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Post-Quantum Cryptography PQC attempts to find cryptographic protocolsresistant to attacks using Shors polynomial time algorithm for numerical fieldproblems or Grovers algorithm to find the unique input to a black-box functionthat produces a particular output value. The use of non-standard algebraicstructures like non-commutative or non-associative structures, combined withone-way trapdoor functions derived from combinatorial group theory, are mainlyunexplored choices for these new kinds of protocols and overlooked in currentPQC solutions. In this paper, we develop an algebraic extension ring frameworkwho could be applied to different asymmetric protocols, i.e. key exchange, keytransport, enciphering, digital signature, zero-knowledge authentication,oblivious transfer, secret sharing etc.. A valuable feature is that there is noneed for big number libraries as all arithmetic is performed in F256 extensionfield operations (precisely the AES field). We assume that the new framework iscryptographical secure against strong classical attacks like thesometimes-useful length-based attack, Romankovs linearization attacks andTsabans algebraic span attack. This statement is based on the non-linearstructure of the selected platform which proved to be useful protecting the AESprotocol. Otherwise, it could resist post-quantum attacks Grover, Shor and beparticularly useful for computational platforms with limited capabilities likeUSB cryptographic keys or smartcards. Semantic security IND-CCA2 could also beinferred for this new platform.

Algebraic Extension Ring Framework for Non-Commutative Asymmetric Cryptography