Post-quantum digital signature scheme with BB84 protocol 1 Giorgi Labadze a , Maksim Iavich b , Giorgi Iashvili b , Avtandil Gagnidze c , Sergiy Gnatyuk d a Georgian Technical University,77 Kostava Street, Tbilisi, 0108, Georgia b Caucasus University, 1 Paata Saakadze street, Tbilisi, 0102, Georgia c Scientific Cyber Security Association, 26 Otar Lortkipanidze, Tbilisi, 0108, Georgia d National Aviation University, Liubomyra Huzara Ave, 1, Kyiv 03058, Ukraine Abstract Data encryption is the classical way of ensuring the various types of the sensitive data. The global release of quantum computers is expected in the near future. Quantum computers have the ability to break the existing classical digital signatures. Because, the classical digital signature schemes are vulnerable to the attacks of quantum computers. This fact involves the different research efforts that look for digital signatures that are secure against quantum computer-based attacks. In the paper, we analyze some digital signature schemes, which are secure against attack of quantum computers. The described schemes have various efficiency problems. Merkle signature scheme is analyzed, it’s great problem is the very big size of the key pair. The paper analyzes the quantum key distribution protocols. BB84 key distribution protocol is described and analyzed. In the paper, we offer the novel scheme with reduced size of the key. The security of the scheme is analyzed. The key of the novel scheme is much less, than in the case of Merkle digital signature scheme. Keywords Post-quantum, digital signature, BB84 protocol; 1. Introduction Scientists are actively working on the creation of quantum computers. Google Corporation, Universities Space Research Association and federal agency NASA together with D-WAVE began to work on design of quantum processors. D-WAVE is the manufacturer of quantum processors. D-Wave 2X is a quantum processor and it contains physical qubits. Google is working on releasing the new CPUs. On February 18, D-Wave Systems, which is the leader in creation of computing systems based on quantum calculations, software, and different services, published a novel study in the collaboration with Google employers. This study demonstrates a big computational advantage of the performance, which increases the size of simulation and problem complexity, to over three million times in comparison with the classical methods used in the real world. The mentioned performance advantage, exhibited in a hard quantum simulation of the materials, and it is a serious step in the journey toward computations advantage in the area of quantum computing. The result of the scientists at D-Wave and Google also shows that quantum calculations can be harnessed in order to offer a big computational advantage in D-Wave CPUs, at the problem scale, which need the thousands of qubits. The last experiments performed on different D-Wave CPUs represent by the most global quantum simulations implemented by the existing quantum computers today. 1 Copyright 2021 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).