**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 $.

**Category / Keywords: **public-key cryptography / Diffie Hellman key exchange protocol, Post Quantum cryptography, Lattice based cryptography, Closest vector problem, Learn with rounding problem.

**Date: **received 27 May 2021, last revised 4 Jun 2021

**Contact author: **crypticator at gmail com

**Available format(s): **PDF | BibTeX Citation

**Version: **20210604:092837 (All versions of this report)

**Short URL: **ia.cr/2021/701

[ Cryptology ePrint archive ]