A kilobit hidden SNFS discrete logarithm computation

We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields. This computation took a little over two months of calendar time on an academic cluster using the open-source CADO-NFS software. Our chosen prime $p$ looks random, and $p--1$ has a 160-bit prime factor, in line with recommended parameters for the Digital Signature Algorithm. However, our p has been trapdoored in such a way that the special number field sieve can be used to compute discrete logarithms in $\mathbb{F}\_p^*$ , yet detecting that p has this trapdoor seems out of reach. Twenty-five years ago, there was considerable controversy around the possibility of back-doored parameters for DSA. Our computations show that trapdoored primes are entirely feasible with current computing technology. We also describe special number field sieve discrete log computations carried out for multiple weak primes found in use in the wild. As can be expected from a trapdoor mechanism which we say is hard to detect, our research did not reveal any trapdoored prime in wide use. The only way for a user to defend against a hypothetical trapdoor of this kind is to require verifiably random primes

MPEG-1 bitstreams processing for audio content analysis

In this paper, we present the MPEG-1 Audio bitstreams processing work which our research group is involved in. This work is primarily based on the processing of the encoded bitstream, and the extraction of useful audio features for the purposes of analysis and browsing. In order to prepare for the discussion of these features, the MPEG-1 audio bitstream format is first described. The Application Interface Protocol (API) which we have been developing in C++ is then introduced, before completing the paper with a discussion on audio feature extraction

Analysis of Random Number Generators Using Monte Carlo Simulation

Revisions are almost entirely in the introduction and conclusion. Results are unchanged, however the comments and recommendations on different generators were changed, and more references were added.Comment: Email: [email protected] 16 pages, Latex with 1 postscript figure. NPAC technical report SCCS-52

Greek-Arabic-Latin: The transmission of mathematical texts in the Middle Ages

During the Middle Ages many Greek mathematical and astronomical texts were translated from Greek into Arabic (ca. ninth century) and from Arabic into Latin (ca. twelfth century). There were many factors complicating the study of them, such as translation from or into other languages, redactions, multiple translations, and independently transmitted scholia. A literal translation risks less in loss of meaning, but can be clumsy. This article includes lists of translations and a large bibliography, divided into sections

Magnetic structures in Co---Cr media for perpendicular magnetic recording

High bit densities have been demonstrated in longitudinal as well as in perpendicular magnetic recording. For the latter an area density of more than 12 Gbit/in2 has been obtained in a sputtered Co---Cr---Ta hard disk with a soft magnetic underlayer recorded with a special single pole head. In this paper the role of microstructure and morphology in relation to the compositional separation is discussed. Very sensitive anomalous Hall measurements have been performed from submicron Co---Cr samples to obtain more detail information about the reversal characteristics of the material. The results obtained have been used in our model for micromagnetic simulations. One of the conclusions is that most of the magnetic entities reversing their magnetisations are much smaller than the volume of one Co---Cr column

Relevance of Dynamic Clustering to Biological Networks

Network of nonlinear dynamical elements often show clustering of synchronization by chaotic instability. Relevance of the clustering to ecological, immune, neural, and cellular networks is discussed, with the emphasis of partially ordered states with chaotic itinerancy. First, clustering with bit structures in a hypercubic lattice is studied. Spontaneous formation and destruction of relevant bits are found, which give self-organizing, and chaotic genetic algorithms. When spontaneous changes of effective couplings are introduced, chaotic itinerancy of clusterings is widely seen through a feedback mechanism, which supports dynamic stability allowing for complexity and diversity, known as homeochaos. Second, synaptic dynamics of couplings is studied in relation with neural dynamics. The clustering structure is formed with a balance between external inputs and internal dynamics. Last, an extension allowing for the growth of the number of elements is given, in connection with cell differentiation. Effective time sharing system of resources is formed in partially ordered states.Comment: submitted to Physica D, no figures include