用于随机性提取的线性变换
Linear Transformations for Randomness Extraction
摘要：
信息有效的方法提取随机性从不完美的来源已被广泛研究，但更简单，更快的要求在高速应用程序的随机数产生。在本文中，我们专注于线性结构，即应用线性变换的随机性提取。我们表明，基于稀疏随机矩阵的线性变换是渐近最佳的独立源和固定位源的随机性提取，他们是有效的（可能不是最佳的）从隐马尔可夫源提取随机性。进一步的研究表明，这种结构的灵活性源模型，以及他们优秀的信息保存能力。由于基于稀疏随机矩阵的线性变换计算速度快，易于用FPGA等硬件实现，因此在高速应用中非常有吸引力。此外，我们探索显式构造的转换矩阵。我们表明，原始BCH码的生成矩阵是很好的选择，但线性变换基于这样的矩阵需要更多的计算时间，由于其高密度。
英文摘要：
Information-efficient approaches for extracting randomness from imperfect sources have been extensively studied, but simpler and faster ones are required in the high-speed applications of random number generation. In this paper, we focus on linear constructions, namely, applying linear transformation for randomness extraction. We show that linear transformations based on sparse random matrices are asymptotically optimal to extract randomness from independent sources and bit-fixing sources, and they are efficient (may not be optimal) to extract randomness from hidden Markov sources. Further study demonstrates the flexibility of such constructions on source models as well as their excellent information-preserving capabilities. Since linear transformations based on sparse random matrices are computationally fast and can be easy to implement using hardware like FPGAs, they are very attractive in the high-speed applications. In addition, we explore explicit constructions of transformation matrices. We show that the generator matrices of primitive BCH codes are good choices, but linear transformations based on such matrices require more computational time due to their high densities.
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