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Development and analysis of a cryptographic algorithm for genetically optimized wireless sensor

Benjamim X. C., Gama F., Semente R. O., Villarrea E., Salazar A.

Przegląd Elektrotechniczny

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2018

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R. 94, nr 8

79--84

EN

This article proposes a methodology for obtaining a cryptographic algorithm, optimized for wireless sensor networks, through genetic algorithm. With the objective of increasing the level of security, computational efficiency and highlighting the energy consumption, considering that the autonomy of the wireless sensor devices is directly influenced by this factor. In aptitude function of genetic algorithm, were used metrics of algorithm runtime, maximum deviation and irregular, space occupied in memory and correlation coefficient (a new proposed metric), in order to find a safe and fast algorithm. The results obtained through computational simulations show the efficiency of the proposed methodology, in terms of processing time, coefficient of correlation and occupation of memory.

PL

W tym artykule zaproponowano metodologię uzyskiwania algorytmu kryptograficznego, zoptymalizowanego dla bezprzewodowych sieci czujników, za pomoca˛ algorytmu genetycznego. W celu zwiększenia poziomu bezpieczeństwa, wydajności obliczeniowej i podkreślenia zużycia energii, biorąc pod uwagę fakt, że ten czynnik ma bezposśredni wpływ na autonomię bezprzewodowych czujników. W funkcji uzdatniania algorytmu genetycznego wykorzystano metryki czasu pracy algorytmu, maksymalnego odchylenia i nieregularności, miejsca zajmowanego w pamięci i współczynnika korelacji (nowa proponowana metryka), aby znaleźć bezpieczny i szybki algorytm. Wyniki uzyskane za pomocą symulacji obliczeniowych pokazują efektywność proponowanej metodologii, pod względem czasu przetwarzania, współczynnika korelacji i zajęcia pamięci.

2

On the family of cubical multivariate cryptosystems based on the algebraic graph over finite commutative rings of characteristic 2

Romańczuk U., Ustimenko V.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

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2012

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Vol. 12, no. 3

89--106

EN

The family of algebraic graphs A(n;K) defined over the finite commutative ring K were used for the design of different multivariate cryptographical algorithms (private and public keys, key exchange protocols). The encryption map corresponds to a special walk on this graph. We expand the class of encryption maps via the use of an automorphism group of A(n;K). In the case of characteristic 2 the encryption transformation is a Boolean map. We change finite field for the commutative ring of characteristic 2 and consider some modifications of algorithm which allow to hide a ground commutative ring.

3

Dynamical systems as the main instrument for the constructions of new quadratic families and their usage in cryptography

Ustimenko V., Wroblewska A.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

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2012

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Vol. 12, no. 3

65--74

EN

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) (solvef^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 = 2 such 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.

4

On the key expansion of D(n, K)-based cryptographical algorithm

Ustimenko V., Wróblewska A.

Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica

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2011

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Vol. 11, no. 2

95--111

EN

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 group τ-1Gτ, where τ is invertible affine transformation of free module P i.e. polynomial automorphism of degree 1. We consider some relations for the discrete logarithm problem for G(n, K) and public key algorithm based on the D(n, K) graphs.