The min-entropy is a widely used metric to quantify the randomness of generated random numbers in cryptographic applications; it measures the difficulty of guessing the most likely output. An important min-entropy estimator is the compression estimator of NIST Special Publication (SP) 800-90B, which relies on Maurer's universal test. In this paper, we propose two kinds of min-entropy estimators to improve computational complexity and estimation accuracy by leveraging two variations of Maurer's test: Coron's test (for Shannon entropy) and Kim's test (for Renyi entropy). First, we propose a min-entropy estimator based on Coron's test. It is computationally more efficient than the compression estimator while maintaining the estimation accuracy. The secondly proposed estimator relies on Kim's test that computes the Renyi entropy. This estimator improves estimation accuracy as well as computational complexity. We analytically characterize the bias-variance tradeoff, which depends on the order of Renyi entropy. By taking into account this tradeoff, we observe that the order of two is a proper assignment and focus on the min-entropy estimation based on the collision entropy (i.e., Renyi entropy of order two). The min-entropy estimation from the collision entropy can be described by a closed-form solution, whereas both the compression estimator and the proposed estimator based on Coron's test do not have closed-form solutions. By leveraging the closed-form solution, we also propose a lightweight estimator that processes data samples in an online manner. Numerical evaluations demonstrate that the first proposed estimator achieves the same accuracy as the compression estimator with much less computation. The proposed estimator based on the collision entropy can even improve the accuracy and reduce the computational complexity.
翻译:薄荷是用来量化加密应用程序中生成的随机随机数字的常用度量; 它测量了测算最可能产出的难度。 首先, 我们提议以 NIST 特殊出版物(SP) 800- 90B 的压缩估计值为重要 。 它依赖于毛雷尔的通用测试。 在本文中, 我们提议了两种薄荷估计值来提高计算复杂性和估计准确性, 方法是利用 Maurer 测试的两个变数: 考隆的测试( 香农摄取) 和Kim 的测试( Reny 摄取) 。 首先, 我们提出一个基于Coron的测试特别出版物(SP) 800- 90B 的压缩估计值估计值。 它在计算效率上比压缩估计值要低。 第二次提议的估算值依靠Kim 测试, 将Reny 摄取的精确性估算值降低准确性, 以及计算复杂性。 我们分析误判交易交易的计算结果, 也是根据Reny Qeral IM 的计算方法, 以正读取内部交易的定序。