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Privacy must be preserved when working with client data in machine learning. Federated learning (FL) provides a way to preserve user data privacy by aggregating locally trained models without sharing the user data. Still, the privacy of user identity is not preserved. Secure aggregation is a popular technique in FL for aggregating gradients without disclosing individual data. However, it is costly and inaccurate. Therefore, we propose a novel, scalable, cost-effective group signature-based secure aggregation algorithm in FL, called GSFedSec, where secure aggregation helps conceal the user's update while the group signature helps conceal their identity. Our algorithm preserves the data and their source. Our simulation results show that the proposed algorithm does not suffer from a loss of accuracy, handles increases in network size competently, offers computational and communication efficiency, and is secure against various security attacks. We have compared the results of efficiency and security against existing algorithms in FL. Also, the security of the algorithm is verified using Burrows–Abadi–Needham (BAN) logic and simulated via the Automated Validation of Internet Security Protocols and Applications (AVISPA) protocol. [ABSTRACT FROM AUTHOR]

To address the issue of medical data leakage or malicious tampering, as well as medical disputes, this paper proposed a medical data privacy protection method based on blockchain. The hash algorithm encrypted the patient’s identity information, the AES (advanced encryption standard) algorithm encrypted treatment results, the ECC (ellipse curve cryptography) algorithm encrypted the AES key. The blockchain stored all encryption keys, treatment results, and patient identity information. By using group signature technology to trace signed hospitals, the group administrator could decrypt medical data, therefore using it as an important basis to assist third parties in resolving medical disputes. Efficiency analysis shows that under the same security conditions, this method improves the encryption and decryption efficiency by about 14% and 46% compared to the compared schemes, at the same time, the method analyzed the time cost of various group signature algorithms. Compared with similar met-hods, this method can not only achieve classification privacy protection of patient identity and medical data, but also ensure reasonable transaction storage costs. It has certain application value in the field of medical data privacy protection. [ABSTRACT FROM AUTHOR]

Current solutions that rely on a single-server architecture have privacy, anonymity, integrity, and confidentiality limitations. Blockchain-based solutions can address some of these issues but face challenges regulating behaviour and protecting access policy privacy. This study proposes a new approach to securing a smart home environment to overcome these limitations.The proposed architecture is based on a group signature scheme, which allows multiple IoT devices to securely exchange keys and authenticate each other without needing a central authority. Our experimental results indicate the effectiveness and efficiency of the proposed architecture and provide insights into its security and privacy features compared to existing IoT authentication methods. [ABSTRACT FROM AUTHOR]

Enhanced Privacy ID (EPID) signatures can be viewed as a direct anonymous attestation mechanism with expanded revocation capabilities. When the device's private key is unknown, the revocation manager can revoke a device based on its signatures. Making these systems post-quantum secure is of great importance due to its widespread application in real-world systems. Boneh et al. first propose two post-quantum EPID signature schemes based on symmetric primitives only. In this work, we propose an EPID signature scheme based on la ttices. To the best of our knowledge, our EPID signature scheme based on lattices is the first strong post-quantum variant of EPID signature scheme which achieves security based on the hardness of standard short integer solution (SIS) problem. Our construction employs an updatable Merkle tree accumulator which provides us the flexibility that our EPID signature scheme supports dynamically joining or revoking of any group members at any time. We provide an estimated efficiency comparison of our EPID signature with the existing similar schemes and we observe that our scheme is comparable with the existing schemes despite the usage of strong post-quantum variant and enjoying post-quantum security. [ABSTRACT FROM AUTHOR]

With the popularization of E-payment, more and more electronic payment protocols have been proposed. In 2021, Lin et al. proposed a trusted third-party E-Payment protocol based on a set of three-particle local indistinguishable orthogonal product (X-LIOP) states. In this paper, we first point out that there is a security flaw where the merchant can forge the purchase goods information to sell something that the customer does not want to buy in Lin et al. protocol. Besides, the X-LIOP states used by Lin are not orthogonal and can be discriminated by Local Operation and Classical Communication (LOCC). Second, we propose a new electronic payment protocol that combines group signature and the three-particle X-LIOP states. Compared with Lin et al. protocol, customers can purchase goods anonymously in our protocol and the unforgeability of messages and signatures is guaranteed. [ABSTRACT FROM AUTHOR]

