Quantum Algorithms for Attacking Hardness Assumptions in Classical and Post‐Quantum Cryptography

In this survey, the authors review the main quantum algorithms for solving the computational problems that serve as hardness assumptions for cryptosystem. To this end, the authors consider both the currently most widely used classically secure cryptosystems, and the most promising candidates for post-quantum secure cryptosystems. The authors provide details on the cost of the quantum algorithms presented in this survey. The authors furthermore discuss ongoing research directions that can impact quantum cryptanalysis in the future

On the Origin of Abstraction : Real and Imaginary Parts of Decidability-Making

International audienceThe behavioral tradition has largely anchored on Simon's early conception of bounded rationality, it is important to engage more explicitly cognitive approaches particularly ones that might link to the issue of identifying novel competitive positions. The purpose of the study is to describe the cognitive processes by which decision-makers manage to work, individually or collectively, through undecidable situations and design innovatively. Most widespread models of rationality developed for preference-making and based on a real dimension should be extended for abstraction-making by adding a visible imaginary one. A development of a core analytical/conceptual apparatus is proposed to purposely account this dual form of reasoning, deductive to prove (then make) equivalence and abstractive to represent (then unmake) it. Complex numbers, comfortable to describe repetitive, expansional and superimposing phenomena (like waves, envelope of waves, interferences or holograms, etc.) appear as generalizable to cognitive processes at work when redesigning a decidable space by abstraction (like relief vision to design a missing depth dimension, Loyd's problem to design a missing degree of freedom, etc.). This theoretical breakthrough may open up vistas capacity in the fields of information systems, knowledge and decision

Interpretations of a constructivist philosophy in mathematics teaching

This thesis is a research biography which reports a study of mathematics teaching. It involves research into the classroom teaching of mathematics of six teachers, and into their associated beliefs and motivations. The teachers were selected because they gave evidence of employing an investigative approach to mathematics teaching, according to the researcher's perspective. A research aim was to characterise such an approach through the practice of these teachers. An investigative approach was seen to be embedded in a radical constructivist philosophy of knowledge and learning. Observations and analysis were undertaken from a constructivist perspective and interpretations made were related to this perspective. Research methodology was ethnographic in form, using techniques of participant-observation and informal interviewing for data collection, and triangulation and respondent validation for verification of analysis. Analysis was qualitative, leading to emergent theory requiring reconciliation with a constructivist theoretical base. Rigour was sought by research being undertaken from a researcher-as-instrwnent position, with the production of a reflexive account in which interpretations were accounted for in terms of their context and the perceptions of the various participants including those of the researcher. Research showed that those teachers who could be seen to operate from a constructivist philosophy regularly made high level cognitive demands which resulted in the incidence of high level mathematical processes and thinldng skills in their pupils. Levels of interpretation within the study led to the identification of investigative teaching both as a style of mathematics teaching and as a form of reflective practice in the teaching of mathematics. These forms were synthesised as a constructivist pedagogy and as an epistemology for practice which may be seen to forge links between the theory of mathematics teaching and its practice. The research is seen to have implications for the teaching of mathematics, and for the development of mathematics teaching itself through professional development of mathematics teachers