Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Non-Commutative Key Exchange Protocol

Version 1 : Received: 6 May 2021 / Approved: 10 May 2021 / Online: 10 May 2021 (11:09:10 CEST)

How to cite: Lizama-Pérez, L.A.; Romero, J.M.L. Non-Commutative Key Exchange Protocol. Preprints 2021, 2021050174 (doi: 10.20944/preprints202105.0174.v1). Lizama-Pérez, L.A.; Romero, J.M.L. Non-Commutative Key Exchange Protocol. Preprints 2021, 2021050174 (doi: 10.20944/preprints202105.0174.v1).

## Abstract

We introduce a novel key exchange protocol based on non-commutative matrix multiplication defined in $\mathbb{Z}_p^{n \times n}$. The security of our method does not rely on computational problems as integer factorization or discrete logarithm whose difficulty is conjectured. We claim that the unique eavesdropper's opportunity to get the secret/private key is by means of an exhaustive search which is equivalent to the unsorted database search problem. Furthermore, we show that the secret/private keys become indistinguishable to the eavesdropper. Remarkably, to achieve a 512-bit security level, the keys (public/private) are of the same size when matrix multiplication is done over a reduced 8-bit size modulo. Also, we discuss how to achieve key certification and Perfect Forward Secrecy (PFS). Therefore, Lizama's algorithm becomes a promising candidate to establish shared keys and secret communication between (IoT) devices in the quantum era.

## Subject Areas

Non-commutative; matrix; cryptography

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