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On Proactive Verifiable Secret Sharing Schemes

Nikov, VentzislavNikova, SvetlaPreneel, Bart — 2007

Serdica Journal of Computing

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at the 11th Workshop on Selected Areas in Cryptography (SAC) 2004 This paper investigates the security of Proactive Secret Sharing Schemes. We first consider the approach of using commitment to 0 in the renewal phase in order to refresh the player's shares and we present...

On Distributed Oblivious Transfer

Nikov, VentzislavNikova, SvetlaPreneel, Bart — 2007

Serdica Journal of Computing

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at INDOCRYPT 2002 This paper is about unconditionally secure distributed protocols for oblivious transfer, as proposed by Naor and Pinkas and generalized by Blundo et al. In this setting a Sender has ζ secrets and a Receiver is interested in one of them. The Sender distributes...

On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

Borissov, YuriHo Lee, MoonNikova, Svetla — 2008

Serdica Journal of Computing

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007. In this paper, we study the ratio θ(n) = λ2 (n) / ψ2 (n), where λ2 (n) is the number of primitive polynomials and ψ2 (n) is the number of irreducible polynomials in GF (2)[x] of degree n. Let n = ∏ pi^ri, i=1,..l be the prime factorization of n. We show that, for fixed l and ri , θ(n) is close to 1 and θ(2n) is not less than 2/3 for sufficiently...

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