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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Multivariate polynomial commitment schemes
 Bžatková, Kateřina ; Hubáček, Pavel (advisor) ; Žemlička, Jan (referee)
This thesis focuses on polynomial commitment schemes - cryptographic protocols that allow committing to a polynomial and, subsequently, proving the correctness of evaluations of the committed polynomial at requested points. As our main results, we present new schemes that enable committing to multivariate polynomials and efficiently proving the correctness of evaluations at multiple points. As the main technical tools for our constructions, we use theorems from abstract algebra related to ideals of polynomial rings and some group-theoretic properties. Compared to the state-of-the-art that inspired our work, our main contribution is the improved communication complexity achieved by our protocol.
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Visibly irreducible polynomials
 Bžatková, Kateřina ; Kala, Vítězslav (advisor) ; Tinková, Magdaléna (referee)
Thesis is focused on the irreducibility of polynomials over finite fields. Paper Evan M. O'Dorney, Visibly irreducible polynomials over finite fields, when prooving irreducibility uses visibly irreducible decomposition VID, which is type of decomposition easily determinating irreducibility. In the thesis we analyse in detail results from this paper. Furthermore we generalize the definition of VID from mentioned paper by omitting a condition on any degree of polynomials.
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