Active work is being done to create and develop quantum computers.Traditional digital signature systems, which are used in practice, are vulnerable to quantum computers attacks. The security of these systems is based on the problem of factoring large numbers and calculating discrete logarithms. Scientists are working on the development of alternatives to RSA, which are protected from attacks by quantum computer. One of thealternatives are hash based digital signature schemes. Merkle digital signature scheme is the very promising alternative to the classical digital signature schemes. It must be emphasized, that the scheme has efficiency problems and can not be used in practice. Major improvements of the scheme lead to security vulnerabilities. I will show that Merkle uses hash functions many times. I will offer the improved implementation of the hash function. I will integrate it into Merkle scheme. By means of this function, I will offer the secure and efficient Pseudo Random Number Generator (PRNG). I will offer the optimized approach for the generation of the seed for this PRNG by quantum source of randomness (using the simulation). During my talk, I will offer the efficient and secure implementation of Merkle signature. This scheme will use the optimized approaches discussed above. The implementation will be significantly speeded up using the threads of CPU. I will analyze the efficiency and the security of the scheme.