On perfect nonlinear functions

Xiyong, Zhang; Wenbao, Han; Shuqin, Fan

doi:10.1002/jcd.20051

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…An alternative construction by means of coordinate functions is suggested in e.g. [11,13]. Much work on an efficient P-box has been done by designers of AES [5].…”

Section: Introductionmentioning

confidence: 99%

On complexity of round transformations

Grošek

Horak

Zajac

2009

Discrete Mathematics

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a b s t r a c tA modern block cipher consists of round transformations, which are obtained by alternatively applying permutations (P-boxes) and substitutions (S-boxes). Clearly, the most important attribute of a block cipher is its security. However, with respect to the hardware implementation, a good block cipher has to have a reasonable complexity as well.In this paper, we study complexity of round transformations satisfying some basic security criteria. There are several ways to define the complexity of a round transformation, and to choose "necessary" security criteria. It turns out, that for our purpose, it is suitable to view a round transformation as a single Boolean function, not separating it into S-boxes and P-boxes. We require that the Boolean function F possesses some fundamental properties imposed on each block cipher for security reasons; namely, we require that the function is a strictly non-linear bijection and that it has a good diffusion. The total number of variables in the normal algebraic form of the component functions of F is taken as its complexity. We find the minimum complexity of such functions, and this way we establish a lower bound on complexity of all round transformations. To show that the lower bound is the best possible, we construct a round transformation F attaining the bound. We stress that it is not an aspiration of this paper to construct a round transformation which would be of practical use; F is useful only from the theoretical point of view.

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“…An alternative construction by means of coordinate functions is suggested in e.g. [11,13]. Much work on an efficient P-box has been done by designers of AES [5].…”

Section: Introductionmentioning

confidence: 99%