The Kish key distribution system has been proposed as a classical alternative to quantum key distribution. The idealized Kish scheme elegantly promises secure key distribution by exploiting thermal noise in a transmission line. However, we demonstrate that it is vulnerable to nonidealities in its components, such as the finite resistance of the transmission line connecting its endpoints. We introduce a novel attack against this nonideality using directional wave measurements, and experimentally demonstrate its efficacy.

This tutorial paper provides a short introduction to geometric algebra, starting with its history and then presenting its benefits and exploring its applications.

The Kish Key Distribution (KKD) system has been proposed as a classical alternative to quantum key distribution, making use of temperature-matched thermal noise. Previous analyses assume instant propagation of signals along the cable connecting the two users. We describe a new attack that takes an advantage of propagation delays. At the start of each bit period, the noise temperature will then be increased from zero to its final value. During this process, the noise temperature variation will take time to propagate along the line, resulting in a temperature mismatch. We analyze the information leak due to this effect and consider several potential mitigation schemes.

As is well known, the common elementary functions defined over the real numbers can be generalized to act not only over the complex number field but also over the skew (non-commuting) field of the quaternions. In this paper, we detail a number of elementary functions extended to act over the skew field of Clifford multivectors, in both two and three dimensions. Complex numbers, quaternions and Cartesian vectors can be described by the various components within a Clifford multivector and from our results we are able to demonstrate new inter-relationships between these algebraic systems. One key relationship that we discover is that a complex number raised to a vector power produces a quaternion thus combining these systems within a single equation. We also find a single formula that produces the square root, amplitude and inverse of a multivector over one, two and three dimensions. Finally, comparing the functions over different dimension we observe that provides a particularly versatile algebraic framework.

Is it possible for a large sequence of measurements or observations, which support a hypothesis, to counterintuitively decrease our confidence? Can unanimous support be too good to be true? The assumption of independence is often made in good faith; however, rarely is consideration given to whether a systemic failure has occurred. Taking this into account can cause certainty in a hypothesis to decrease as the evidence for it becomes apparently stronger. We perform a probabilistic Bayesian analysis of this effect with examples based on (i) archaeological evidence, (ii) weighing of legal evidence and (iii) cryptographic primality testing. In this paper, we investigate the effects of small error rates in a set of measurements or observations. We find that even with very low systemic failure rates, high confidence is surprisingly difficult to achieve; in particular, we find that certain analyses of cryptographically important numerical tests are highly optimistic, underestimating their false-negative rate by as much as a factor of 2.

Parrondo's paradox is a well-known situation where losing strategies can be combined to win, and is based on a thermodynamic Brownian ratchet principle. We demonstrate a new extension of Parrondo's paradox called the Allison mixture where it is possible to paradoxically generate random sequences with nonzero autocovariance, out of sub-sequences of zero autocovariance. We explain the effect with a ratchet analogy and show the behavior of random digits follows a thermodynamic analogy. As Kish-based cipher techniques rely on the Second Law for their security, this raises the tantalizing open question of whether the Allison mixture can be exploited for new Kish-inspired digital security schemes.

Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multi-person strategic decision making that can be used to model the interactions of decision makers in security problems who compete for limited and shared resources. This article presents a review of the literature in the area of game theoretical modelling of network/cybersecurity and identifies a number of challenges in this area that need to be addressed. INDEX TERMS Cyberspace, mathematical model, optimization methods, cybersecurity, game theory, network security. AZHAR IQBAL received the B.Sc. (Hons.

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