In this paper, we propose a novel authenticated key exchange scheme based on the Bi-GISIS problem for the post-quantum world. The security of the proposed scheme is based on the hardness assumption of the Bi-GISIS problem described in [1]. The reusable key property is provided for the proposed scheme in the random oracle model by using the bilateral pasteurization method. To obtain an authenticated key exchange scheme, we use the implicit authentication steps. The security analysis of the proposed scheme is presented in the Bellare-Rogaway security model, where weak perfect forward secrecy is provided. We also give a novel perspective to the problem defined in [1].

The two-party authenticated key agreement (2PAKA) protocol allows two users to generate a shared session key between themselves over a public channel without any assistance from a centralized server. Many of the state-of-the-art 2PAKA protocols are not secure in quantum environments. This article proposes a hybrid module learning with rounding (MLWR)-based 2PAKA (MLWR-2PAKA) protocol for the post-quantum world. The constructed MLWR-2PAKA protocol provides entity authentication based on the Saber scheme. The hardness assumption of MLWR-2PAKA relies on MLWR since it does not require any complex reduction and sampling processes. The security analysis is done in the random oracle model based on the basic Dolev–Yao threat model. In addition, the chosen reconciliation structure makes the session keys unbiased. By using different parameter sets, a comparison analysis is presented regarding key sizes, failure probability, and bandwidth requirements.