A non-interactive (t,n)-publicly veriable secret sharing scheme (non-interactive (t,n)-PVSS scheme) is a (t,n)-secret sharing scheme in which anyone, not only the participants of the scheme, can verify the correctness of the produced shares without interacting with the dealer and participants. The (t,n)-PVSS schemes have found a lot of applications in cryptography because they are suitable for<...

Inthispaper,wepropose twosecureverifiablemulti-secret sharingschemes thatarebasedonnon-homogeneous linearrecursionsandelliptic curvesoverZN .Suchschemeshavesimpleconstructionandverificationphases.Moreover thesehavevarious techniques for the reconstruction phase. The security of the proposed schemes is based on the security of the ECRSA cryptosystem and the intractability of the ECDLP. 2007 Else...

N-chain recursions are important because the majority of single-linear recursions can be compiled to N-chain recursions or so-called bounded recursions [8], which are not recursive at all. It appeared for some time [3, 5] that ALL single linear recursions could be converted to N-chain recursions. Although that is now known [13] to be inaccurate it is still clear that the most popular forms of S...

This paper begins with a brief discussion of a class of polynomial Riemann hypotheses, which leads to the consideration of sequences of orthogonal polynomials and 3-term recursions. The discussion further leads to higher order polynomial recursions, including 4-term recursions where orthogonality is lost. Nevertheless, we show that classical results on the nature of zeros of real orthogonal pol...

The Large Deviation Principle is established for stochastic models defined by past-dependent non linear recursions with small noise. In the Markov case we use the result to obtain an explicit expression for the asymptotics of exit time.