In this paper, three types of post-quantum algebraic digital signature schemes are proposed, differing in the methods of ensuring high security to signature forgery using the matrix S as a fitting attack parameter. The first type uses the method of exponentiation of the product, which includes the matrix S, to a large power, the second type includes performing the exponentiation operation to a power equal to the value of the hash function calculated from S, and the third type consists in combining the first two methods. Algorithmic implementations of each type of digital signature schemes are carried out and the correctness of the developed algorithms is shown. Security to the direct attack, to the attack based on known signatures, and to signature forgery are assessed. A comparison of the proposed digital signature algorithms with known analogues is presented.