Achieving secure communication between an Implantable Medical Device (IMD) inside the body and a gateway outside the body has showed its criticality with recent reports of hackings. The use of asymmetric cryptography is not a practical solution for IMDs due to the scarce computational and power resources, symmetric key cryptography is preferred. One of the factors in security of a symmetric cryptographic system is to use a strong key for encryption. A solution without using extensive resources in an IMD, is to extract it from the body physiological signals. To have a strong enough key, the physiological signal must be a strong source of randomness and InterPulse Interval (IPI) has been advised to be such that. A strong randomness source should have five conditions: Universality, Liveness, Robustness Permanence and Uniqueness. Nevertheless, for current proposed random extraction methods from IPI these conditions (mainly last three conditions) were not examined. In this study, firstly, we proposed a methodology to measure the last three conditions. Then, using a huge dataset of IPI values, we showed that IPI does not have conditions of Robustness and Permanence. Thus, extraction of a strong uniform random number from IPI value, mathematically, is impossible. Thirdly, rather than using the value of IPI, we proposed the trend of IPI as a source for a new randomness extraction method named as Martingale Randomness Extraction from IPI (MRE-IPI). MRE-IPI satisfies the Robustness condition completely and Permanence to some level. We, also, used randomness test suites and showed that MRE-IPI is able to outperform all recent randomness extraction methods from IPIs and its quality is half of the AES random number. To the best of our knowledge, this is the first work in this area which uses such a comprehensive method and large dataset to examine the randomness of a physiological signal.
Whatever the extraction method is, it needs to be evaluated for the quality of generated randomness. Several extracting methods did not perform any randomness test to examine the quality of proposed algorithm (e.g. @cite_36 @cite_26 @cite_9 @cite_8 @cite_16 @cite_34 @cite_52 ). In these works the aim of the paper was not examining the randomness of proposed extraction method. There are other randomness extraction works in which there was an attempt to measure the quality of proposed method. However, in these works, two aspects have been somewhat ignored. To evaluate the quality of a randomness extractor, the dataset and the methodology of evaluation are the key points. For instance, @cite_39 evaluated the randomness property of their algorithm with 5 minutes ECG data of 10 subject by NIST Statistical Test Suite (STS) @cite_54 randomness test. @cite_50 @cite_31 @cite_13 tested their algorithm using 5 minutes ECG signal of 40 subjects with NIST STS. In another work, @cite_0 used histogram analysis on 1500 consecutive IPI values. @cite_21 tested their proposed method with 100 subjects' ECG data with Entropy test. @cite_1 , to evaluate the randomness of proposed algorithm, used Temporal Ratio @cite_58 method over 5 minutes ECG data of 50 subjects.
@cite_26 @cite_8 @cite_36 @cite_9 @cite_54 @cite_21 @cite_52 @cite_34 @cite_39 @cite_0 @cite_1 @cite_58 @cite_50 @cite_31 @cite_16 @cite_13
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The problem of assessing the significance of data mining results on high-dimensional 0--1 datasets has been studied extensively in the literature. For problems such as mining frequent sets and finding correlations, significance testing can be done by standard statistical tests such as chi-square, or other methods. However, the results of such tests depend only on the specific attributes and not on the dataset as a whole. Moreover, the tests are difficult to apply to sets of patterns or other complex results of data mining algorithms. In this article, we consider a simple randomization technique that deals with this shortcoming. The approach consists of producing random datasets that have the same row and column margins as the given dataset, computing the results of interest on the randomized instances and comparing them to the results on the actual data. This randomization technique can be used to assess the results of many different types of data mining algorithms, such as frequent sets, clustering, and spectral analysis. To generate random datasets with given margins, we use variations of a Markov chain approach which is based on a simple swap operation. We give theoretical results on the efficiency of different randomization methods, and apply the swap randomization method to several well-known datasets. Our results indicate that for some datasets the structure discovered by the data mining algorithms is expected, given the row and column margins of the datasets, while for other datasets the discovered structure conveys information that is not captured by the margin counts. A randomness extractor is an algorithm which extracts randomness from a low-quality random source, using some additional truly random bits. We construct new extractors which require only log n + O(1) additional random bits for sources with constant entropy rate. We further construct dispersers, which are similar to one-sided extractors, which use an arbitrarily small constant times log n additional random bits for sources with constant entropy rate. Our extractors and dispersers output 1-α fraction of the randomness, for any α>0.We use our dispersers to derandomize results of Hastad [23] and Feige-Kilian [19] and show that for all e>0, approximating MAX CLIQUE and CHROMATIC NUMBER to within n1-e are NP-hard. We also derandomize the results of Khot [29] and show that for some γ > 0, no quasi-polynomial time algorithm approximates MAX CLIQUE or CHROMATIC NUMBER to within n 2(log n)1-γ, unless NP = P.Our constructions rely on recent results in additive number theory and extractors by Bourgain-Katz-Tao [11], Barak-Impagliazzo-Wigderson [5], Barak-Kindler-Shaltiel-Sudakov-Wigderson [6], and Raz [36]. We also simplify and slightly strengthen key theorems in the second and third of these papers, and strengthen a related theorem by Bourgain [10]. The problem of assessing the significance of data mining results on high-dimensional 0-1 data sets has been studied extensively in the literature. For problems such as mining frequent sets and finding correlations, significance testing can be done by, e.g., chi-square tests, or many other methods. However, the results of such tests depend only on the specific attributes and not on the dataset as a whole. Moreover, the tests are more difficult to apply to sets of patterns or other complex results of data mining. In this paper, we consider a simple randomization technique that deals with this shortcoming. The approach consists of producing random datasets that have the same row and column margins with the given dataset, computing the results of interest on the randomized instances, and comparing them against the results on the actual data. This randomization technique can be used to assess the results of many different types of data mining algorithms, such as frequent sets, clustering, and rankings. To generate random datasets with given margins, we use variations of a Markov chain approach, which is based on a simple swap operation. We give theoretical results on the efficiency of different randomization methods, and apply the swap randomization method to several well-known datasets. Our results indicate that for some datasets the structure discovered by the data mining algorithms is a random artifact, while for other datasets the discovered structure conveys meaningful information. Randomness extraction is of fundamental importance for information-theoretic cryptography. It allows to transform a raw key about which an attacker has some limited knowledge into a fully secure random key, on which the attacker has essentially no information. Up to date, only very few randomness-extraction techniques are known to work against an attacker holding quantum information on the raw key. This is very much in contrast to the classical (non-quantum) setting, which is much better understood and for which a vast amount of different techniques are known and proven to work. We prove a new randomness-extraction technique, which is known to work in the classical setting, to be secure against a quantum attacker as well. Randomness extraction is done by xor'ing a so-called δ-biased mask to the raw key. Our result allows to extend the classical applications of this extractor to the quantum setting. We discuss the following two applications. We show how to encrypt a long message with a short key, information-theoretically secure against a quantum attacker, provided that the attacker has enough quantum uncertainty on the message. This generalizes the concept of entropically-secure encryption to the case of a quantum attacker. As second application, we show how to do errorcorrection without leaking partial information to a quantum attacker. Such a technique is useful in settings where the raw key may contain errors, since standard error-correction techniques may provide the attacker with information on, say, a secret key that was used to obtain the raw key.