arXiv subjects

P. Vanchinathan

Publications and source records attributed to P. Vanchinathan.

4 recordsLinked to original sources

arXiv2023

Higher Level Completeness for Permutation Polynomials

Generalising the concept of a complete permutation polynomial over a finite field, we define completness to level $k$ for $k\ge1$ in fields of odd characteristic. We construct two families of polynomials that satisfy the condition of high level completeness for all finite fields, and two more families complete to the maximum level a possible for large collection of finite fields. Under the binary operation of composition of functions one family of polynomials is an abelian group isomorphic to the additive group, while the other is isomorphic to the multiplicative group.

math.NT↗

arXiv2017

Dimension formula for the space of relative symmetric polynomials of D_n with respect to any irreducible representation

We provide a formula and a generating function for the dimension of the vector space of relative symmetric polynomials of D_n for all its irreducible one-dimensional and two-dimensional representations which were defined originally by M. Shahryari.

math.AC↗

arXiv2017

Symmetric Key Encryption for Arbitrary Block Sizes from Affine Spaces

A symmetric key encryption scheme is described for blocks of general size N that is a product of powers of many prime numbers. This is accomplished by realising each number (representing a message unit) as a point in a product of affine spaces over various finite fields. Then algebro-geometric transformations on those affine spaces is transported back to provide encryption. For a specific block size${}<2^{128}$ we get more than $2^{5478}$ keys.

cs.CR↗

arXiv2009

Nondegeneracy for Quotient Varieties under Finite Group Actions

We prove that for an abelian group $G$ of order $n$ the morphism $ φ\colon \mathbf{P}(V^*)\longrightarrow \mathbf{P} ((\mathrm{sym}^n V^*)^G)$ defined by $φ([f]) = [\prod_{σ\in G} σ\cdot f ]$ is nondegenerate for every finite-dimensional representation $V$ of $G$ if and only if either $n$ is a prime number or $n=4$.

math.AG↗