As IoT technology evolves, developments of ubiquitous computing accelerates. At the same time, threats of privacy exposure also increase since the IoT systems expose the information such as user's location or medical status collected from all sorts of things. To handle the data elaborately, the ubiquitous systems need to employ a technology that provides anonymity to prevent exposure of personal information. The group signature scheme is widely used for a cryptographic base for privacy protection which do not reveal user's identity but prove that he/she is a legitimate user. Recently, a number of researches concerning the basic group signature schemes with a differentiated linkability have been conducted to provide a more flexible service. However, existing researches focused on providing flexible services from the service provider's position. The systems are exposed to high possibilities of unnecessary breach of privacy. In this paper, we define a restrictive linkability for the anonymous services that require an adequate linkability with a minimum user-designated privacy exposure in anonymous services and propose an efficient group signature scheme providing restrictive linkability. [ABSTRACT FROM AUTHOR]

Group signatures and their variants have been widely used in privacy-sensitive scenarios such as anonymous authentication and attestation. In this paper, we present a new post-quantum group signature scheme from symmetric primitives. Using only symmetric primitives makes the scheme less prone to unknown attacks than basing the design on newly proposed hard problems whose security is less well-understood. However, symmetric primitives do not have rich algebraic properties, and this makes it extremely challenging to design a group signature scheme on top of them. It is even more challenging if we want a group signature scheme suitable for real-world applications, one that can support large groups and require few trust assumptions. Our scheme is based on MPC-in-the-head non-interactive zero-knowledge proofs, and we specifically design a novel hash-based group credential scheme, which is rooted in the SPHINCS+ signature scheme but with various modifications to make it MPC (multi-party computation) friendly. The security of the scheme has been proved under the fully dynamic group signature model. We provide an implementation of the scheme and demonstrate the feasibility of handling a group size as large as 260. This is the first group signature scheme from symmetric primitives that supports such a large group size and meets all the security requirements. [ABSTRACT FROM AUTHOR]

Blockchain technology provides transparency and reliability by sharing transactions and maintaining the same information through consensus among all participants. However, single-signature applications in transactions can lead to user identification issues due to the reuse of public keys. To address this issue, group signatures can be used, where the same group public key is used to verify signatures from group members to provide anonymity to users. However, in dynamic groups where membership may change, an attack can occur where a user who has left the group can disguise themselves as a group member by leaking a partial key. This problem cannot be traced back to the partial key leaker. In this paper, we propose assigning different partial keys to group members to trace partial key leakers and partially alleviate the damage caused by partial key leaks. Exist schemes have shown that arbitrary tracing issues occurred when a single administrator had exclusive key generation and tracing authority. This paper proposes a group signature scheme that solves the synchronization problem by involving a threshold number of TMs while preventing arbitrary tracing by distributing authority among multiple TMs.

Privacy must be preserved when working with client data in machine learning. Federated learning (FL) provides a way to preserve user data privacy by aggregating locally trained models without sharing the user data. Still, the privacy of user identity is not preserved. Secure aggregation is a popular technique in FL for aggregating gradients without disclosing individual data. However, it is costly and inaccurate. Therefore, we propose a novel, scalable, cost-effective group signature-based secure aggregation algorithm in FL, called GSFedSec, where secure aggregation helps conceal the user’s update while the group signature helps conceal their identity. Our algorithm preserves the data and their source. Our simulation results show that the proposed algorithm does not suffer from a loss of accuracy, handles increases in network size competently, offers computational and communication efficiency, and is secure against various security attacks. We have compared the results of efficiency and security against existing algorithms in FL. Also, the security of the algorithm is verified using Burrows–Abadi–Needham (BAN) logic and simulated via the Automated Validation of Internet Security Protocols and Applications (AVISPA) protocol.

Blockchain technology has attracted significant attention since its publication. However, most existing blockchain platforms are isolated systems, which makes it difficult to exchange data among different blockchains. The industry has proposed the notary schemes to enhance blockchain interoperability, which can exchange messages among different blockchains through a notary. However, conventional notary schemes are centralized, which suffers from single point of failures. To address these issues, this paper proposes a distributed cross-chain notary model with regulatory mechanisms, based on improved threshold group signatures. We improve the group signature scheme by setting up a group of tracing authorities to achieve distributed tracing. Furthermore, we incorporate this signature scheme into our notary scheme, where a group of notaries signs cross-chain transactions using group signatures. We also introduce a group of regulators to reveal the true identities of malicious notaries when disputes occur. Finally, we prove the security of our signature scheme based on the Random Oracle Model. In our experiments, when the number of notaries is 102 and the threshold is 2/3 of that, it takes 166 ms to set up and generate signature. Also, it takes 161 ms for regulators to reveal the true identities of malicious notaries.

