Discrete Logarithms in Generalized Jacobians

D\'ech\`ene has proposed generalized Jacobians as a source of groups for public-key cryptosystems based on the hardness of the Discrete Logarithm Problem (DLP). Her specific proposal gives rise to a group isomorphic to the semidirect product of an elliptic curve and a multiplicative group of a finite field. We explain why her proposal has no advantages over simply taking the direct product of groups. We then argue that generalized Jacobians offer poorer security and efficiency than standard Jacobians

Finding Significant Fourier Coefficients: Clarifications, Simplifications, Applications and Limitations

Ideas from Fourier analysis have been used in cryptography for the last three decades. Akavia, Goldwasser and Safra unified some of these ideas to give a complete algorithm that finds significant Fourier coefficients of functions on any finite abelian group. Their algorithm stimulated a lot of interest in the cryptography community, especially in the context of `bit security'. This manuscript attempts to be a friendly and comprehensive guide to the tools and results in this field. The intended readership is cryptographers who have heard about these tools and seek an understanding of their mechanics and their usefulness and limitations. A compact overview of the algorithm is presented with emphasis on the ideas behind it. We show how these ideas can be extended to a `modulus-switching' variant of the algorithm. We survey some applications of this algorithm, and explain that several results should be taken in the right context. In particular, we point out that some of the most important bit security problems are still open. Our original contributions include: a discussion of the limitations on the usefulness of these tools; an answer to an open question about the modular inversion hidden number problem

Distortion maps for genus two curves

Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full torsion subgroup has rank 2g. In this paper we prove that distortion maps always exist for supersingular curves of genus g>1 and we construct distortion maps in genus 2 (for embedding degrees 4,5,6 and 12).Comment: 16 page

Medical education on fitness to drive : a survey of all UK medical schools

Aim: To identify the extent to which medical aspects of fitness to drive (FTD) are taught within UK medical schools. Methods: A survey of all 32 UK medical schools. In-depth interviews with a range of staff at two medical schools; telephone survey of 30 schools. Results: Two thirds of schools reported specific teaching on medical aspects of FTD but few covered it in any depth or in relation to specific medical conditions. Only one school taught FTD in relation to elderly medicine. FTD was an examination topic at only 12 schools. Conclusion: Teaching on FTD is inconsistent across UK medical schools. Many new doctors will graduate with limited knowledge of medical aspects of FTD

Remembering the Public Domain

Rapid advances in communication technology over the past decade have resulted in the previously unimaginable ability to seamlessly exchange ideas and data on a global basis. Nonetheless, despite the undeniable progress that has been made, access to information is ironically becoming progressively more. This is due in large part to the fact that resources which belong in the public domain are increasingly being transformed into private property. The carefully balanced provisions of copyright law are gradually becoming displaced by contractual, technological, and legislative constraints that allow for the tight control of access to and use of the materials in question. Although in limited circumstances generally unrestricted power to limit access and use may seem reasonable, in most situations this is not the case. Frequently the end results of such unwarranted restraints are considerable impediments to public access to ideas and information. Such a state of affairs has potentially serious consequences, as the ability to access and make use of these resources is critically important to creativity, competition, innovation, and a democratic culture. Unfortunately, lawmakers promulgating statutes and judges resolving disputes concerning data have failed to adequately take into account the multi-dimensional problems involved in disputes concerning access to information. The focus is often inappropriately centered on the tangible property within which information is contained, for example in a software program or a computer server. Additionally, once an owner of such property is ascertained, all of the conventional attributes of ownership are normally granted, including the right to exclude. As a result, almost insurmountable obstacles are faced by any other party whose interests might be affected by a lack of access, as the burden almost always falls on these other parties to explain why the previously identified owner\u27s rights should be limited. Furthermore, facts and ideas increasingly are viewed merely as commodities in the marketplace, even though they constitute the building blocks of knowledge and are supposed to remain within the public domain. This myopic view of property rights fails to ensure that future creators, innovators, and participants in democratic culture have the benefit of these essential materials. Therefore, it is imperative that judges and policy makers give more comprehensive attention to the various interests involved in controversies affecting such resources and recognize that the way in which property rights are structured reflect the values we find important and the type of society we wish to create

Efficient algorithms for pairing-based cryptosystems

We describe fast new algorithms to implement recent cryptosystems based on the Tate pairing. In particular, our techniques improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain performance comparable to that of RSA in larger characteristics.We also propose faster algorithms for scalar multiplication in characteristic 3 and square root extraction over Fpm, the latter technique being also useful in contexts other than that of pairing-based cryptography