| At present,with the increasing maturity of information technology and bringing many convenient services to people,the problem of information leakage has become more and more prominent,and people have become more and more aware of the importance of information security.As we all know,digital signature is one of the important tools to guarantee information integrity and identity authentication,and it is also the core mechanism to ensure information security.It can be found in all aspects of social life.Ring signature is widely used in electronic voting,blockchain and anonymous tip-off because it can maintain the unconditional anonymity of the signer,and has become the focus topic in the field of cryptography research.Existing ring signature schemes based on assumptions of traditional number theory are difficult to achieve security under quantum computers.Therefore,it has long been an urgent demand in the field of ring signature research to find a scientific and effective alternative mechanism of quantum security.Lattice-based ring signature schemes not only can resist quantum algorithm attacks and prevent possible security problems,but also have the advantages of simple operation and high efficiency.At the same time,it has the reduction of average-case and worst-case,which brings great convenience to the scheme instantiation.The main work of this paper is to improve the privacy protection technology in blockchain system by constructing ring signature scheme on lattice and further applying it to blockchain.The specific work is divided into the following three parts:（1）Ring signature scheme over lattice based on R<n-SIS problem.Most current lattice-based ring signature schemes are built upon Module-Short Integer Solution（R-SIS）or Module-Learning with Errors（R-LWE）problems.The difficulty of these problems depends on the selection of polynomial f defining polynomial ring[x]/〈f〉,that is,R-SIS and R-LWE problems based on a certain f may be more difficult than R-SIS and R-LWE problems based on other f.R<n-SIS problem proposed by Lyubashevsky avoids the defects of R-SIS and R-LWE problems,and its difficulty degree no longer depends on the selection of polynomial f,that is,for any f,R<n-SIS problem is difficult to solve.Based on R<n-SIS problem,we construct a ring signature scheme by using Fiat-Shamir transform technology and rejection sampling technology.The scheme satisfies anonymity against full key exposure and unforgeability against chosen-subring attacks.Finally,based on R<n-SIS problem,the security analysis and efficiency analysis of the scheme are carried out.（2）Linkable ring signature scheme over NTRU lattice with unconditional anonymity.Most lattice-based linkable ring signature schemes only satisfy computational anonymity,and the anonymity of ring signatures is destroyed,if the potential problem can be solved by adversary.Thus,it is more ideal to construct lattice-based linkable ring signature scheme with unconditional anonymity,i.e.,even suppose the adversary has unlimited computing power and time,the ring signature is still anonymous.As far as we know,only the lattice-based linkable ring signature scheme proposed by Torres et al.can achieve unconditional anonymity.But the efficiency of signature generation and verification of the scheme is very low,and the signature length is also relatively long.Based on preimage sampling,trapdoor generation and rejection sampling algorithms,this study propose a linkable ring signature scheme with unconditional anonymity based on the e-NTRU problem under the random oracle model.We implemented our scheme and Torres et al.’s scheme,as well as other four efficient lattice-based linkable ring signature schemes.It is shown that under the same security level,the signature generation time,signature verification time and signature size of our scheme are reduced by about 94.52%,97.18%and 58.03%respectively,compared with Torres et al.’s scheme.（3）Based on linkable ring signature scheme with unconditional anonymity proposed in this paper,a blockchain electronic voting scheme is designed.The scheme includes voter registration stage,voting stage,and vote counting stage.In the voting stage,linkable ring signatures are used to protect the privacy of voters,and in the vote counting stage,the validity of the linkable ring signatures is verified to ensure correct vote counting.Finally,the security analysis of the electronic voting scheme is carried out in terms of anonymity,unforgeability,vote privacy,verifiability,legitimacy,integrity,uniqueness and robustness. |
