Assessing security of some group based cryptosystems

One of the possible generalizations of the discrete logarithm problem to arbitrary groups is the so-called conjugacy search problem (sometimes erroneously called just the conjugacy problem): given two elements a, b of a group G and the information that a^x=b for some x \in G, find at least one particular element x like that. Here a^x stands for xax^{-1}. The computational difficulty of this problem in some particular groups has been used in several group based cryptosystems. Recently, a few preprints have been in circulation that suggested various "neighbourhood search" type heuristic attacks on the conjugacy search problem. The goal of the present survey is to stress a (probably well known) fact that these heuristic attacks alone are not a threat to the security of a cryptosystem, and, more importantly, to suggest a more credible approach to assessing security of group based cryptosystems. Such an approach should be necessarily based on the concept of the average case complexity (or expected running time) of an algorithm. These arguments support the following conclusion: although it is generally feasible to base the security of a cryptosystem on the difficulty of the conjugacy search problem, the group G itself (the "platform") has to be chosen very carefully. In particular, experimental as well as theoretical evidence collected so far makes it appear likely that braid groups are not a good choice for the platform. We also reflect on possible replacements.Comment: 10 page

The relation between prior knowledge and students' collaborative discovery learning processes

In this study we investigate how prior knowledge influences knowledge development during collaborative discovery learning. Fifteen dyads of students (pre-university education, 15-16 years old) worked on a discovery learning task in the physics field of kinematics. The (face-to-face) communication between students was recorded and the interaction with the environment was logged. Based on students' individual judgments of the truth-value and testability of a series of domain-specific propositions, a detailed description of the knowledge configuration for each dyad was created before they entered the learning environment. Qualitative analyses of two dialogues illustrated that prior knowledge influences the discovery learning processes, and knowledge development in a pair of students. Assessments of student and dyad definitional (domain-specific) knowledge, generic (mathematical and graph) knowledge, and generic (discovery) skills were related to the students' dialogue in different discovery learning processes. Results show that a high level of definitional prior knowledge is positively related to the proportion of communication regarding the interpretation of results. Heterogeneity with respect to generic prior knowledge was positively related to the number of utterances made in the discovery process categories hypotheses generation and experimentation. Results of the qualitative analyses indicated that collaboration between extremely heterogeneous dyads is difficult when the high achiever is not willing to scaffold information and work in the low achiever's zone of proximal development

Accommodating disability in higher education: a closer look at the evidence for a mainstream framework of learning support

In a recently published research article in this journal, Avramidis & Skidmore (2004) argued that it is time we placed issues of disability provision more in the context of provision for the generic student. They presented a study based on the Learning for All Questionnaire (LfAQ), which investigated certain implied issues. Findings indicated a need for improved educational provision for all students. No differences were found between disabled and non-disabled students in perceived level of needs or support for university, tutoring and lecturing systems. This null finding was the same for the learning support needs of disabled versus non-disabled students, with both groups wanting identical changes to the way the university's central learning support service responds to learning needs. These findings were taken as calling for a move away from a ‘specialist’ framework of disability provision and towards a ‘mainstream’ framework instead, in which the needs of disabled students are accommodated within improvements made in learning for all. Further, the Disabled Students' Allowance should be given over to departments in order to help fund this change in ‘institutional habitus’. In this article, four serious failings of the study and analyses are outlined. When these are addressed in a disability-theoretic reanalysis of the LfAQ data, every main finding is reversed. It is concluded that educational provisions are generally adequate. Students would welcome changes but these are more to do with increasing levels of convenience rather than learning support issues. Furthermore, the LfAQ data actually refute rather than support a mainstream framework of disability provision

Heterotic/Heterotic Duality in D=6,4

We consider $E_8\times E_8$ heterotic compactifications on $K3$ and $K3\times T^2$. The idea of heterotic/heterotic duality in $D=6$ has difficulties for generic compactifications since for large dilaton values some gauge groups acquire negative kinetic terms. Recently Duff, Minasian and Witten (DMW) suggested a solution to this problem which only works if the compactification is performed assuming the presence of symmetric gauge embeddings on both $E_8$'s. We consider an alternative in which asymmetric embeddings are possible and the wrong sign of kinetic terms for large dilaton value is a signal of spontaneous symmetry breaking. Upon further toroidal compactification to $D=4$, we find that the duals in the DMW case correspond to $N=2$ models in which the $\beta$-function of the different group factors verify ${\beta }_\alpha=12$, whereas the asymmetric solutions that we propose have ${\beta }_\alpha=24$. We check the consistency of these dualities by studying the different large $T,S$ limits of the gauge kinetic function. Dual $N=1$, $D=4$ models can also be obtained by the operation of appropriate freely acting twists, as shown in specific examples.Comment: 15 pages, late

Society seen through the prism of space: outline of a theory of society and space

Two questions challenge the student of space and society above all others: will new technologies change the spatial basis of society ? And if so, will this have an impact on society itself ? For the urbanist, these two questions crystallise into one: what will the future of cities have to do with their past ? Too often these questions are dealt with as though they were only matters of technology. But they are much more than that. They are deep and difficult questions about the interdependence of technology, space and society that we do not yet have the theoretical apparatus to answer. We know that previous �revolutions� in technology such as agriculture, urbanism and industrialisation associated radical changes in space with no less radical changes in social institutions. But we do not know how far these linkages were contingent or necessary. We do not, in short, have a theory of society and space adequate to account for where we are now, and therefore we have no reasonable theoretical base for speculating about the future. In this paper, I suggest that a major reason for this theoretical deficit is that most previous attempts to build a theory of society and space have looked at society and tried to find space in its output. The result has been that the constructive role of space in creating and and sustaining society has not been brought to the fore, or if it has, only in a way which is too general to permit the detailed specification of mechanisms. In this paper I try to reverse the normal order of things this by looking first at space and trying the discern society through space: by looking at society through the prism of space. Through this I try to define key mechanisms linking space to society and then use these to suggest how the questions about the future of cities and societies might be better defined