Distribution and Polynomial Interpolation of the Dodis-Yampolskiy Pseudo-Random Function

机译：Dodis-Yampolskiy伪随机函数的分布和多项式插值

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We give some theoretical support to the security of the cryptographic pseudo-random function proposed by Dodis and Yampolskiy in 2005. We study the distribution of the function values over general finite fields and over elliptic curves defined over prime finite fields. We also prove lower bounds on the degree of polynomials interpolating the values of these functions in these two settings.

机译：我们为Dodis和Yampolskiy在2005年提出的密码学伪随机函数的安全性提供了一些理论支持。我们研究了该函数值在一般有限域上以及在本征有限域上定义的椭圆曲线上的分布。我们还证明了在这两个设置中对这些函数的值进行插值的多项式的阶数的下界。

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《International workshop on arithmetic of finite fields》|2016年|125-140|共16页
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Thierry Mefenza; Damien Vergnaud;
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Dodis-Yampolskiy pseudo-random function; Discrepancy; Polynomial interpolation; Finite fields; Elliptic curves;

机译：Dodis-Yampolskiy伪随机函数;差异;多项式插值有限域椭圆曲线;

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1. Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses [J] . Tijana Rakic, Zorica Stanimirovic, Aleksandar Denic Journal of Chemometrics . 2013,第12期

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2. Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier Series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions [J] . Boyd J.P., Yu F. Journal of Computational Physics . 2011,第4期

机译：比较用于插值和求解圆盘中泊松方程的七个频谱方法：Zernike多项式，Logan-Shepp脊形多项式，Chebyshev-Fourier级数，圆柱Robert函数，Bessel-Fourier展开，方圆盘共形映射和径向基函数
3. ON INTERPOLATION APPROXIMATION: CONVERGENCE RATES FOR POLYNOMIAL INTERPOLATION FOR FUNCTIONS OF LIMITED REGULARITY [J] . Xiang Shuhuang SIAM Journal on Numerical Analysis . 2016,第4期

机译：关于插值逼近：有限规则函数的多项式插值的收敛速度
4. Distribution and Polynomial Interpolation of the Dodis-Yampolskiy Pseudo-Random Function [C] . Thierry Mefenza, Damien Vergnaud International workshop on arithmetic of finite fields . 2016

机译：Dodis-yampolskiy伪随机函数的分布和多项式插值
5. SELECTED TOPICS IN INTERPOLATION AND APPROXIMATION BY POLYNOMIALS, RATIONAL FUNCTIONS, AND MEROMORPHIC FUNCTIONS [D] . SAFF, EDWARD BARRY -1

机译：通过多项式，有理函数和亚纯函数进行插值和逼近的选定主题
6. Note on Polynomial Interpolation to Analytic Functions [O] . J. L. Walsh 1933

机译：关于解析函数的多项式插值的注记
7. On Interpolation Approximation: Convergence rates for polynomial interpolation for functions of limited regularity [O] . Xiang, Shuhuang 2015

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8. Polynomial Interpolation of Real Functions I: Interpolation in an Interval. [R] . 1993

机译：实函数的多项式插值I：区间插值。

Distribution and Polynomial Interpolation of the Dodis-Yampolskiy Pseudo-Random Function

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