Papers by Aneta Wroblewska
Proceedings of the 2018 Federated Conference on Computer Science and Information Systems
Certain families of graphs can be used to obtain multivariate polynomials for cryptographic algor... more Certain families of graphs can be used to obtain multivariate polynomials for cryptographic algorithms. In particular, in this paper, we introduce stream ciphers based on nonbijective multivariate maps. The presented symmetric encryption algorithms are based on three families of bipartite graphs with partition sets isomorphic to K n , where K is selected as the finite commutative ring. The plainspace of the algorithm is
Proceedings of the 2018 Federated Conference on Computer Science and Information Systems
Certain families of graphs can be used to obtain multivariate polynomials for cryptographic algor... more Certain families of graphs can be used to obtain multivariate polynomials for cryptographic algorithms. In particular, in this paper, we introduce stream ciphers based on nonbijective multivariate maps. The presented symmetric encryption algorithms are based on three families of bipartite graphs with partition sets isomorphic to K n , where K is selected as the finite commutative ring. The plainspace of the algorithm is
We say that the sequence g n , n ≥ 3, n → ∞ of polynomial transformation bijective maps of free m... more We say that the sequence g n , n ≥ 3, n → ∞ of polynomial transformation bijective maps of free module K n over commutative ring K is a sequence of stable degree if the order of g n is growing with n and the degree of each nonidentical polynomial map of kind g n k is an independent constant c. A transformation b = τ g n k τ −1 , where τ is affine bijection, n is large and k is relatively small, can be used as a base of group theoretical Diffie-Hellman key exchange algorithm for the Cremona group C(K n) of all regular automorphisms of K n. The specific feature of this method is that the order of the base may be unknown for the adversary because of the complexity of its computation. The exchange can be implemented by tools of Computer Algebra (symbolic computations). The adversary can not use the degree of righthandside in b x = d to evaluate unknown x in this form for the discrete logarithm problem. In the paper we introduce the explicit constructions of sequences of elements of stable degree for cases c = 3 for each commutative ring K containing at least 3 regular elements and discuss the implementation of related key exchange and public key algorithms.
Security and Communication Networks, 2019
The main purpose of this paper is to introduce stream ciphers with the nonbijective encryption fu... more The main purpose of this paper is to introduce stream ciphers with the nonbijective encryption function of multivariate nature constructed in terms of algebraic graph theory. More precisely, we describe the two main symmetric algorithms for creation of multivariate encryption transformations based on three families of bipartite graphs with partition sets isomorphic to Kn, where K is selected as the finite commutative ring. The plainspace of the algorithm is Ω={x∣∑xi∈K⁎, x∈Kn}⊂Kn,Ω≅K⁎×Kn-1. The second algorithm is a generalization of the first one with using the jump operator, where generalized encryption map has an essentially higher degree in comparison with the previous version. Moreover, the degree of this generalized map is not bounded by some constant. This property guarantees resistance of the cipher to linearization attacks.
ChemInform, 2015
Studies on the Reaction of Aryl Glyoxals with-Prolinol: Unexpected Formation of Morpholin-2-one D... more Studies on the Reaction of Aryl Glyoxals with-Prolinol: Unexpected Formation of Morpholin-2-one Derivatives and Stereoselective Trifluoromethylation of the Bicyclic System.-The reaction of L-prolinol with aryl glyoxals affords labile bicyclic products (III), which undergo isomerization in the presence of an acid to form morpholine derivatives as single diastereomer (IV) or mixtures of diastereomers (VII). These morpholine derivatives can be stereospecifically trifluoromethylated using the Ruppert-Prakash reagent.-(MLOSTON*, G.; WROBLEWSKA, A.;
Asian Journal of Organic Chemistry, 2015
Reactions of l-prolinol with aryl glyoxals lead to labile bicyclic 2-aryloyl-1,3-oxazolidines, wh... more Reactions of l-prolinol with aryl glyoxals lead to labile bicyclic 2-aryloyl-1,3-oxazolidines, which smoothly undergo isomerization in the presence of an acid via ac ascade of reactions involving a1 ,2-aryl shift. The products formed thereby were identified as bicyclic derivatives of morpholin-2-one. Both 1,3-oxazolidines and morpholin-2-ones were used for the nucleophilic trifluoromethylation by treatment with trifluoromethyltrimethylsilane (Ruppert-Prakash reagent)i nt he presence of ac atalytic amount of CsF.W hereas in the case of the 1,3-oxazolidines only modest diastereoselectivity was achieved, the reactions with the morpholinone derivatives occurred with complete stereoselectivity. Scheme1.Reactionofl-prolinol with aryl glyoxal hydrates.
