**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 $\textbf{X}$ 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 $ .

**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 21 Jul 2021

**Contact author: **crypticator at gmail com

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

**Version: **20210721:085142 (All versions of this report)

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

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