Group signatures are a leading competing signature technique with a substantial amount of research. With group settings, group signatures provide user anonymity. Any group member with access to the group can generate a signature while remaining anonymous. The group manager, however, has the authority to expose and identify the signer if required. Since the privacy of the sender should be preserved, this is a conflict between privacy and accountability. Concerning high performance on security, we propose a novel, well-balanced security and privacy group signature scheme based on a general linear group over group ring. To the best of our knowledge, our work represents the first comprehensive framework for a group signature scheme that utilizes generic linear groups over group rings. We demonstrate that the competing security goals of message trustworthiness, privacy, and accountability are effectively resolved by our protocol. The results of the performance evaluation and simulation demonstrate that our protocol achieves strong security, system robustness, and high-performance efficiency, making it suitable for practical applications. [ABSTRACT FROM AUTHOR]

With the advent of smart cities, the significance of the Internet of Things (IoT) is gaining greater prominence. At the same time, the safety early warning system in the IoT has a significant impact on real-time monitoring and the response to potential risks. Despite the advancements made in edge-assisted IoT deployments, several challenges and constraints persist. Given the potential threat to life posed by safety-related messages, ensuring the authenticity of messages in the edge-assisted IoT safety warning system is crucial. However, considering the identity privacy of devices participating in the edge-assisted Internet of Things system, directly verifying the identity of the sending device is undesirable. To address this issue, in this work, we design a linkable group signature scheme that allows devices to anonymously send safety-related messages to edge nodes, defending against Sybil attacks while ensuring the traceability of malicious device identities. Then, we present a high-efficiency conditional privacy-preserving authentication (CPPA) scheme based on the designed group signatures for the safety warning system in edge-assisted IoT. This scheme effectively protects device identity privacy while providing a reliable authentication mechanism to ensure the credibility and traceability of alert messages. The proposed scheme contributes to the field of safety warning systems in the context of edge-assisted IoT, providing a robust solution for privacy preservation and authentication. [ABSTRACT FROM AUTHOR]

With the outbreak of Covid‐19, both people's health and the world economy are facing great challenges. Contact tracing scheme based on Bluetooth of smartphones has been regarded as a viable way to mitigate the spread of Covid‐19. The existing schemes mainly belong to the centralized or the decentralized structure, both of which have their own limitations. It is infeasible for the existing schemes to balance the different demands of governments and users for user privacy and tracing efficiency at different periods of the epidemic. In this paper, we propose a hybrid contact tracing scheme named MLCT (multi‐level contact tracing scheme) which is mainly based on short group signature. MLCT provides multiple privacy levels by applying anonymous credential technology and secret sharing technology to desensitize user identity privacy and encounter privacy. Comparing to the previous schemes, MLCT fully considers the different demands of the government, patients, and close contacts for user privacy and tracing efficiency in the different stages of Covid‐19. The experimental results show viability in terms of the required resource from both server and mobile phone perspectives. And the security analysis demonstrates that MLCT can achieve the five targets security goals. It is expected that MLCT can contribute to the design and development of contact tracing schemes. [ABSTRACT FROM AUTHOR]

Federal learning and privacy protection are inseparable. The participants in federated learning need to be the targets of privacy protection. On the other hand, federated learning can also be used as a tool for privacy attacks. Group signature is regarded as an effective tool for preserving user privacy. Additionally, message recovery is a useful cryptographic primitive that ensures message recovery during the verification phase. In federated learning, message recovery can reduce the transmission of parameters and help protect parameter privacy. In this paper, we propose a lattice-based group signature with message recovery (GS-MR). We then prove that the GS-MR scheme has full anonymity and traceability under the random oracle model, and we reduce anonymity and traceability to the hardness assumptions of ring learning with errors (RLWE) and ring short integer solution (RSIS), respectively. Furthermore, we conduct some experiments to evaluate the sizes of key and signature, and make a performance comparison between three lattice-based group signature schemes and the GS-MR scheme. The results show that the message–signature size of GS-MR is reduced by an average of 39.17% for less than 2000 members. [ABSTRACT FROM AUTHOR]

