Let H be a subgroup of the multiplicative group of a finite field. In this note we give a method for constructing permutation polynomials over the field using a bijective map from H to a coset of H. A similar, but inequivalent, method for lifting permutation behaviour of a polynomial to an extension field is also given.

In this paper, we first prove beyond-birthyday-bound security for the Misty structure. Specifically, we show that an r-round Misty structure is secure against CCA attacks up to O(2 rn r+7 ) query complexity, where n is the size of each round permutation. So for any > 0, a sufficient number of rounds would guarantee the security of the Misty structure up to 2n(1− ) query complexity.

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...

The image encryption is widely used to secure transmission of data in an open internet and internet works. For image based cryptosystems chaotic maps can be used as a key because of its nonlinear component. Due to sensitivity to initial conditions, chaotic maps have best alternative for designing dynamic permutation of the image based cryptosystem. A chaotic map is used to generate permutation ...

Abstract We construct via Fraïssé amalgamation an ????-categorical structure whose automorphism group is infinite oligomorphic Jordan primitive permutation preserving a “limit of ????-relations”. The construction based on semilinear order elements are labelled by sets carrying ????-relation, with strong coherence conditions governing how these ????-sets inter-related.

Abstract Background The search for statistically significant relationships between molecular markers and outcomes is challenging when dealing with high-dimensional, noisy collinear multivariate omics data, such as metabolomic profiles. Permutation procedures allow the estimation of adjusted significance levels without assuming independence among variables. Nevertheless, complex non-normal struc...

We must protect inherently fragile quantum data to unlock the potential of technologies. A pertinent concern in schemes for storage is their near-term implementation. Since Heisenberg ferromagnets are readily available, we investigate robust storage. propose use permutation-invariant codes store ferromagnets, because ground space any ferromagnet be symmetric under permutation underlying qubits....

The properties of a representation, such as smoothness, adaptability, generality, equivariance/invariance, depend on restrictions imposed during learning. In this paper, we propose using data symmetries, in the sense of equivalences under transformations, as a means for learning symmetryadapted representations, i.e., representations that are equivariant to transformations in the original space....