[PDF] Top 20 Constant-Size Commitments to Polynomials and Their Applications

... polynomial commitments and presents our constructions. §4 is devoted to applications while §5 presents some open ...has size O(log n) as compared to O(1) in our scheme, where n is the total number of ... See full document

... Ma and Zhang [], Li [], Wang and Zhang [], Cesarano [], Lee and Wong [] also proved a series of identities involving Chebyshev polynomials. Bhrawy et al. (see [–]) and Bircan and Pommerenke [] obtained ... See full document

... Bernstein-type polynomials, Bernoulli polynomials, Euler numbers and Stirling numbers of the second ...and applications of the Bernstein-type polynomials related to solving high even-order ... See full document

... exponential polynomials and develop the the- ory of new form of Hermite polynomials, which can be constructed using the truncated exponential as a generating ...in applications, with particular ... See full document

... -Stirling polynomials of the first kind and r-truncated λ -Stirling polynomials of the first ...special polynomials for those polynomials. Further, as applications, we show that both of ... See full document

... and polynomials have been used in various applications in such di- verse areas as mathematics, probability and statistics, mathematical physics, and engineer- ...multiplication, polynomials can be ... See full document

... Euler-type polynomials and ...Euler-type polynomials and ...Euler-type polynomials is eigenfunctions for the generalized partial Hecke ...also applications for these polynomials and ... See full document

... In Section 4, we consider the random variable W which denotes the number of Bernoulli trials with common success probability p until the occurrence of the kth con- secutive success or the rth consecutive failure, ... See full document

... Abstract. We investigate the hardness of finding solutions to bivariate polynomial congruences modulo RSA composites. We establish necessary conditions for a bivariate polynomial to be one-way, second preimage re- ... See full document

... and polynomials, see details ...and polynomials, which are related to the many known polynomials and numbers such as Frobenius-Euler polynomials and numbers, Apostol-Euler polynomials ... See full document

... modular polynomials, and by Elkies, using a theory of explicit ...modular polynomials for genus-2 curves whose Jacobians have real multiplication by maximal orders of small ...modular polynomials to ... See full document

... Chebyshev polynomials to study the power sum problem involving Fibonacci and Lucas polynomials and prove some new divisible properties involving these ... See full document

... Considering several factors at the same time and linear combinations of those is at the core of many financial models: Fama and French’s three-factor model for asset returns, Brennan and Schwarz’ two-factor model, Lang- ... See full document

... Bernstein polynomials have been defined and studied in many different ways, for example, by q-series, by complex functions, by p-adic Volkenborn integrals, and many algorithms ... See full document

... These polynomials are very important in different areas of mathematics, and many scholars have studied various properties of them and obtained a series of interesting and important ... See full document

... Equation (.) is important in deriving our results in this paper. The purpose of this pa- per is to investigate some properties of Sheffer sequences of several polynomials arising from umbral calculus. From our ... See full document

... Cover, Weights, Complete Graph, F-polynomial, Incorporated Graph, Proper Complete Graph, Proper Cover, Matching Polynomial.. 1980 AMS SUBJECT CLASSIEICATION CODE..[r] ... See full document

... Ryoo, “On the fermionic p-adic integral representation of Bernstein polynomials associated with Euler numbers and polynomials,” Journal of Inequalities and Applications, vol... Operation[r] ... See full document

... The Boubaker polynomials were established for the first by Boubaker et al. as a guide for solving heat equation inside physical model and then for other physical applications [10,11,12]. During resolution ... See full document

... composable commitments [27,20] are commitment schemes that provably remain se- cure when composed with arbitrary other ...bit commitments based on chosen-ciphertext-secure public-key ...opening ... See full document