On the use of stochastic systems for sensing and security

Abstract

No measurement system is perfect, and two varieties of error compete to frustrate their designers and operators. Random errors produce measurement-to-measurement to variation, while systematic errors result in consistently-incorrect results. The interplay between these two phenomena has been the subject of research for many years, particularly within the area of stochastic resonance, which focusses upon cases where the signal-to-noise ratio of a nonlinear system can increase with the addition of noise to its input signal. While it has been demonstrated many times that noise can overcome systematic deficiencies in a measurement system, there remain open questions on how to take advantage of this in practical systems, what information can be extracted, and whether such ‘randomised’ systems are useful in other settings. In this thesis, we consider this general theme in the context of two main settings: the adversarial, and the nonadversarial. In both cases, there is a significant advantage to be gained from the use of techniques that are adapted to the problem domain, in contrast to previous ad-hoc approaches that have failed to take advantage of the structures of the problems at hand. The first part of this thesis considers the elimination of static nonlinearity from noisy measurements. We start with the phenomenon of ‘classical’ stochastic resonance, showing how input noise can be used to linearise the response of a nonlinear system. This phenomenon has been observed in the past, however we demonstrate that the use of nonlinear signal processing allows the linearisation to take place with far smaller levels of noise. We then investigate several approaches to the implementation of this technique, with the aim of supporting real-time operation in embedded systems and vlsi. The remainder of the thesis concerns the use of randomness in measurements made as part of adversarial systems. This can be split into two situations: that where the operation of a system requires that measurement be difficult, and that where measurement must be straightforward. We first discuss the Kish key distribution system, a proposed classical alternative to quantum key distribution. This system claims to derive its security from the second law of thermodynamics, however these claims have been the subject of controversy. We examine the claims in detail, and show that the use of random signals does not render implausible the measurement of the system state. Finally, we describe a number of approaches to the topical problems of key distribution and identity verification. We show how various forms of multi-path probing can be treated as a form of random sampling; much like in the first section, this randomness allows for the characterisation of systematic errors, in this case the consistent changes introduced by an attacker. We then compute bounds on the probability that an attacker achieves a deception against a user taking part in this sampling process. The first approach that we consider uses an anonymising system such as Tor or a mixnet; if all users make anonymous requests to a service in lock-step, then a malicious service cannot guarantee a self-consistent set of responses to anyone without providing the malicious response to all users. This allows the development of a statistically guaranteed consensus, and thus permits auditors to assure themselves that they have examined the same data as has been provided to other users. This provides an attractive alternative to blockchain technology, avoiding the complexity of the proof-of-work and proof-of-stake-based systems that dominate the landscape today. We have developed a second approach that allows the random-sampling approach to be used with the existing public-key infrastructure. By demonstrating that the entities chosen to carry out the verification of an identity holder are selected at random from a substantial number of independent entities, relying parties can be confident that small numbers of compromised verifiers cannot unilaterally issue certificates for identities that they do not hold. This provides a basis for the development of highly robust distributed certificate issuance systems that do not share the current ‘weakest-link’ nature of the existing public-key infrastructure. Ultimately, these systems all hold in common the use of randomness in their measurement conditions in order to characterise systematic effects. While this phenomenon has been acknowledged, its potential to characterise real systems has until now not been realised. We demonstrate that randomness, whether natural and unavoidable or artificially introduced, can ironically render far more predictable the behaviour of many systems, and in more realistic situations than have been seen in the literature to date.