  Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols
resistant to attacks using Shor polynomial time algorithm for numerical field
problems or Grover search algorithm. A mostly overlooked but valuable line of
solutions is provided by non-commutative algebraic structures, specifically
canonical protocols that rely on one-way trapdoor functions (OWTF). Here we
develop an algebraic framework who could be applied to different asymmetric
protocols like D-H KE (Diffie-Hellman key exchange), Public Key Encryption,
Digital Signature, ZKP (zero-knowledge proof) authentication, Oblivious
Transfer, Multi-Party Computing, and so on. The trapdoor one-way functions
selected are (a) Triple decomposition Problem (TDP) developed by Kurt, where a
known element is factored into a product of three unknown factors and (b) a new
version of conjugacy search that we refer from now on as Blind Conjugacy Search
Problem (BCSP). Our platform structure is the general linear group GL(d,F_p)
d-square non-singular matrices of prime field values. We give support to the
fact that this framework is cryptographically secure against classical attacks
like linear algebra attacks, length-based attacks, side-channel attacks against
square (or duplicate) and multiply (or sum) algorithm, high sensitivity to
pseudo random deterministic generators, etc. At same time it is immune against
quantum attacks (using Grover and Shor), if the size parameters are carefully
selected. Semantic security and IND-CCA2 compliance for this framework is
discussed.
