On complexity of formal coding method for analysis of generator with monocycle substitutional transition function
Prikladnaâ diskretnaâ matematika, no. 3 (2009), pp. 21-28
Citer cet article
Voir la notice de l'article provenant de la source Math-Net.Ru
Here we investigate autonomous automata with automaton states being binary $n$-dimensional vectors and transition function being a monocycle substitution. The complexity $T_n$ of solving gamma generating equations system by formal coding method is estimated asuming the number of equations is not constrained. Bounds of $T_n$ are obtained by estimating line complexity and the order monomial sets for the output functions sequence. It is stated that $TL(2^{n-1}) where $TL(m)$ is a complexity of solving linear equations system of size $m\times m$ over field $\mathrm{GF}(2)$.
[1] Schaumüller-Bichl I., “Cryptanalysis of the Data Encryption Standard by a method of formal coding”, Cryptography, Proc. (Burg Feuerstein, 1982), LNCS, 149, 1983, 235–255 | Zbl
[2] Courtois N., Klimov A., Patarin J., Shamir A., “Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations”, LNCS, 1807, 2000, 392–407 | MR | Zbl
[3] Fomichëv V. M., Diskretnaya matematika i kriptologiya, DIALOG–MIFI, M., 2003, 400 pp.