The telecare medical information system (TMIS) allows patients to access health services from their homes. It is therefore necessary to preserve privacy of the patient and to secure the communications between the patient/user and the gateway/server for TMIS (Gw, briefly).

We propose a new ring learning with error (RLWE) based on two-factor authentication and key exchange protocol, post-quantum secure, for healthcare platform by using a similar protocol of Ding et al. at Cryptographers’ Track at the RSA Conference in 2017 [32]. Our protocol involves four phases: user registration phase, login phase, mutual authentication and key agreement phase, and user’s password change phase.

Gw has a long-term public key (p_s) and a private key (x_s). The user has a password pwd. The user’s personal device/smartphone (PD, briefly) has a long-term secret key x_u. This secret key x_u is encrypted by pwd and stored on PD. The PD and the Gw share a long-term password S. This shared password S is calculated by Gw from its secret  and the hash of the user’s id (H₁(..., id, x_u)) Gw sends S to PD through a secure channel. At user’s side, S is encrypted (stored on PD) with pwd and the PD’s long-term secret key x_u. Note that S and id are not stored on Gw. For privacy, all the information required for user’s authentication are securely stored on PD and no information of the user is stored on Gw. pwd can be frequently changed offline (inside the PD).

lattices, number theory, healthcare, security, RLWE, authentication and key exchange, post quantum cryptography.

Received: January 7, 2023;  Accepted: February 25, 2023; Published: December 4, 2023

How to cite this article: Sidoine Djimnaibeye, Aminata Ngom and Djiby Sow, Post-quantum cryptography for healthcare: a number theory based two-factor mutual authentication and key exchange protocol over lattices for TMIS, Advances and Applications in Discrete Mathematics 41(1) (2024), 1-26. http://dx.doi.org/10.17654/0974165824001

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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