PQC standards alternatives -- reliable semantically secure key encapsulation mechanism and digital signature protocols using the rank-deficient matrix power function

Abstract: Post-quantum cryptography-PQC- aims to develop public-key primitives that are secure against adversaries using classical and quantum computing technologies. This study introduces novel protocols, a key encapsulation mechanism, a digital signature scheme, and special protection against linear attacks. Our purpose is to create reliable alternatives to current standards, seeking compact, fast, and secure replacements of the key interchange and digital signature in the TLS 1_3 protocol, which safeguards Internet traffic, allowing an easy post-quantum transition to protect current data from the harvest now, decrypt later threat.