منابع مشابه
On nest modules of matrices over division rings
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We ...
متن کاملon nest modules of matrices over division rings
let $ m , n in mathbb{n}$, $d$ be a division ring, and $m_{m times n}(d)$ denote the bimodule of all $m times n$ matrices with entries from $d$. first, we characterize one-sided submodules of $m_{m times n}(d)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $d$. next, we introduce the notion of a nest module of matrices with entries from $d$. we ...
متن کاملA CCA secure cryptosystem using matrices over group rings
We propose a cryptosystem based on matrices over group rings and claim that it is secure against adaptive chosen ciphertext attack. 1. Cramer-Shoup cryptosystem The Cramer-Shoup cryptosystem is a generalization of ElGamal’s protocol. It is provably secure against adaptive chosen ciphertext attack (CCA). Moreover, the proof of security relies only on a standard intractability assumption, namely,...
متن کاملSmall-span Hermitian matrices over quadratic integer rings
A totally real polynomial in Z[x] with zeros α1 6 α2 6 · · · 6 αn has span αn − α1. Building on the classification of all characteristic polynomials of integer symmetric matrices having span less than 4, we obtain a classification of polynomials having span less than 4 that are the characteristic polynomial of a Hermitian matrix over some quadratic integer ring. We obtain as characteristic poly...
متن کاملCryptanalysis of Some Protocols Using Matrices over Group Rings
It is important to search for easily implementable groups, for which the DL problem is hard and there is no known subexponential time algorithm for computing DL. The group of points over Fq of an elliptic curve is such a group. In [8], the group of invertible matrices with coefficients in a finite field was considered for such a key exchange. In [6], using the Jordan form it was shown that the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1990
ISSN: 0022-4049
DOI: 10.1016/0022-4049(90)90003-z