Download Cryptography and Security Systems: Third International by Zbigniew Kotulski, Bogdan Ksiezopolski, Katarzyna Mazur PDF

By Zbigniew Kotulski, Bogdan Ksiezopolski, Katarzyna Mazur

This booklet constitutes the refereed complaints of the 3rd overseas convention on Cryptography and protection platforms, CSS 2014, held in Lublin, Poland, in September 2014. The 17 revised complete papers offered have been conscientiously reviewed and chosen from forty three submissions. 7 of these papers predicament assorted parts of cryptography, whereas the rest 10 take care of contemporary difficulties of cryptographic protocols.

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Extra resources for Cryptography and Security Systems: Third International Conference, CSS 2014, Lublin, Poland, September 22-24, 2014. Proceedings

Example text

Alice works with the flag space of the graph D(n, K). She chooses the walk in the graph via strings α1 , α2 , . . , αk and β1 , β2 , . . , βk from the affine space K k . She generates the cubical map: E = N Pα1 N Lβ1 N Pα2 N Lβ2 . . N Pαk N Lβk . (31) Together with its fast invertible decomposition into transformations corresponding to the edges of the walk. The inverse map is given as: E = N L−βk N P−αk . . N L−β2 N P−α2 N L−β1 N P−α1 . (32) The existence of invertible decomposition allows computation of E and E for kO(n) elementary operation.

Its restrictions are publicly presented on W1 which is a polynomial map from K n+1−[(n+2)/4] into K n+1 . It can be computed in given point for (n + 1 − [(n + 2)/4])n3 . So, the complexity is O(n4 ). The computation has to be done after the expansion of a plaintext by the compression rules. If each bivariate function φ(z1 , z2 ) has the polynomial density O(ns ) and polynomial degree O(st ). All of them can be computed for time O(ns+t+1 ). If we assume that s + t ≤ 3, then compression does not increase significantly the complexity of ciphertext computation.

Then the value of f (n) in the point x ∈ K n can be computed by O(ns+d ) elementary steps. We say that the family f (n) ∈ C(K n ) has an invertible decomposition of speed d if f (n) can be written as a composition of elements f 1 (n), f 2 (n), . . , f k(n) (n) and this decomposition will allow us to compute the value of y = f (x) and the re-image of given y in time k(n)O(nd ). In the case d = 1 we state that invertible decomposition is of linear speed. The complexity of computation of the value of each f i (n) in a given point x is O(nd ).

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