We say that the sequence g n , n ≥ 3, n → ∞ of polynomial transformation bijective maps of free m... more We say that the sequence g n , n ≥ 3, n → ∞ of polynomial transformation bijective maps of free module K n over commutative ring K is a sequence of stable degree if the order of g n is growing with n and the degree of each nonidentical polynomial map of kind g n k is an independent constant c. A transformation b = τ g n k τ −1 , where τ is affine bijection, n is large and k is relatively small, can be used as a base of group theoretical Diffie-Hellman key exchange algorithm for the Cremona group C(K n) of all regular automorphisms of K n. The specific feature of this method is that the order of the base may be unknown for the adversary because of the complexity of its computation. The exchange can be implemented by tools of Computer Algebra (symbolic computations). The adversary can not use the degree of righthandside in b x = d to evaluate unknown x in this form for the discrete logarithm problem. In the paper we introduce the explicit constructions of sequences of elements of stable degree for cases c = 3 for each commutative ring K containing at least 3 regular elements and discuss the implementation of related key exchange and public key algorithms.
ChemInform, 2015
The N-Boc-protected (S)-prolinamine reacts readily with formaldehyde and diverse alphahydroxyimin... 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 reactions leads to optically active tricyclic products. In all these processes, the stereogenic center is preserved. In one case, the bis-heterocyclic imidazole N-oxide was transformed into the corresponding optically active imidazole-2-thione via a sulfurtransfer reaction with 2,2,4,4-tetramethylcyclobutane-1,3-dithione.
Tetrahedron: Asymmetry, 2012
A convenient synthesis of (S)-proline hydrazide 2a via the reaction of ethyl (S)-N-benzylprolinat... 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 hydrazones of type 7 in good yields. The structure of the product with furan-2-carbaldehyde 7b, proving the (E)-configuration of the hydrazone, was established by X-ray crystallography. In the case of the unprotected (S)-proline hydrazide 2a, the analogous reaction with aromatic aldehydes led either to the expected hydrazones 7 or the 1H-pyrrolo[1,2-c]imidazol-1-one derivatives 8, depending on the reaction conditions. The latter were formed via a secondary cyclocondensation of the initially formed 7 with a second molecule of the aldehyde. Whereas the reaction of (S)-Nbenzyl proline hydrazide 5 with butyl isocyanate and isothiocyanate gave the corresponding semicarbazide and thiosemicarbazide, respectively, of type 9, the unprotected (S)-proline hydrazide 2a yielded the 1:2 adducts 10. Thiosemicarbazide 9b underwent cyclization reactions under basic (NaOH) and acidic (H2SO4) conditions to yield (S)-prolinyl-substituted 1,2,4-triazole-3-thione 11 and 1,3,4-thiadiazole-2amine 12, respectively.
Annales UMCS, Informatica, 2014
>IJH=?J Let K be a general nite commutative ring. We refer to a family gn, n = 1, 2,. .. of bijec... more >IJH=?J Let K be a general nite commutative ring. We refer to a family gn, n = 1, 2,. .. of bijective polynomial multivariate maps of K n as a family with invertible decomposition gn = g 1 n g 2 n. .. g k n , such that the knowledge of the composition of g i n allows computation of g i n for O(n s) (s > 0) elementary steps. A polynomial map g is stable if all non-identical elements of kind g t , t > 0 are of the same degree. We construct a new family of stable elements with invertible decomposition. This is the rst construction of the family of maps based on walks on the bipartite algebraic graphs dened over K, which are not edge transitive. We describe the application of the above mentioned construction for the development of stream ciphers, public key algorithms and key exchange protocols. The absence of edge transitive group essentially complicates cryptanalysis.
Annales UMCS, Informatica, 2013
We say that the sequence gn, n ≥ 3, n → ∞ of polynomial transformation bijective maps of free mod... more We say that the sequence gn, n ≥ 3, n → ∞ of polynomial transformation bijective maps of free module K n 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. Transformation b = τ gn k τ −1 , where τ is the affine bijection, n is large and k is relatively small, can be used as a base of group theoretical Diffie-Hellman key exchange algorithm for the Cremona group C(K n) of all regular automorphisms of K n. The specific feature of this method is that the order of the base may be unknown for the adversary because of the complexity of its computation. The exchange can be implemented by tools of Computer Algebra (symbolic computations). The adversary can not use the degree of righthandside in b x = d to evaluate unknown x in this form for the discrete logarithm problem. In the paper we introduce the explicit constructions of sequences of elements of stable degree for the cases c = 3 and c = n+2 4 for each commutative ring K containing at least 3 regular elements and discuss the implementation of related key exchange and multivariate map algorithms.
Annales UMCS, Informatica, 2012
Let K be a finite commutative ring and f = f (n) a bijective polynomial map f (n) of the Cartesia... more Let K be a finite commutative ring and f = f (n) a bijective polynomial map f (n) of the Cartesian power K n onto itself of a small degree c and of a large order. Let f y be a multiple composition of f with itself in the group of all polynomial automorphisms, of free module K n. The discrete logarithm problem with the "pseudorandom" base f (n) (solve f y = b for y) is a hard task if n is "sufficiently large". We will use families of algebraic graphs defined over K and corresponding dynamical systems for the explicit constructions of such maps f (n) of a large order with c =2such that all nonidentical powers f y are quadratic polynomial maps. The above mentioned result is used in the cryptographical algorithms based on the maps f (n)-in the symbolic key exchange protocols and public keys algorithms.
