Merkle's post-quantum signature based on the modified Lamport algorithm

The development of a Merkle post-quantum signature scheme based on a modified Lamport one-time signature algorithm is presented. The Merkle signature algorithm and the Lamport one-time signature algorithm are described. There is also a review of the current literature on the subject of the Merkle signature algorithm. A modified algorithm for Lamport's one-time electronic digital signature is described. The algorithms for key generation, signature generation, and verification of a previously generated signature are described in detail. The paper presents a software implementation of an electronic digital signature system with a graphical interface based on the developed algorithm, which allows key generation, signature generation and verification. A flowchart is provided for each of the main modules of the program, and the graphical interface of the developed software for each module is also demonstrated. The results of testing the modified algorithm are presented and its performance is compared with the standard algorithm. The test results confirm that using the modified algorithm allows faster verification of messages, while the speed of key generation and signature does not increase in comparison with the standard algorithm. The modified algorithm speeds up verification regardless of the message length. The results of the performed research are a modified Lamport one-time signature algorithm, which provides a higher signature verification rate compared to the classical algorithm, and a software tool with a graphical interface for generating and verifying a post-quantum electronic digital signature.