Hardware processors for pairing-based cryptography

Bilinear pairings can be used to construct cryptographic systems with very desirable properties. A pairing performs a mapping on members of groups on elliptic and genus 2 hyperelliptic curves to an extension of the finite field on which the curves are defined. The finite fields must, however, be large to ensure adequate security. The complicated group structure of the curves and the expensive field operations result in time consuming computations that are an impediment to the practicality of pairing-based systems. The Tate pairing can be computed efficiently using the ɳT method. Hardware architectures can be used to accelerate the required operations by exploiting the parallelism inherent to the algorithmic and finite field calculations. The Tate pairing can be performed on elliptic curves of characteristic 2 and 3 and on genus 2 hyperelliptic curves of characteristic 2. Curve selection is dependent on several factors including desired computational speed, the area constraints of the target device and the required security level. In this thesis, custom hardware processors for the acceleration of the Tate pairing are presented and implemented on an FPGA. The underlying hardware architectures are designed with care to exploit available parallelism while ensuring resource efficiency. The characteristic 2 elliptic curve processor contains novel units that return a pairing result in a very low number of clock cycles. Despite the more complicated computational algorithm, the speed of the genus 2 processor is comparable. Pairing computation on each of these curves can be appealing in applications with various attributes. A flexible processor that can perform pairing computation on elliptic curves of characteristic 2 and 3 has also been designed. An integrated hardware/software design and verification environment has been developed. This system automates the procedures required for robust processor creation and enables the rapid provision of solutions for a wide range of cryptographic applications.

Accuracy of computer-aided design/computer-assisted manufacture (CAD/CAM) fabricated dental restorations: a comparative study

Introduction: Computer-Aided-Design (CAD) and Computer-Aided-Manufacture (CAM) has been developed to fabricate fixed dental restorations accurately, faster and improve cost effectiveness of manufacture when compared to the conventional method. Two main methods exist in dental CAD/CAM technology: the subtractive and additive methods. While fitting accuracy of both methods has been explored, no study yet has compared the fabricated restoration (CAM output) to its CAD in terms of accuracy. The aim of this present study was to compare the output of various dental CAM routes to a sole initial CAD and establish the accuracy of fabrication. The internal fit of the various CAM routes were also investigated. The null hypotheses tested were: 1) no significant differences observed between the CAM output to the CAD and 2) no significant differences observed between the various CAM routes. Methods: An aluminium master model of a standard premolar preparation was scanned with a contact dental scanner (Incise, Renishaw, UK). A single CAD was created on the scanned master model (InciseCAD software, V2.5.0.140, UK). Twenty copings were then fabricated by sending the single CAD to a multitude of CAM routes. The copings were grouped (n=5) as: Laser sintered CoCrMo (LS), 5-axis milled CoCrMo (MCoCrMo), 3-axis milled zirconia (ZAx3) and 4-axis milled zirconia (ZAx4). All copings were micro-CT scanned (Phoenix X-Ray, Nanotom-S, Germany, power: 155kV, current: 60µA, 3600 projections) to produce 3-Dimensional (3D) models. A novel methodology was created to superimpose the micro-CT scans with the CAD (GOM Inspect software, V7.5SR2, Germany) to indicate inaccuracies in manufacturing. The accuracy in terms of coping volume was explored. The distances from the surfaces of the micro-CT 3D models to the surfaces of the CAD model (CAD Deviation) were investigated after creating surface colour deviation maps. Localised digital sections of the deviations (Occlusal, Axial and Cervical) and selected focussed areas were then quantitatively measured using software (GOM Inspect software, Germany). A novel methodology was also explored to digitally align (Rhino software, V5, USA) the micro-CT scans with the master model to investigate internal fit. Fifty digital cross sections of the aligned scans were created. Point-to-point distances were measured at 5 levels at each cross section. The five levels were: Vertical Marginal Fit (VF), Absolute Marginal Fit (AM), Axio-margin Fit (AMF), Axial Fit (AF) and Occlusal Fit (OF). Results: The results of the volume measurement were summarised as: VM-CoCrMo (62.8mm3 ) > VZax3 (59.4mm3 ) > VCAD (57mm3 ) > VZax4 (56.1mm3 ) > VLS (52.5mm3 ) and were all significantly different (p presented as areas with different colour. No significant differences were observed at the internal aspect of the cervical aspect between all groups of copings. Significant differences (p< M-CoCrMo Internal Occlusal, Internal Axial and External Axial 2 ZAx3 > ZAx4 External Occlusal, External Cervical 3 ZAx3 < ZAx4 Internal Occlusal 4 M-CoCrMo > ZAx4 Internal Occlusal and Internal Axial The mean values of AMF and AF were significantly (p M-CoCrMo and CAD > ZAx4. Only VF of M-CoCrMo was comparable with the CAD Internal Fit. All VF and AM values were within the clinically acceptable fit (120µm). Conclusion: The investigated CAM methods reproduced the CAD accurately at the internal cervical aspect of the copings. However, localised deviations at axial and occlusal aspects of the copings may suggest the need for modifications in these areas prior to fitting and veneering with porcelain. The CAM groups evaluated also showed different levels of Internal Fit thus rejecting the null hypotheses. The novel non-destructive methodologies for CAD/CAM accuracy and internal fit testing presented in this thesis may be a useful evaluation tool for similar applications.