论文标题
使用椭圆曲线和应用的伪随机矢量生成
Pseudorandom Vector Generation Using Elliptic Curves And Applications
论文作者
论文摘要
在本文中，我们使用有限场上的椭圆曲线的算术，这是一种在高维度中有效地生成一系列均匀的伪和词的算法，该算法模拟了I.I.D序列的样本。随机变量，具有均匀分布的HyperCube $ [0,1]^D $中的值。作为应用程序，我们在离散时间模拟中获得了一种有效的算法，以模拟一系列独立标准Wiener过程的序列均匀分布的样品路径序列。这可以用于使用，在整个历史记录递归多级PICARD近似方法中，用于求解Kolmogorov类型的半连接抛物线偏微分方程的类别。
In this paper we present, using the arithmetic of elliptic curves over finite fields, an algorithm for the efficient generation of a sequence of uniform pseudorandom vectors in high dimensions, that simulates a sample of a sequence of i.i.d. random variables, with values in the hypercube $[0,1]^d$ with uniform distribution. As an application, we obtain, in the discrete time simulation, an efficient algorithm to simulate, uniformly distributed sample path sequence of a sequence of independent standard Wiener processes. This could be employed for use, in the full history recursive multi-level Picard approximation method, for numerically solving the class of semilinear parabolic partial differential equations of the Kolmogorov type.
