Open Access
ARTICLE
Post-Quantum Blockchain over Lattice
Xiao Zhang1, 2, 3, Faguo Wu1, 2, 3, Wang Yao1, 2, 3, *, Wenhua Wang4, Zhiming Zheng1, 2, 3
1 School of Mathematics and Systems Science, Beihang University, and Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, 100191, China.
2 Peng Cheng Laboratory, Shenzhen, 518055, China.
3 Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, 100191, China.
4 Aviation Industry Development Research Center of China, Beijing, China.
* Corresponding Author: Wang Yao. Email: .
Computers, Materials & Continua 2020, 63(2), 845-859. https://doi.org/10.32604/cmc.2020.08008
Received 20 July 2019; Accepted 20 August 2019; Issue published 01 May 2020
Abstract
Blockchain is an emerging decentralized architecture and distributed
computing paradigm underlying Bitcoin and other cryptocurrencies, and has recently
attracted intensive attention from governments, financial institutions, high-tech
enterprises, and the capital markets. Its cryptographic security relies on asymmetric
cryptography, such as ECC, RSA. However, with the surprising development of quantum
technology, asymmetric cryptography schemes mentioned above would become
vulnerable. Recently, lattice-based cryptography scheme was proposed to be secure
against attacks in the quantum era. In 2018, with the aid of Bonsai Trees technology, Yin
et al. [Yin, Wen, Li et al. (2018)] proposed a lattice-based authentication method which
can extend a lattice space to multiple lattice spaces accompanied by the corresponding
key. Although their scheme has theoretical significance, it is unpractical in actual
situation due to extremely large key size and signature size. In this paper, aiming at
tackling the critical issue of transaction size, we propose a post quantum blockchain over
lattice. By using SampleMat and signature without trapdoor, we can reduce the key size
and signature size of our transaction authentication approach by a significant amount.
Instead of using a whole set of vectors as a basis, we can use only one vector and rotate it
enough times to form a basis. Based on the hardness assumption of Short Integer Solution
(SIS), we demonstrate that the proposed anti-quantum transaction authentication scheme
over lattice provides existential unforgeability against adaptive chosen-message attacks in
the random oracle. As compared to the Yin et al. [Yin, Wen, Li et al. (2018)] scheme, our
scheme has better performance in terms of energy consumption, signature size and
signing key size. As the underlying lattice problem is intractable even for quantum
computers, our scheme would work well in the quantum age.
Keywords
Cite This Article
X. Zhang, F. Wu, W. Yao, W. Wang and Z. Zheng, "Post-quantum blockchain over lattice,"
Computers, Materials & Continua, vol. 63, no.2, pp. 845–859, 2020.