Dot-Product Sets and Simplices Over Finite Rings
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-022-09933-7
Abstract: In this paper, we study dot-product sets and k -simplices in $$\mathbb {Z}_n^d$$ Z n d for odd n , where $$\mathbb {Z}_n$$ Z n is the ring of residues modulo n . We show… read more here.
Keywords: dot product; product; finite rings; sets simplices ... See more keywords
Random Motion on Finite Rings, I: Commutative Rings
Sign Up to like & getrecommendations! Published in 2019 at "Algebras and Representation Theory"
DOI: 10.1007/s10468-019-09864-w
Abstract: We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first prove… read more here.
Keywords: commutative rings; random motion; multiplication; rings commutative ... See more keywords
Counting points of schemes over finite rings and counting representations of arithmetic lattices
Sign Up to like & getrecommendations! Published in 2018 at "Duke Mathematical Journal"
DOI: 10.1215/00127094-2018-0021
Abstract: We relate the singularities of a scheme $X$ to the asymptotics of the number of points of $X$ over finite rings. This gives a partial answer to a question of Mustata. We use this result… read more here.
Keywords: points schemes; representations arithmetic; arithmetic lattices; finite rings ... See more keywords
A Novel Image Encryption Scheme Based on Elliptic Curves over Finite Rings
Sign Up to like & getrecommendations! Published in 2022 at "Entropy"
DOI: 10.3390/e24050571
Abstract: Image encryption based on elliptic curves (ECs) is emerging as a new trend in cryptography because it provides high security with a relatively smaller key size when compared with well-known cryptosystems. Recently, it has been… read more here.
Keywords: finite rings; encryption; image encryption; based elliptic ... See more keywords