Elliptic curve algorithm integration in the secure shell transport layer

This document describes algorithms based on Elliptic Cryptography (ECC) for use within the Secure Shell (SSH) transport protocol. In particular, it specifies Elliptic Curve Diffie-Hellman (ECDH) key agreement, Elliptic Curve Menezes-Qu-Vanstone (ECMQV) key agreement, and Elliptic Curve Digital Signature Algorithm (ECDSA) for use in the SSH Transport Layer protocol.

Up the e-learning curve : ensuring quality online education within an Australian university

The paper describes the implementation of a project within Australian Catholic University designed to launch the Faculties into online education in a manner which ensured quality in all aspects of the teaching-learning experiences of academics and students. Key elements of the strategic approach adopted by the project leaders, including the involvement of a specialist commercial provider of web-based delivery systems as a partner in the project, mechanisms to support the initiative through the first stages, careful choice of the programs offered online, and staff development matched to the emerging needs of those involved in the teaching of courses, are described. Challenges encountered in the implementation process, and the factors which assisted in overcoming these problems are identified. The paper draws upon this experience to raise some important issues relevant to the successful introduction of online education as an integral component of the teaching repertoire of Faculties.

Secondary curve behaviour in Lenke IC class adolescent idiopathic scoliosis following video assisted thoracoscopic spinal fusion

Introduction. Ideally after selective thoracic fusion for Lenke Class IC (i.e. major thoracic / secondary lumbar) curves, the lumbar spine will spontaneously accommodate to the corrected position of the thoracic curve, thereby achieving a balanced spine, avoiding the need for fusion of lumbar spinal segments1. The purpose of this study was to evaluate the behaviour of the lumbar curve in Lenke IC class adolescent idiopathic scoliosis (AIS) following video-assisted thoracoscopic spinal fusion and instrumentation (VATS) of the major thoracic curve. Methods. A retrospective review of 22 consecutive patients with AIS who underwent VATS by a single surgeon was conducted. The results were compared to published literature examining the behaviour of the secondary lumbar curve where other surgical approaches were employed. Results. Twenty-two patients (all female) with AIS underwent VATS. All major thoracic curves were right convex. The average age at surgery was 14 years (range 10 to 22 years). On average 6.7 levels (6 to 8) were instrumented. The mean follow-up was 25.1 months (6 to 36). The pre-operative major thoracic Cobb angle mean was 53.8° (40° to 75°). The pre-operative secondary lumbar Cobb angle mean was 43.9° (34° to 55°). On bending radiographs, the secondary curve corrected to 11.3° (0° to 35°). The rib hump mean measurement was 15.0° (7° to 21°). At latest follow-up the major thoracic Cobb angle measured on average 27.2° (20° to 41°) (p<0.001 – univariate ANOVA) and the mean secondary lumbar curve was 27.3° (15° to 42°) (p<0.001). This represented an uninstrumented secondary curve correction factor of 37.8%. The mean rib hump measured was 6.5° (2° to 15°) (p<0.001). The results above were comparable to published series when open surgery was performed. Discussion. VATS is an effective method of correcting major thoracic curves with secondary lumbar curves. The behaviour of the secondary lumbar curve is consistent with published series when open surgery, both anterior and posterior, is performed.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Stochastic analysis of the VEGF receptor response curve

Recently, an analysis of the response curve of the vascular endothelial growth factor (VEGF) receptor and its application to cancer therapy was described in [T. Alarcón, and K. Page, J. R. Soc. Lond. Interface 4, 283–304 (2007)]. The analysis is significantly extended here by demonstrating that an alternative computational strategy, namely the Krylov FSP algorithm for the direct solution of the chemical master equation, is feasible for the study of the receptor model. The new method allows us to further investigate the hypothesis of symmetry in the stochastic fluctuations of the response. Also, by augmenting the original model with a single reversible reaction we formulate a plausible mechanism capable of realizing a bimodal response, which is reported experimentally but which is not exhibited by the original model. The significance of these findings for mechanisms of tumour resistance to antiangiogenic therapy is discussed.

High-resolution DNA melt curve analysis of the clustered, regularly interspaced short-palindromic-repeat locus of Campylobacter jejuni

A novel method for genotyping the clustered, regularly interspaced short-palindromic-repeat (CRISPR) locus of Campylobacter jejuni is described. Following real-time PCR, CRISPR products were subjected to high-resolution melt (HRM) analysis, a new technology that allows precise melt profile determination of amplicons. This investigation shows that the CRISPR HRM assay provides a powerful addition to existing C. jejuni genotyping methods and emphasizes the potential of HRM for genotyping short sequence repeats in other species