We study the problem of Oblivious Polynomial Evaluation (OPE), where one party has a polynomial P and the other party, with an input x, wants to learn P (x) in an oblivious way. Previously existing protocols are based on some intractability assumptions that have not been well studied [10, 9], and these protocols are only applicable for polynomials over finite fields. In this paper, we propose e...

This paper presents two sufficient conditions to ensure a faithful evaluation of polynomial in IEEE-754 floating point arithmetic. Faithfulness means that the computed value is one of the two floating point neighbours of the exact result; it can be satisfied using a more accurate algorithm than the classic Horner scheme. One condition here provided is an a priori bound of the polynomial conditi...

A floating-point error analysis is given for the evaluation of a real polynomial at a real argument by Horner's scheme. A computable error bound is derived. It is observed that when a polynomial has coefficients of constant sign or of strictly alternating sign, one cannot expect better accuracy by reformulating the problem in terms of Chebyshev polynomials. Given that the real polynomial P{x) =...

Side Channel Analysis (SCA) is a class of attacks that exploits leakage of information from a cryptographic implementation during execution. To thwart it, masking is a common countermeasure. The principle is to randomly split every sensitive intermediate variable occurring in the computation into several shares and the number of shares, called the masking order, plays the role of a security par...

Polynomial and rational interpolation and multipoint evaluation are classical subjects, which remain central for the theory and practice of algebraic and numerical computing and have extensive applications to sciences, engineering and signal and image processing. In spite of long and intensive study of these subjects, several major problems remained open. We achieve substantial progress, based ...