Annales UMCS, Informatica, 2011
The family of algebraic graphs D(n, K) defined over finite commutative ring K have been used in d... 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 graph D(n, K) and related directed graphs are disconnected. So private keys corresponding to walks preserve each connected component. The group G(n, K) of transformations generated by an expanded set of encryption maps acts transitively on the plainspace. Thus we have a great difference with block ciphers, any plaintexts can be transformed to an arbitrarily chosen ciphertex by an encryption map. The plainspace for the D(n, K) graph based encryption is a free module P over the ring K. The group G(n, K) is a subgroup of Cremona group of all polynomial automorphisms. The maximal degree for a polynomial from G(n, K) is 3. We discuss the Diffie-Hellman algorithm based on the discrete logarithm problem for the
Nonlocal and Abstract Parabolic Equations and their Applications, 2009
The paper concerns uniqueness of weak solutions to non-Newtonian fluids with nonstandard growth c... more The paper concerns uniqueness of weak solutions to non-Newtonian fluids with nonstandard growth conditions for the Cauchy stress tensor. We recall the results on existence of weak solutions and additionally provide the proof of existence of measure-valued solutions. Motivated by the fluids of strongly inhomogeneous behaviour and having the property of rapid shear thickening we observe that the described situation cannot be captured by power-lawtype rheology. We describe the growth conditions with the help of general x-dependent convex functions. This formulation yields the existence of solutions in generalized Orlicz spaces. These considerations are motivated by e.g. electrorheological fluids, magnetorheological fluids, and shear thickening fluids.
Tetrahedron: Asymmetry, 2013
Starting with (S)-1-benzylprolinamine and alpha-hydroxyimino ketones, enantiomerically pure bishe... more Starting with (S)-1-benzylprolinamine and alpha-hydroxyimino ketones, enantiomerically pure bisheterocyclic imidazole N-oxides bearing the (S)-configured N-benzyl(pyrrolidin-2-yl)methyl residue were prepared. These N-oxides reacted with 2,2,4,4-tetramethylcyclobutane-1,3-dithione to give the corresponding optically active imidazole-2-thione derivatives via a sulfur transfer reaction. Reduction of the N-oxides with Raney-nickel led to deoxygenation, whereas catalytic hydrogenation (Pd/C) in ethanol occurred with simultaneous deoxygenation and debenzylation, leading to optically active 1-(pyrrolidin-2yl)methyl-1H-imidazoles. Alkylation of the prepared imidazole N-oxides and their respective imidazoles with butyl and hexyl bromide and subsequent anion exchange gave optically active N-alkoxy-and N-alkylimidazolium tetrafluoroborates, respectively, with the properties of 'room temperature ionic liquids'.
Phosphorus, Sulfur, and Silicon and the Related Elements, 2013
ABSTRACT Enantiopure thiourea derivatives, containing pyrrolidine ring, were prepared by the reac... more ABSTRACT Enantiopure thiourea derivatives, containing pyrrolidine ring, were prepared by the reaction of N-Boc-(S)-2-aminomethylpyrrolidine (6) with thioisocyanates 8.
Mathematical Methods in the Applied Sciences, 2009
Communicated by M. Lachowicz The paper concerns existence of weak solutions to the equations desc... more Communicated by M. Lachowicz The paper concerns existence of weak solutions to the equations describing a motion of some non-Newtonian fluids with non-standard growth conditions of the Cauchy stress tensor. Motivated by the fluids of strongly inhomogeneous behavior and having the property of rapid shear thickening, we observe that the L p framework is not suitable to capture the described situation. We describe the growth conditions with the help of general x-dependent convex function. This formulation yields the existence of solutions in generalized Orlicz spaces. As examples of motivation for considering non-Newtonian fluids in such spaces, we recall the electrorheological fluids, magnetorheological fluids, and shear thickening fluids. The existence of solutions is established by the generalization of the classical Minty method to non-reflexive spaces. The result holds under the assumption that the lowest growth of the Cauchy stress is greater than the critical exponent q = (3d+2) / (d+2), where d is for space dimension. The restriction on the exponent q is forced by the convective term.
Journal of Differential Equations, 2012
We study a general class of nonlinear elliptic problems associated with the differential inclusio... more We study a general class of nonlinear elliptic problems associated with the differential inclusion β(x, u) − div(a(x, ∇u) + F (u)) f , where f ∈ L 1 (Ω). The vector field a(•,•) is monotone in the second variable and satisfies a non-standard growth condition described by an x-dependent convex function that generalizes both L p(x) and classical Orlicz settings. Using truncation techniques and a generalized Minty method in the functional setting of non-reflexive spaces we prove existence of renormalized solutions for general L 1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established. Sufficient conditions are specified which guarantee that the renormalized solution is already a weak solution to the problem.
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Papers by Aneta Wroblewska