Extracting Randomness From The Trend of IPI for Cryptographic Operators in Implantable Medical Devices

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.