Multidimentional ModDiv public key exchange protocol

Abstract

This paper presents Multidimentional ModDiv public key exchange protocol which security is based on the hardness of an LWR problem instance consisting on finding a secret vector $\textbf{X}$ in $\mathbb{Z}_{q}^{n}$ knowing vectors $\textbf{A}$ and $\textbf{B}$ respectively in $\mathbb{Z}_{p}^{m}$ and $\mathbb{Z}_{p-q}^{m-n}$, where elements of vector $\textbf{B}$ are defined as follows : $B(i)$ = ($\sum_{j=1}^{j=n} A(i+n-j) \times X(j)$) $Mod(P)Div(Q)$. Mod is integer modulo, Div is integer division, P and Q are known positive integers which sizes in bits are respectively p and q which satisfy $p > 2 \times q$. m and n satisfy $m >2 \times n$