Artículo
A computational algebraic geometry approach to analyze pseudo-random sequences based on Latin squares
Autor/es | Falcón Ganfornina, Raúl Manuel
Álvarez Solano, Víctor Gudiel Rodríguez, Félix |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Fecha de publicación | 2019 |
Fecha de depósito | 2019-10-14 |
Publicado en |
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Resumen | Latin squares are used as scramblers on symmetric-key algorithms that generate
pseudo-random sequences of the same length. The robustness and effectiveness of
these algorithms are respectively based on the extremely large ... Latin squares are used as scramblers on symmetric-key algorithms that generate pseudo-random sequences of the same length. The robustness and effectiveness of these algorithms are respectively based on the extremely large key space and the appropriate choice of the Latin square under consideration. It is also known the importance that isomorphism classes of Latin squares have to design an effective algorithm. In order to delve into this last aspect, we improve in this paper the efficiency of the known methods on computational algebraic geometry to enumerate and classify partial Latin squares. Particularly, we introduce the notion of affine algebraic set of a partial Latin square L = (lij ) of order n over a field K as the set of zeros of the binomial ideal xi xj − xlij : (i, j) is a non-empty cell inL ⊆ K[x1, . . . , xn]. Since isomorphic partial Latin squares give rise to isomorphic affine algebraic sets, every isomorphism invariant of the latter constitutes an isomorphism invariant of the former. In particular, we deal computationally with the problem of deciding whether two given partial Latin squares have either the same or isomorphic affine algebraic sets. To this end, we introduce a new pair of equivalence relations among partial Latin squares: being partial transpose and being partial isotopic. |
Cita | Falcón Ganfornina, R.M., Álvarez Solano, V. y Gudiel Rodríguez, F. (2019). A computational algebraic geometry approach to analyze pseudo-random sequences based on Latin squares. Advances in Computational Mathematics, 45 (4), 1769-1792. |
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