by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fait...

$$\mathsf {Gimli}$$ is a family of cryptographic primitives (both hash function and an AEAD scheme) that has been selected for the second round NIST competition standardizing new lightweight designs. The candidate based on permutation , which was presented at CHES 2017. In this paper, we study security both constructions are it. We exploit slow diffusion in its internal symmetries to build, fir...

A special class of cubic graphs are the cycle permutation graphs. A cycle permutation graph Pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.In this paper we determine a good upper bound for tenacity of cycle permutation graphs.

In 2007, Tenner established a connection between pattern avoidance in permutations and the Bruhat order on permutations by showing that the downset of a permutation in the Bruhat order is a Boolean algebra if and only if the permutation is 3412 and 321 avoiding. Tenner mentioned, but did not prove, that if the permutation is 321 avoiding and contains exactly one 3412 pattern, or if the permutat...

The current study focuses on the problem of determining investment attrаctiveness of countries by means of monitoring regional stock markets. The method of using the permutation entropy as a model of investment attractiveness estimation is suggested. We have calculated the permutation entropy for the time series of stock markets of countries for the period from 2005 to 2018. The countries with ...

This paper deals with the amount of disorder that is left in a permutation after one of its elements has been selected with quickselect with or without median-of-three pivoting. Five measures of disorder are considered: inversions, cycles of length less than or equal to some m, cycles of any length, expected cycle length, and the distance to the identity permutation. “Grand averages” for each m...

Authenticated encryption schemes establish both privacy and authenticity. This paper specifies a family of the dedicated authenticated encryption schemes, Artemia. It is an online nonce-based authenticated encryption scheme which supports the associated data. Artemia uses the permutation based mode, JHAE, that is provably secure in the ideal permutation model. The scheme does not require the in...