On walks of variable length in the Schubert incidence systems and multivariate flow ciphers

TitleOn walks of variable length in the Schubert incidence systems and multivariate flow ciphers
Publication TypeJournal Article
Year of Publication2014
AuthorsUstimenko, VA
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
SectionInformation Science and Cybernetics
Date Published3/2014

The flow cipher algorithm based on walks at the flag variety of a Schubert system over the finite commutative ring is proposed. The restriction of the incidence relation of the geometry of a finite simple Lie group of the normal type on the union of large Schubert cells of the maximal dimension is an example of the Schubert system. More general examples are connected with Kac–Moody groups. We introduce some applications of such ciphers based on periodic walks for the construction of multivariate private keys, security of which is connected with the discrete logarithm problem for cyclic subgroups of polynomial transformations of increasing order.

Keywordsflow ciphers, Schubert incidence, walks

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