@Article{cmc.2020.08008,
AUTHOR = {Xiao Zhang, Faguo Wu, Wang Yao, Wenhua Wang, Zhiming Zheng},
TITLE = {Post-Quantum Blockchain over Lattice},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {63},
YEAR = {2020},
NUMBER = {2},
PAGES = {845--859},
URL = {http://www.techscience.com/cmc/v63n2/38547},
ISSN = {1546-2226},
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.},
DOI = {10.32604/cmc.2020.08008}
}