Lachlan J. Gunn

Geometric Algebra for Electrical and Electronic Engineers

In this paper, we explicate the suggested benefits of Cliffords geometric algebra (GA) when applied to the field of electrical engineering. Engineers are always interested in keeping formulas as simple or compact as possible, and we illustrate that geometric algebra does provide such a simplified representation in many cases. We also demonstrate an additional structural check provided by GA for formulas in addition to the usual checking of physical dimensions. Naturally, there is an initial learning curve when applying a new method, but it appears to be worth the effort, as we show significantly simplified formulas, greater intuition, and improved problem solving in many cases.

A directional wave measurement attack against the Kish key distribution system

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.

A New Transient Attack on the Kish Key Distribution System

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.

Functions of Multivector Variables

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 Cℓ(ℜ3) provides a particularly versatile algebraic framework.

Too good to be true: when overwhelming evidence fails to convince.

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 280.

Simplified Three-Cornered-Hat Technique for Frequency Stability Measurements

We propose a novel technique allowing the use of the three-cornered-hat method with two devices under test (DUTs) and a time-tagging system that employs a common reference oscillator. The precision of a time-tagging system is reduced by fluctuations in the timebase, which are canceled when the relative phase between the two DUTs is measured. However, the raw time-tags in this system provide a phase comparison between the DUTs and the system timebase, allowing the use of the three-cornered hat with some dual-channel measurement instruments.

Physical-layer encryption on the public internet: A stochastic approach to the Kish-Sethuraman cipher

While information-theoretic security is often associated with the one-time pad and quantum key distribution, noisy transport media leave room for classical techniques and even covert operation. Transit times across the public internet exhibit a degree of randomness, and cannot be determined noiselessly by an eavesdropper. We demonstrate the use of these measurements for information-theoretically secure communication over the public internet.

Towards an information-theoretic model of the Allison mixture stochastic process

The Allison mixture is a random process formed by stochastically switching between two random and uncorrelated input processes. Unintuitively, these samples—independent prior to being drawn—can acquire dependence as a result of the sampling process. It has previously been shown that correlation can occur subject to certain conditions, however in general dependence does not imply correlation. In this paper we provide an initial information-theoretic analysis of the Allison mixture, and derive the autoinformation function of its sampling process as the first step towards a fuller information-theoretic analysis of its output.

Towards quantitative atmospheric water vapor profiling with differential absorption lidar

Differential Absorption Lidar (DIAL) is a powerful laser-based technique for trace gas profiling of the atmosphere. However, this technique is still under active development requiring precise and accurate wavelength stabilization, as well as accurate spectroscopic parameters of the specific resonance line and the effective absorption cross-section of the system. In this paper we describe a novel master laser system that extends our previous work for robust stabilization to virtually any number of multiple side-line laser wavelengths for the future probing to greater altitudes. In this paper, we also highlight the significance of laser spectral purity on DIAL accuracy, and illustrate a simple re-arrangement of a system for measuring effective absorption cross-section. We present a calibration technique where the laser light is guided to an absorption cell with 33 m path length, and a quantitative number density measurement is then used to obtain the effective absorption cross-section. The same absorption cell is then used for on-line laser stabilization, while microwave beat-frequencies are used to stabilize any number of off-line lasers. We present preliminary results using ∼300 nJ, 1 μs pulses at 3 kHz, with the seed laser operating as a nanojoule transmitter at 822.922 nm, and a receiver consisting of a photomultiplier tube (PMT) coupled to a 356 mm mirror.

Real-time compensation of static distortion by measurement of differential noise gain

It is well-known that in a cascaded system of amplifiers the majority of noise is due to the first stage and the majority of distortion due to the final stage. Consequently, the observed noise at the output is subject to the same nonlinear process as the signal of interest. We use this fact to characterise the distorting process and linearise the system in real-time using statistical measurements of this noise.