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.
Using IPI as a source of randomness has been proposed by @cite_48 , where a random extraction algorithm is needed to convert IPI value to a random number. A few randomness extractor algorithms from IPI have been proposed in the literature. Proposed methods are including using XOR function @cite_64 , gray-coding @cite_39 and using frequency domain @cite_35 @cite_8 @cite_52 . In some studies, a combination of algorithms is used for randomness extraction. For instance, @cite_50 @cite_31 @cite_13 used accumulation, modulo, contract mapping and gray-coding for the extractor and @cite_1 proposed a combination of concatenation, quantization and gray-coding as the randomness extractor from IPI.
@cite_35 @cite_64 @cite_8 @cite_48 @cite_1 @cite_52 @cite_39 @cite_50 @cite_31 @cite_13
2126186592 2949560198 1973956822 2106664865
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]. We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman succeeds in correcting a constant fraction of errors with high probability. The fraction of correctable errors guaranteed by our analysis surpasses previous nonasymptotic results for LDPC codes, and in particular, exceeds the best previous finite-length result on LP decoding by a factor greater than ten. This improvement stems in part from our analysis of probabilistic bit-flipping channels, as opposed to adversarial channels. At the core of our analysis is a novel combinatorial characterization of LP decoding success, based on the notion of a flow on the Tanner graph of the code. An interesting by-product of our analysis is to establish the existence of ldquoprobabilistic expansionrdquo in random bipartite graphs, in which one requires only that almost every (as opposed to every) set of a certain size expands, for sets much larger than in the classical worst case setting. We design and analyze a method to extract secret keys from the randomness inherent to wireless channels. We study a channel model for a multipath wireless channel and exploit the channel diversity in generating secret key bits. We compare the key extraction methods based both on entire channel state information (CSI) and on single channel parameter such as the received signal strength indicators (RSSI). Due to the reduction in the degree-of-freedom when going from CSI to RSSI, the rate of key extraction based on CSI is far higher than that based on RSSI. This suggests that exploiting channel diversity and making CSI information available to higher layers would greatly benefit the secret key generation. We propose a key generation system based on low-density parity-check (LDPC) codes and describe the design and performance of two systems: one based on binary LDPC codes and the other (useful at higher signal-to-noise ratios) based on four-ary LDPC codes. In this correspondence, a new method for improving hard-decision bit-flipping decoding of low-density parity-check (LDPC) codes is presented. Bits with a number of unsatisfied check sums larger than a predetermined threshold are flipped with a probability p spl les 1 which is independent of the code considered. The probability p is incremented during decoding according to some rule. With a proper choice of the initial p, the proposed improved bit-flipping (BF) algorithm achieves gain not only in performance, but also in average decoding time for signal-to-noise ratio (SNR) values of interest with respect to p = 1.