Paper 2021/701

Multidimentional ModDiv public key exchange protocol

Samir Bouftass

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 $ X $ in $\mathbb{Z}_{r}^{n}$ knowing vectors $A$ and $B$ respectively in $\mathbb{Z}_{s}^{m}$ and $\mathbb{Z}_{t}^{l}$, where elements of vector B are defined as follows : $ B(i)$ = ($\sum_{j=1}^{j=n} A(i+j) \times X(j)$) $ Mod(2^p)Div(2^q)$. Mod is integer modulo operation, Div is integer division operation, p and q are known positive integers satisfying $ p > 2 \times q $. Size in bits of s equals p, size in bits of r equals q, and size in bits of t equals $p-q$, $ m >2 \times n $ and $ l = m - n $.