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Post-Quantum Cryptography (PQC) attempts to find cryptographic protocolsresistant to attacks using Shor polynomial time algorithm for numerical fieldproblems or Grover search algorithm. A mostly overlooked but valuable line ofsolutions is provided by non-commutative algebraic structures, specificallycanonical protocols that rely on one-way trapdoor functions (OWTF). Here wedevelop an evolved algebraic framework who could be applied to differentasymmetric protocols. The (canonic) trapdoor one-way function here selected isa fortified version of the Triple decomposition Problem (TDP) developed byKurt. The original protocol relies on two linear and one quadratic algebraicpublic equation. As quadratic equations are much more difficult tocryptanalyze, an Algebraic Span Attack (ASA) developed by Boaz Tsaban, focus onthe linear ones. This seems to break our previous work. As a countermeasure, wepresent here an Extended TDP (cited as XTDP in this work). The main point isthat the original public linear equations are transformed into quadratic onesand the same is accomplished for exchanged tokens between the entities. Alldetails not presented here could be found at the cited references.

PQC: Extended Triple Decomposition Problem (XTDP) Applied To GL(d, Fp)-An Evolved Framework For Canonical Non-Commutative Cryptography