Abstract
Since the entropy is a popular randomness measure, there are many studies for the estimation of entropies for given random samples. In this paper, we propose an estimation method of the Rényi entropy of order . Since the Rényi entropy of order is a generalized entropy measure including the Shannon entropy as a special case, the proposed estimation method for Rényi entropy can detect any significant deviation of an ergodic stationary random source’s output. It is shown that the expected test value of the proposed scheme is equivalent to the Rényi entropy of order . After deriving a general representation of parameters of the proposed estimator, we discuss on the particular orders of Rényi entropy such as , , and . Because the Rényi entropy of order 2 is the most popular one, we present an iterative estimation method for the application with stringent resource restrictions.
Highlights
Since the entropy is a popular randomness measure, many studies are devoted to the efficient estimation of the Shannon or Rényi entropy for given random samples
Since a statistical bias in random numbers can be exploited to reduce the computational complexity of the exhaustive search by an attacker, the entire security of the crypto-systems usually depends on the statistically quality of random number generators (RNGs) output
Let us start from the case of α approaching to 1, where Rényi entropy converges to Shannon entropy
Summary
Since the entropy is a popular randomness measure, many studies are devoted to the efficient estimation of the Shannon or Rényi entropy for given random samples. We propose a low complexity estimation method of the Rényi entropy of order α, where α is a real number This method does not require any initialization phase contrary to the previous Maurer’s universal statistical test [8] and Coron’s refined test [7] which are widely used for estimating Shannon entropy especially in cryptographic applications [5,20]. Using the simple counting method, we can efficiently implement test module of RNGs based on the Rényi entropy of order 2 It can be used as a statistical tester of RNGs for many embedded security systems such as smart cards.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
