Method, apparatus, and system for post-quantum electronic signature based on infinite hash function

A method for generating a message with an electronic signature using a computing device, the method comprising:

• obtaining a message to be electronically signed;
• generating a public key and a private key by a key generation algorithm;
• generating at least one alpha-verification factor;
• generating at least one beta-verification factor;
• generating at least one gamma-verification factor;
• storing the at least one public key, the at least one private key, and the at least one alpha-verification factor in the memory of the computing device;
• generating electronic signature data based on the message and the private key;
• generating at least one verification factor for verifying integrity of the electronic signature data;
• generating a verification value including at least one of the verification factors;
• and
• generating an electronically signed message including the message, the electronic signature data, the public key, and the verification value, wherein
• the generating the electronic signature data includes generating the electronic signature data based on the message, the at least one alpha-verification factor, the at least one beta-verification factor, and the at least one gamma-verification factor, and
• the at least one verification factor includes the at least one beta-verification factor and the at least one gamma-verification factor.