The possibility of superradiation without the Penrose process

In the traditional theory, it is impossible to produce superradiation in a straight time and space without a Penrose process. We know that similar entities can be artificially created by formulas that exist in the algebraic field. We have found that when a certain potential is created, there will be a superradiation phenomenon without the Penrose process in flat space and time.

Analysis of the complexity of attacks on multivariate cryptographic transformations using algebraic field structure

In recent years, interest in cryptosystems based on multidimensional quadratic transformations (MQ transformations) has grown significantly. This is primarily due to the NIST PQC competition [1] and the need for practical electronic signature schemes that are resistant to attacks on quantum computers. Despite the fact that the world community has done a lot of work on cryptanalysis of the presented schemes, many issues need further clarification. NIST specialists are very cautious about the standardization process and urge cryptologists [4] in the next 3 years to conduct a comprehensive analysis of the finalists of the NIST PQC competition before their standardization. One of the finalists is the Rainbow electronic signature scheme [2]. It is a generalization of the UOV (Unbalanced Oil and Vinegar) scheme [3]. Recently, another generalization of this scheme – LUOV (Lifted UOV) [5] was found to attack [6], which in polynomial time is able to recover completely the private key. The peculiarity of this attack is the use of the algebraic structure of the field over which the MQ transformation is given. This line of attack has emerged recently and it is still unclear whether it is possible to use the field structure in the Rainbow scheme. The aim of this work is to systematize the techniques used in attacks using the algebraic field structure for UOV-based cryptosystems and to analyze the obstacles for their generalization to the Rainbow scheme.

On the Integral Degree of Integral Ring Extensions

Let A ⊂ B be an integral ring extension of integral domains with fields of fractions K and L, respectively. The integral degree of A ⊂ B, denoted by dA(B), is defined as the supremum of the degrees of minimal integral equations of elements of B over A. It is an invariant that lies in between dK(L) and μA(B), the minimal number of generators of the A-module B. Our purpose is to study this invariant. We prove that it is sub-multiplicative and upper-semicontinuous in the following three cases: if A ⊂ B is simple; if A ⊂ B is projective and finite and K ⊂ L is a simple algebraic field extension; or if A is integrally closed. Furthermore, d is upper-semicontinuous if A is noetherian of dimension 1 and with finite integral closure. In general, however, d is neither sub-multiplicative nor upper-semicontinuous.

A model for massless higher spin field interacting with a geometrical background

We study a very general four-dimensional field theory model describing the dynamics of a massless higher spin N symmetric tensor field particle interacting with a geometrical background. This model is invariant under the action of an extended linear diffeomorphism. We investigate the consistency of the equations of motion, and the highest spin degrees of freedom are extracted by means of a set of covariant constraints. Moreover, the highest spin equations of motions (and in general all the highest spin field 1-PI irreducible Green functions) are invariant under a chain of transformations induced by a set of N - 2 Ward operators, while the auxiliary fields equations of motion spoil this symmetry. The first steps to a quantum extension of the model are discussed on the basis of the algebraic field theory. Technical aspects are reported in Appendices, in particular, one of them is devoted to illustrate the spin-2 case.