Natalia Tokareva

 Senior researcher at the Laboratory of Discrete Analysis in the Sobolev Institute of Mathematics
Associate professor at Novosibirsk State University
A head of the Cryptographic Center (Novosibirsk)
A head of the Laboratory of Cryptography JetBrains Research
A general chair of the International Olympiad in Cryptography NSUCRYPTO
Chief of the Programme "Master in Crypto"

Contacts
Address: Sobolev Institute of Mathematics
4 Acad. Koptyug avenue, 630090 Novosibirsk, Russia
Phone: +007 383 329 76 40; Fax: +007 383 333 25 98
Rooms: 362, 247
e-mail: tokareva at math.nsc.ru
web: www.math.nsc.ru/~tokareva

Research interests
Cryptographic Boolean functions. Block ciphers and S-boxes.
Cryptanalysis of symmetric ciphers. Light-weight cryptography.
Biometric data in cryptography. Blockchains. Quantum cryptography.
Discrete mathematics. Combinatorics. Graph theory. Algebra.

Teaching
Courses on cryptology at the Department of Mechanics and Mathematics in Novosibirsk State University.
Chair of the seminar "Cryptography and cryptanalysis" at the Sobolev Institute of Mathematics.
Supervisor for BS, MS and PhD students in discrete mathematics and cryptology: Cryptographic Center (Novosibirsk)

Profiles at mathematical networks
Math-Net;     ResearchGate;     dblp;     Scopus

PhD supervison
Nikolay Kolomeec (defended in 2014)
Anastasiya Gorodilova (defended in 2016)
Valeria Idrisova (defended in 2019)
Alexander Kutsenko (since 2018)
Alexey Oblaukhov (since 2018)
Polina Sazonova (since 2019)
Dmitrii Kondyrev (since 2019)
Roman Lebedev (since 2019)
Alexander Tkachev (since 2019)
Ilya Koryakin (since 2019)

MS supervison
Alina Belousova (since 2018)
Alexander Shaporenko (since 2018)
Dmitry Bader (since 2018)
Artemii Doronin (since 2018)
Tatiana Kuzmina (since 2018)
George Pintus (since 2018)
Elena Zavalishina (since 2019)
Nikita Zbitnev (since 2019)
Dmitrii Shishlyannikov (since 2019)

Monographs, tutorials

                Tokareva N. Bent functions: results and applications to cryptography // Acad. Press. Elsevier, 2015. 220 pages. ISBN-10: 012802318X. ISBN-13: 978-0128023181. To buy the book click here (Els-Store) or here (Amazon).


Abstract. This book is devoted to such objects of discrete mathematics as Boolean bent functions. These functions have the remarkable property: each of them is on the maximal possible Hamming distance from the class of all affine Boolean functions. This extremal property distinguishes bent functions as the special mysterious class and leads to numerous applications of bent functions in combinatorics, coding theory and cryptography.
In this book the detailed overview of results in bent functions is given. We discuss historical aspects of invention of bent functions and describe their applications in cryptography and discrete mathematics. Basic properties and equivalent representations of bent functions are studied. Detailed classifications of bent functions in small number of variables, combinatorial and algebraic constructions of bent functions are considered. Connections between bent functions and other cryptographic functions are studied. Hamming distances between bent functions and the group of automorphisms of the set of all bent functions are considered. Upper and lower bounds for the number of bent functions and hypotheses on asymptotic value of this number are discussed. A detailed systematic survey on generalizations of bent functions with respect to their algebraic, combinatorial and cryptographic properties is given: we consider at least 25 distinct generalizations. Open problems in bent functions are also discussed.
There are about 125 theorems in bent functions. Some results were presented before only in Russian and are still not widely known. The book is oriented to specialists in Boolean functions and cryptography, professors and students.

      Tokareva N. N. Nonlinear Boolean functions: bent functions and their generalizations // LAP LAMBERT Academic Publishing (Saarbrucken, Germany), 2011. ISBN: 978-3-8433-0904-2. 180 pages, in Russian. (download pdf). To buy the book click here.

      Tokareva N.N. Symmetric cryptography. A short course // Novosibirsk State University, 2012. ISBN: 978-5-4437-0067-0. 234 p., in Russian.

      Gorodilova A. A., Tokareva N. N., Shushuev G. I. Cryptography and cryptanalysis. Mathematical tasks // Novosibirsk State University, 2014. ISBN: 978-5-4437-0226-1. 325 p., in Russian.

Selected articles

  • Agievich S., Gorodilova A., Idrisova V., Kolomeec N., Shushuev G., Tokareva N. Mathematical problems of the Second International Students’ Olympiad in Cryptography // Cryptologia. 2017. Pages 1-32.

