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- Vasyl Ustimenko, Aneta Wróblewska
- ArXiv
- 2013

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,… (More)

- Vasyl Ustimenko, Aneta Wroblewska, Maria Curie-Sklodowska
- 2013

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)

- Vasyl Ustimenko, Aneta Wróblewska
- Annales UMCS, Informatica
- 2011

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)

- Vasyl Ustimenko, Aneta Wróblewska
- Annales UMCS, Informatica
- 2012

– 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… (More)

- Vasyl Ustimenko, Aneta Wróblewska
- Annales UMCS, Informatica
- 2013

– 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,… (More)

- Aneta Wróblewska, Vasyl Ustimenko
- Annales UMCS, Informatica
- 2014

>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… (More)

- Monika Polak, Urszula Romanczuk, Vasyl Ustimenko, Aneta Wróblewska
- Electronic Notes in Discrete Mathematics
- 2013

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