Novel Provably Secure and Quantum Resistant Message Authentication Codes (MACs) and Their New Related LWE-Based Key Exchange Protocols (KEPs)

The literature review shows the need for Key Exchange Protocols and Message Authentication Codes in secure communication protocols such as SSH, IPsec, and TLS. Nevertheless, the hardness of the Learning With Errors (LWE) problem and the security of SHA3 hashes have been proven critical to developing secure and quantum-safe cryptographic schemes, which are critical in this digital era. Indeed, current privacy laws and regulations worldwide require protecting citizens' personally identifiable data in different sectors such as healthcare, finance, and e-government. This paper proposes new asymmetric cryptographic schemes for key exchange and new symmetric ones for authentication. My Key Exchange Protocols rely on mathematical concepts such as the newly defined “new paradigm related to the learning with errors” problem and the symmetric matrix. In addition, my new Message Authentication Codes rely on the aforementioned hard problem and the secure hash function SHA3. This paper provides correctness, security, quantum safety, and efficiency proofs of my cryptographic schemes. It is important to highlight the urgency of developing quantum-safe protocols. Indeed, with the growth of the storage capacity, when democratized, quantum computers can threaten the currently stored data.