Their Applications, Fq'09, Dublin, July 2009.

• L.Budaghyan and C.Carlet. On CCZ-equivalence and its use in secondary constructions of bent functions. Preproceedings of the International Workshop on Coding and Cryptography, WCC 2009, pp. 19-36, Ullensvang, Norway, May 2009.

• L.Budaghyan, C.Carlet, G.Leander. Constructing new APN functions from known ones. Finite Fields and Their Applications 15(2), pp. 150-159, April 2009. 

• L.Budaghyan and A.Pott. On Differential Uniformity and Nonlinearity of Functions. Special Issue of Discrete Mathematics devoted to "Combinatorics 2006", 309(2), pp. 371-384, 2009.

• L.Budaghyan and T.Helleseth. New perfect nonlinear multinomials over F_{p^{2k}} for any odd prime p. Proceedings of Sequences and Their Applications SETA 2008, Lecture Notes in Computer Science 5203, pp. 403-414, Lexington, USA, Sep. 2008.

• L.Budaghyan, C.Carlet, G.Leander. On inequivalence between known power APN functions. Proceedings of the International Workshop on Boolean Functions: Cryptography and Applications, BFCA 2008, Copenhagen, Denmark, May 2008. 

• L.Budaghyan, C.Carlet, G.Leander. Two classes of quadratic APN binomials inequivalent to power functions. IEEE Trans. Inform. Theory, 54(9), pp. 4218-4229, 2008.

• L.Budaghyan and C.Carlet. Classes of Quadratic APN Trinomials and Hexanomials and Related Structures. IEEE Trans. Inform. Theory, 54(5), pp. 2354-2357, 2008.

• L. Budaghyan. The Simplest Method for Constructing APN Polynomials EA-Inequivalent to Power Functions. Proceedings of the International Workshop on the Arithmetic of Finite Fields, WAIFI 2007, Lecture Notes in Computer Science 4547, pp. 177-188, Madrid, Spain, June 2007.

• L.Budaghyan, C.Carlet, G.Leander. Another class of quadratic APN binomials over F_{2^n}: the case n divisible by 4. Proceedings of the International Workshop on Coding and Cryptography, WCC 2007, dedicated to the memory of Hans Dobbertin, pp. 49-58, Versailles, France, Apr. 2007. 

• L.Budaghyan, C.Carlet, P.Felke, G.Leander. An infinite class of quadratic APN functions which are not equivalent to power mappings. Proceedings of the IEEE International Symposium on Information Theory, ISIT 2006, pp. 2637-2641, Seattle, Washington, USA, Jul. 2006.

• L.Budaghyan, C.Carlet, A.Pott. New Classes of Almost Bent and Almost Perfect Nonlinear Functions. IEEE Trans. Inform. Theory, vol. 52, no. 3, pp. 1141- 1152, March 2006.

• L.Budaghyan. On APN and AB polynomials which are not equivalent to power functions. Book of Abstracts of the Workshop on Groebner Bases in Cryptography, Coding Theory, and Algebraic Combinatorics, (poster presentation) Linz, Austria, May 2006.

• L.Budaghyan, C.Carlet, A.Pott. New Constructions of Almost Bent and Almost Perfect Nonlinear Functions. Proceedings of the Workshop on Coding and Cryptography, WCC 2005, pp. 306-315, Bergen, Norway, March 2005. 

• L.Budaghyan, A.Pott. Differentially Uniform and Nonlinear functions. Book of Abstracts of Yet Another Conference on Cryptography, YACC 2004, Book of Abstracts, Porquerolles, France, June 2004. 

• L.Budaghyan, Yu.M.Movsisyan. On Elementary Decidability of Quasi-Boolean Algebras. Book of Abstracts of International Conference "Mathematics in Armenia", Tsahkadzor, Armenia, Oct. 2003.

• L.Budaghyan. Elementary Classification of Quasi-Boolean Algebras. Scientific Notes of YSU, 3(199), pp. 12-20, 2002. 

• L.Budaghyan, Yu.M.Movsisyan. Elementary Theories of Algebras with Hyperidentities of Boolean Algebras. Book of Abstracts of the Scientific Congress of Armenian Mathematical Union, Yerevan, Armenia, 2002.

• L.Budaghyan, Yu.M.Movsisyan. On Hyperidentities of Algebraic Systems. Proceedings of International Conference on Computer Science and Information Technologies, CSIT 2001, Yerevan, Armenia, 2001. 

• L.Budaghyan, Yu.M.Movsisyan. On Algebras with Hyperidentities of Boolean Algebras. Proceedings of Algebra International Conference Dedicated to the 100-th Anniversary of P.S.Novikov, Moscow, Russia, 2001. 

• L.Budaghyan, Yu.M.Movsisyan. Elementary Classification of Algebras with Hyperidentities of Boolean Algebras. Book of Abstracts of the Scientific Congress of Armenian Mathematical Union, Yerevan, Armenia, 2001.