Method for defining finite noncommutative associative algebras of arbitrary even dimension for development of cryptoschemes

The paper introduces a new unified method for defining finite noncommutative associative algebras of arbitrary even dimension $m$ and describes the investigated properties of the algebras for the cases $m = 4$ and $6$, when the algebras are defined over the ground field $GF(p)$ with a large size of the prime number $p$. Formulas describing the set of $p^2$ ($p^4$) global left-sided units contained in the 4-dimensional (6-dimensional) algebra are derived. Only local invertibility takes place in the algebras investigated. Formulas for computing the unique local two-sided unit related to the fixed locally invertible vector are derived for each of the algebras. A new form of the hidden discrete logarithm problem is proposed as postquantum cryptographic primitive. The latter was used to develop the postquantum digital signature scheme.