Asymmetric cryptographic protocols with a blockchain core: development problems and their solutions

The problem of axiomatic construction of secure cryptographic protocols is closely related to the choice of basic cryptographic blocks from which a cryptographic protocol of arbitrary complexity can be built. Let’s call such blocks primitive cryptographic protocols. Along with a traditional choice as primitive secret sharing protocols and non-interactive proof protocols today blockchain is considered to be a primitive cryptographic protocol. The security of such cryptographic protocols with a blockchain core is studied a bit today. We consider the methods for increasing the security of protocols with blockchain core by using a new agreement protocol in the blockchain, which is secure in the information theoretically sense.

Tensors in Newtonian Physics and the Foundations of Classical Continuum Mechanics

In the Newtonian approach to mechanics, the concepts of objective tensors of various ranks and types are introduced. The tough classification of objective tensors is given, including tensors of material and spatial types. The diagrams are constructed for non-degenerate (“analogous”) relations between tensors of one and the same (any) rank, and of various types of objectivity. Mappings expressing dependence between objective tensor processes of various ranks and types are considered. The fundamental concept of frame-independence of such mappings is introduced as being inherent to constitutive relations of various physical and mechanical properties in the Newtonian approach. The criteria are established for such frame-independence. The mathematical restrictions imposed on the frame-independent mappings by the objectivity types of connected tensors are simultaneously revealed. The absence of such restrictions is established exclusively for mappings and equations linking tensors of material types. Using this, a generalizing concept of objective differentiation of tensor processes in time, and a new concept of objective integration, are introduced. The axiomatic construction of the generalized theory of stress and strain tensors in continuum mechanics is given, which leads to the emergence of continuum classes and families of new tensor measures. The axioms are proposed and a variant of the general theory of constitutive relations of mechanical properties of continuous media is constructed, generalizing the known approaches by Ilyushin and Noll, taking into account the possible presence of internal kinematic constraints and internal body-forces in the body. The concepts of the process image and the properties of the five-dimensional Ilyushin’s isotropy are generalized on the range of finite strains.

A CONSTRUCTION FOR SEMI-COMPACTIFICATIONS

Some new concepts of semi-compact spaces and semi-compactifications are introduced. An axiomatic construction for all Hausdorff compactifications is extended to construct semi-compactifications.

Axiomatic Construction for Language Creativity and Self-Actualization

Piagetian theory views intellective development in children as the unfolding of the axioms which form the basis of symbolic logic through maturation and learning. The modern derivation of set theory from these axioms may be seen as a model of how we formulate valid inferences. The axiomatic construction of the aleph null as equal to 1, which may be derived from the Cantorian algebra, can be used to extend the axiomatic basis of propositional calculus seen as the epistemological root of human knowledge by Piaget. A central postulation regarding natural languages proposed by Chomsky is the creative aspect of language. This axiomatic construction for the Continuum Hypothesis of Gregor Cantor, which permits a nonconfirmatory decision regarding this hypothesis, may be generalized to account for the various aspects of creativity in personality theory, forming (as an extension to Piaget's theory) essential mechanisms of cognition, language behaviour, and self-actualization.