Generalised Mersenne Numbers Revisited

Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST (FIPS 186-2) and SECG standards for use in elliptic curve cryptography. Their form is such that modular reduction is extremely efficient, thus making them an attractive choice for modular multiplication implementation. However, the issue of residue multiplication efficiency seems to have been overlooked. Asymptotically, using a cyclic rather than a linear convolution, residue multiplication modulo a Mersenne number is twice as fast as integer multiplication; this property does not hold for prime GMNs, unless they are of Mersenne's form. In this work we exploit an alternative generalisation of Mersenne numbers for which an analogue of the above property --- and hence the same efficiency ratio --- holds, even at bitlengths for which schoolbook multiplication is optimal, while also maintaining very efficient reduction. Moreover, our proposed primes are abundant at any bitlength, whereas GMNs are extremely rare. Our multiplication and reduction algorithms can also be easily parallelised, making our arithmetic particularly suitable for hardware implementation. Furthermore, the field representation we propose also naturally protects against side-channel attacks, including timing attacks, simple power analysis and differential power analysis, which is essential in many cryptographic scenarios, in constrast to GMNs.Comment: 32 pages. Accepted to Mathematics of Computatio

Open to change: slowing down to explore and innovate

A specific type of knowing comes from the handling of materials in the handcrafting of an artifact. This research looks at the relationship between the handcraft of weaving, and the decision-making process and knowledge of the textile designer. It investigates the potential for new design opportunities to be opened up for the commercial designer by moving out of the studio and back into the workshop environment. As an educator, manager and formerly a designer trained in textile design, this research explores an established industrial production method of weaving but revisited using a craft-like approach. Slowing down the creative process to engage with the materials themselves, this paper starts to explore the potential of hand woven leno structures to be used within the landscape and to explore the process of change in response to environmental factors. Architect Philip Beesleys’ work seeks to achieve a balance with nature, submitting itself to the natural cycles and inevitable decay, in which he deliberately designs mesh structures with weak and fragile links, whose materials soak up environmental forces. This paper starts to further explore the value of haptic intelligence and empathy for materials, also adopted by Beesley in his Haystack Veil (1997) and later Holozoic series. The process of creating leno structures on a handloom, has resulted in outcomes difficult to predict using digital software, confirming weaving as an emergent system (Philpott, 2011), where disparate threads are combined into dynamic structures. There is a delicate relationship between textiles and the landscape, in response to which the designer of performance fabrics is required to create, indestructible solutions, with a lifetime guarantee. By embracing the science of uncertainty, fresh ideas and new solutions have the potential to be created

Movement around real and virtual cluttered environments

Two experiments investigated participants’ ability to search for targets in a cluttered small-scale space. The first experiment was conducted in the real world with two field of view conditions (full vs. restricted), and participants found the task trivial to perform in both. The second experiment used the same search task but was conducted in a desktop virtual environment (VE), and investigated two movement interfaces and two visual scene conditions. Participants restricted to forward only movement performed the search task quicker and more efficiently (visiting fewer targets) than those who used an interface that allowed more flexible movement (forward, backward, left, right, and diagonal). Also, participants using a high fidelity visual scene performed the task significantly quicker and more efficiently than those who used a low fidelity scene. The performance differences between all the conditions decreased with practice, but the performance of the best VE group approached that of the real-world participants. These results indicate the importance of using high fidelity scenes in VEs, and suggest that the use of a simple control system is sufficient for maintaining ones spatial orientation during searching

Movement around real and virtual cluttered environments

Two experiments investigated participants’ ability to search for targets in a cluttered small-scale space. The first experiment was conducted in the real world with two field of view conditions (full vs. restricted), and participants found the task trivial to perform in both. The second experiment used the same search task but was conducted in a desktop virtual environment (VE), and investigated two movement interfaces and two visual scene conditions. Participants restricted to forward only movement performed the search task quicker and more efficiently (visiting fewer targets) than those who used an interface that allowed more flexible movement (forward, backward, left, right, and diagonal). Also, participants using a high fidelity visual scene performed the task significantly quicker and more efficiently than those who used a low fidelity scene. The performance differences between all the conditions decreased with practice, but the performance of the best VE group approached that of the real-world participants. These results indicate the importance of using high fidelity scenes in VEs, and suggest that the use of a simple control system is sufficient for maintaining ones spatial orientation during searching

Models of everywhere revisited: a technological perspective

The concept ‘models of everywhere’ was first introduced in the mid 2000s as a means of reasoning about the environmental science of a place, changing the nature of the underlying modelling process, from one in which general model structures are used to one in which modelling becomes a learning process about specific places, in particular capturing the idiosyncrasies of that place. At one level, this is a straightforward concept, but at another it is a rich multi-dimensional conceptual framework involving the following key dimensions: models of everywhere, models of everything and models at all times, being constantly re-evaluated against the most current evidence. This is a compelling approach with the potential to deal with epistemic uncertainties and nonlinearities. However, the approach has, as yet, not been fully utilised or explored. This paper examines the concept of models of everywhere in the light of recent advances in technology. The paper argues that, when first proposed, technology was a limiting factor but now, with advances in areas such as Internet of Things, cloud computing and data analytics, many of the barriers have been alleviated. Consequently, it is timely to look again at the concept of models of everywhere in practical conditions as part of a trans-disciplinary effort to tackle the remaining research questions. The paper concludes by identifying the key elements of a research agenda that should underpin such experimentation and deployment