Finite non-commutative associative algebras for setting the hidden discrete logarithm problem and post-quantum cryptoschemes on its base

The paper considers finite non-commutative associative algebras every of which contains a large set of the global one-sided (right and left) units. Formulas describing all of the global units are derived for each of the algebras. Finite algebras of such type are introduced as carriers of the hidden discrete logarithm problem that is defined in three new forms. One of them is used to design the post-quantum cryptoscheme for public key-distribution. Two others are applied to design the post-quantum digital signature schemes.