Oblivious polynomial evaluation is a protocol involving two parties, a sender whose input is a polynomial P , and a receiver whose input is a value α. At the end of the protocol the receiver learns P (α) and the sender learns nothing. We describe efficient constructions for this protocol, which are based on new intractability assumptions that are closely related to noisy polynomial reconstructi...

Delegating the computation of a polynomial to a server in a verifiable way is challenging. An even more challenging problem is ensuring that this polynomial remains hidden to clients who are able to query such a server. In this paper, we formally define the notion of Private Polynomial Evaluation (PPE). Our main contribution is to design a rigorous security model along with relations between th...

The evaluation of several polynomial forms is considered. New algorithms for the evaluation of a polynomial and its derivative, a polynomial at two points, a polynomial of high degree using multiple precision arithmetic, and a bivariate polynomial of the form ~a(i)xiy "-i are presented. Various "coefficient splitting techniques" are introduced in these algorithms and the optimality of certain t...

We outline an approach to enumeration problems which relies on the algebra of free abelian groups, giving as our main application a generalisa-tion of the chromatic polynomial of a simple graph G. Our polynomial lies in the free abelian group generated by the poset K(G) of contractions of G, and reduces to the classical case after a simple substitution. Its main properties may be stated in term...

In this paper, we develop two piecewise polynomial methods for the numerical evaluation of Cauchy Principal Value integrals of oscillatory kind. The two piecewisepolynomial quadratures are compact, easy to implement, and are numerically stable. Two numerical examples are presented to illustrate the two rules developed, The convergence of the two schemes is proved and some error bounds obtai...

We prove that for a subring R⊆Q and free group F of rank at least 2 the length Bousfield's HR-localization tower is ω+ω. The key ingredient proof theory polynomial functors over Q.