Vysoce nelineární funkce a (lehkotonážní) kryptografie

• Thesis title in Czech: Vysoce nelineární funkce a (lehkotonážní) kryptografie
• Thesis title in English: Highly nonlinear functions and (lightweight) cryptography
• Key words: APN funkce, permutační polynomy, lehkotonážní kryptografie
• English key words: APN functions, permutation polynomials, lightweight cryptography
• Academic year of topic announcement: 2017/2018
• Thesis type: dissertation
• Department: Department of Algebra (32-KA)
• Supervisor: doc. Faruk Göloglu, Dr. rer. nat.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 27.09.2018
• Date of assignment: 27.09.2018
• Confirmed by Study dept. on: 29.10.2018

Guidelines

Symmetrical cryptographic algorithms use S-Boxes to introduce confusion to the system which is one of Shannon's principles. One of the most important property of an S-Box is its nonlinearity. The higher nonlinearity the safer an S-Box is against differential cryptanalysis. However the Internet of Things (IoT) puts another constraint on ciphers to be usable: they must be computationally lightweight to be implemented on smaller and slower microchips.

The goal of this dissertation is investigating highly nonlinear (vectorial Boolean) functions, their equivalence to permutations, and also studying their multiplicative complexity. Other cryptographic properties (algebraic degree, differential uniformity, etc.) of these functions and their usability as S-Boxes will also be investigated in the thesis.

References

[1] Y. Crama, P.L. Hammer (Eds.), Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Encycl. Math. Appl., vol.134, Cambridge University Press, Cambridge, 2010.