Aneta Wróblewska

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Let K be a general nite commutative ring. We refer to a family gn, n = 1, 2, . . . of bijective polynomial multivariate maps of K as a family with invertible decomposition gn = g ng 2 n . . . g k n, such that the knowledge of the composition of g n allows computation of g i n for O(n ) (s > 0) elementary steps. A polynomial map g is stable if all(More)
We say that the sequence gn, n ≥ 3, n → ∞ of polynomial transformation bijective maps of free module K over commutative ring K is a sequence of stable degree if the order of gn is growing with n and the degree of each nonidentical polynomial map of kind gn k is an independent constant c. A transformation b = τgn kτ−1, where τ is affine bijection, n is large(More)
The paper is dedicated to ideas of homomorphic encryption and multivariate key dependent cryptography. We observe recent theoretical results on the above-mentioned topics together with their applications to cloud security. Post Quantum Cryptography could not use many security tools based on Number Theory, because of the factorization algorithm developed by(More)
The family of algebraic graphs D(n,K) defined over finite commutative ring K have been used in different cryptographical algorithms (private and public keys, key exchange protocols). The encryption maps correspond to special walks on this graph. We expand the class of encryption maps via the use of edge transitive automorphism group G(n,K) of D(n,K). The(More)
We say that the sequence gn, n ≥ 3, n → ∞ of polynomial transformation bijective maps of free module Kn over commutative ring K is a sequence of stable degree if the order of gn is growing with n and the degree of each nonidentical polynomial map of kind gn is an independent constant c. Transformation b = τgnkτ−1, where τ is the affine bijection, n is large(More)
The N-Boc-protected (S)-prolinamine reacts readily with formaldehyde and diverse alphahydroxyimino ketones to give imidazole N-oxides with an enantiomerically pure N-protected (pyrrolidin-2yl)methyl substituent. Subsequent deprotection yields the corresponding NH derivatives. Upon treatment of these products with Ac2O at room temperature, a cascade of(More)
A convenient synthesis of (S)-proline hydrazide 2a via the reaction of ethyl (S)-N-benzylprolinate with hydrazine hydrate and subsequent deprotection of (S)-N-benzyl proline hydrazide 5 is described. The latter, in methanolic solution, reacted with aromatic aldehydes as well as with cycloaliphatic ketones at room temperature to give the corresponding(More)
In the present paper we provide the decomposition and local estimates for the pressure function for the non-stationary flow of incompressible non-Newtonian fluids in Orlicz spaces. We show that this method can be applied to prove the existence of weak solutions to the problem of motion of one or several rigid bodies in a non-Newtonian incompressible fluid(More)
A unique approach in mechanosynthesis, joining solid-state NMR spectroscopy, X-ray crystallography, and theoretical calculations, is employed for the first time to study the mechanism of the formation of the C-N amide bond using EDC·HCl as a coupling reagent. It has been proved that EDC·HCl, which in the crystal lattice exists exclusively in the cyclic form(More)
Let K be a finite commutative ring and f = f(n) a bijective polynomial map f(n) of the Cartesian power K onto itself of a small degree c and of a large order. Let f be a multiple composition of f with itself in the group of all polynomial automorphisms, of free module K. The discrete logarithm problem with the "pseudorandom" base f(n) (solve f = b for y) is(More)