  • S. Agievich, A.Gorodilova, N.Kolomeeñ, S.Nikova, B.Preneel, V.Rijmen, G.Shushuev, N.Tokareva, V.Vitkup Problems, solutions and experience of the first international student's Olympiad in cryptography // Applied Discrete Mathematics. 2015. V. 8. N 3. P. 41-62. (eng).

  • B. Bilgin, S. Nikova, V. Nikov, V. Rijmen, N. Tokareva, V. Vitkup Threshold implementations of small S-boxes // Cryptography and Communications. 2015. V. 7. N 1. P. 3-33.

  • Tokareva N.N. On decomposition of a Boolean function into sum of bent functions // Siberian Electronic Math. Reports. 2014. V. 11. P. 745-751. (eng).

  • Tokareva N. Duality between bent functions and affine functions // Discrete Mathematics, V. 312. 2012. P. 666-670.

  • Tokareva N. On the number of bent functions from iterative constructions: lower bounds and hypotheses // Advances in Mathematics of Communications (AMC). 2011. V. 5, N 4. P. 609-621. (eng).

  • Kiselev S. A., Tokareva N. N. On reduction of key space of the cipher A5/1 and on reversibility of the next-state function for a stream generator // Discrete Analysis and Operation Research. 2011. V. 18. N 2. P. 51-63 in Russian. (rus)

  • Tokareva N. N. The group of automorphisms of the set of bent functions // Discrete Mathematics and Applications. 2010. V. 20. N 5-6. P. 655-664. (eng), (rus)

  • Tokareva N. N. Generalizations of bent functions. A survey // Discrete Analysis and Operation Research. 2010. V. 17. N 1. P. 34-64 in Russian. (English translation: Journal of Applied and Industrial Mathematics, 2011, V. 5. N 1. P. 110-129. See also Cryptology ePrint Archive, Report 2011/111. http://eprint.iacr.org). (eng), (rus)

  • Tokareva N. N. Bent functions: results and applications. Survey // Applied Discrete Mathematics. 2009. V. 2. N 1. P. 15-37. (rus)

  • P. Sole, N. Tokareva Connections between quaternary and binary bent functions // Cryptology ePrint Archive, Report 2009/544. http://eprint.iacr.org (eng)

  • PhD Thesis defended November 12, 2008. Advisor: Yuri L. Vasil'ev. Speciality: discrete mathematics and mathematical cybernetics.
    Theme: Strongly nonlinear Boolean functions: bent functions and their generalizations Abstract (in Russian) Thesis (in Russian)
    For english-speakers the summary of the thesis can be found as the paper in proceedings of BFCA 2008.

  • Tokareva N. N. On quadratic approximations in block ciphers // Problems of Inform. Transm. 2008. V. 44. N. 3. P. 266-286. (eng), (rus)

  • Tokareva N. N. Description of k-bent functions in four variables // Discrete Analysis and Operation Research, 2008. V. 15. N. 4. P. 74-83. (eng), (rus)

  • Tokareva N. N. k-Bent functions and quadratic approximations in block ciphers // Proc. Fourth International Workshop "Boolean Functions: Cryptography and Applications" - BFCA 2008. Copenhagen, Denmark. May, 19-21. to appear, 2008. (eng)

  • Solov'eva F. I., Tokareva N. N. The distance regularity of Kerdock codes // Siberian Mathematical Journal. 2008. V. 49. N. 3. P. 668-681. (eng), (rus)

  • Tokareva N. N. On upper bound for the number of uniformly packed binary codes // Discrete Analysis and Operation Research, 2007. V. 14. N. 3. P. 90-97 in Russian
    (English translation: Journal of Applied and Industrial Mathematics, 2008, V. 2. N 3. P. 426-431). (eng), (rus)

  • Tokareva N. N. Bent functions with stronger nonlinear properties: k-bent functions // Discrete Analysis and Operation Research, 2007. V. 14. N. 4. P. 76-102.
    (English translation: Journal of Applied and Industrial Mathematics, 2008, V. 2. N 4. P. 566-584) (eng), (rus)

  • Tokareva N. N. An Upper Bound for the Number of Uniformly Packed Codes // Proc. IEEE International Symposium on Information Theory - ISIT'2007. Nice, France. June, 24-29. pp. 346-350. 2007. (eng)

  • Solov'eva F. I., Tokareva N. N. On the distance nonregularity of Preparata codes // Siberian Mathematical Journal. 2007. V. 48. N. 2. P. 408-416. (eng), (rus)

  • Tokareva N. N. A representation of Z_4-linear Preparata codes using vector fields // Problems of Inform. Transm. 2005. V. 41. N. 2., P. 113-124. (eng) (rus)

  • Tokareva N. N. On the components of Preparata codes // Problems of Inform. Transm. 2004. V. 40. N. 2. P. 159-164. (eng), (rus)