The magic words are squeamish ossifrage [RSA public key cryptography]

We describe the computation which resulted in the title of this paper. Furthermore, we give an analysis of the data collected during this computation. From this data, we derive the important observation that in the final stages, the progress of the double large prime variation of the quadratic sieve integer factoring algorithm can more effectively be approximated by a quartic function of the time spent, than by the more familiar quadratic function. We also present, as an update to “Factoring by electronic mail” by Lenstra and Manasse (1990), some of our experiences with the management of a large computation distributed over the Internet. Based on this experience, we give some realistic estimates of the current readily available computational power of the Internet. We conclude that commonly-used 512-bit RSA moduli are vulnerable to any organization prepared to spend a few million dollars and to wait a few month

Universal coalgebra: a theory of systems

In the semantics of programming, finite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with infinite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (1988) on a theory of non-wellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages (Milner, 1980; Park, 1981). Using the notion of c

A Parallel Algorithm for Computing Minimum Spanning Trees

We present a simple and implementable algorithm that computes a minimum spanning tree of an undirected weighted graph G = (V, E) of n = |V| vertices and m = |E| edges on an EREW PRAM in O(log 3=2 n) time using n+m processors. This represents a substantial improvement in the running time over the previous results for this problem using at the same time the weakest of the PRAM models. It also implies the existence of algorithms having the same complexity bounds for the EREW PRAM, for connectivity, ear decomposition, biconnectivity, strong orientation, st-numbering and Euler tours problems

A New Jerusalem ‘at the ends of the earth’: interpreting Charles Thomas’s excavations at Iona Abbey 1956-63

Iona was a major European intellectual and artistic centre during the seventh to ninth centuries, with outstanding illustrated manuscripts, sculpture and religious writings produced there, despite its apparently peripheral location ‘at the ends of the earth’. Recent theological discourse has emphasised the leading role of Iona, and particularly its ninth abbot, Adomnán, in developing the metaphor of the earthly monastery as a mirror of heavenly Jerusalem, allowing us to suggest a new appreciation of the innovative monastic layout at Iona and its influence on other monasteries in northern Britain. The authors contend that the unique paved roadway and the schematic layout of the early church, shrine chapel and free-standing crosses were intended to evoke Jerusalem, and that the journey to the sacred heart of the site mirrored a pilgrim’s journey to the tomb of Christ. The key to this transformative understanding is Charles Thomas’s 1956–63 campaign of excavations on Iona, which this article is publishing for the first time. These excavations were influential in the history of early Christian archaeology in Britain as they helped to form many of Thomas’s ideas, later expressed in a series of influential books. They also revealed important new information on the layout and function of the monastic complex, and produced some unique metalwork and glass artefacts that considerably expand our knowledge of activities on the site. This article collates this new information with a re-assessment of the evidence from a large series of other excavations on Iona, and relates the results to recent explorations at other Insular monastic sites

Prefetching and Caching Techniques in File Systems for Mimd Multiprocessors

The increasing speed of the most powerful computers, especially multiprocessors, makes it difficult to provide sufficient I/O bandwidth to keep them running at full speed for the largest problems. Trends show that the difference in the speed of disk hardware and the speed of processors is increasing, with I/O severely limiting the performance of otherwise fast machines. This widening access-time gap is known as the “I/O bottleneck crisis.” One solution to the crisis, suggested by many researchers, is to use many disks in parallel to increase the overall bandwidth. \par This dissertation studies some of the file system issues needed to get high performance from parallel disk systems, since parallel hardware alone cannot guarantee good performance. The target systems are large MIMD multiprocessors used for scientific applications, with large files spread over multiple disks attached in parallel. The focus is on automatic caching and prefetching techniques. We show that caching and prefetching can transparently provide the power of parallel disk hardware to both sequential and parallel applications using a conventional file system interface. We also propose a new file system interface (compatible with the conventional interface) that could make it easier to use parallel disks effectively. \par Our methodology is a mixture of implementation and simulation, using a software testbed that we built to run on a BBN GP1000 multiprocessor. The testbed simulates the disks and fully implements the caching and prefetching policies. Using a synthetic workload as input, we use the testbed in an extensive set of experiments. The results show that prefetching and caching improved the performance of parallel file systems, often dramatically