In the field of quantum communication, classical communication processes have become a central open problem, especially in quantum threshold signature schemes. However, the existing quantum threshold signature schemes do not solve this problem well, and the signature verification process is relatively complicated. Therefore, the aim of this study is to propose a novel quantum threshold digital signature scheme that aims to realize classical communication and simplify the quantum threshold digital signature communication model while ensuring the security of the signature. Our approach constructs a binary linear secret-sharing matrix based on the properties of the coset states in the quantum state to share the master secret value and distribute the quantum tokens of the members. Unlike traditional schemes, our verification operation does not require the intervention of an arbitrator, thus simplifying the signature-verification process. In addition, we propose a novel reuse quantum-token protocol based on the length of the hash message to-be-signed to enable single-member signatures over multiple bits. This scheme has other potential applications, including eavesdropper identification, quantum threshold proxy signatures, and more flexible quantum threshold schemes. In addition, complex measurement operations are not required to verify the signatures, thus fulfilling the requirements of practical applications. In this paper, we present an innovative approach for solving the classical communication problem in quantum threshold signature schemes, which successfully solves the central open problem in this field by transforming the measurements of quantum states into classical communication. We believe that this approach will provide a more feasible solution for secure communication.

The Internet has penetrated into every aspect of life. Large amounts of data are generated by multimedia collection equipment every day. As an asset, data can achieve value circulation through transactions. However, the existing centralized transaction model is not secure enough, has the risk of user privacy leakage, and the protection of data copyright is insufficient. In this paper, in order to solve the transaction security and traceability problems of multimedia data, especially high-definition data such as vector graphics, we implement a transaction scheme STTS without third-party based on blockchain. For high-definition multimedia data, we use zero watermarking combined with oblivious transfer to embed copyright information. A two-stage verification process is then implemented by using group signature and a secret sharing scheme to complete data distribution. Finally, the smart contract is used to complete copyright tracking. We test the performance of our scheme by simulating the real transaction environment in the Internet of Things (IoT) and demonstrate the feasibility of our scheme, which can be applied to large-scale multimedia data trading schemes in the IoT. [ABSTRACT FROM AUTHOR]

Cross-domain authentication requires that there is no trust gap between different trust domains that can cause cross-domain devices to exceed the security control scope of the original trust domain and further expose cross-domain authentication systems to security threats. In addition, as relying on the traditional cross-domain authentication means built by centralized institutions cannot meet the data security needs in a big data environment. Therefore, it is necessary to design a secure dynamic cross-domain authentication scheme. In this paper, we propose a dynamic cross-domain authentication scheme (DCAGS-IoT) in the Internet of Things environment using the group signature technology and the distributed system architecture of blockchain. Specifically aiming at the problem of increasing and revoking users in dynamic cross-domain authentication, a user update algorithm with the complexity of O (logN) was designed to manage users in the trust domain. Moreover, we used the characteristics that group signature users can sign on behalf of a group to protect the users' privacy and track suspicious users. Since the size of the signature generated by the scheme is independent of the number of group members N and only depends on the security parameters λ, the efficiency of the protocol implementation is improved, and the security and availability of the authentication scheme are guaranteed. [ABSTRACT FROM AUTHOR]

In a Vehicular Cloud (VC) network, an announcement protocol plays a critical role in promoting safety and efficiency by enabling vehicles to disseminate safety-related messages. The reliability of message exchange is essential for improving traffic safety and road conditions. However, verifying the message authenticity could lead to the potential compromise of vehicle privacy, presenting a significant security challenge in the VC network. In contrast, if any misbehavior occurs, the accountable vehicle must be identifiable and removed from the network to ensure public safety. Addressing this conflict between message reliability and privacy requires a secure protocol that satisfies accountability properties while preserving user privacy. This paper presents a novel announcement protocol for secure communication in VC networks that utilizes group signature to achieve seemingly contradictory goals of reliability, privacy, and accountability. We have developed the first comprehensive announcement protocol for VC using group signature, which has been shown to improve the performance efficiency and feasibility of the VC network through performance analysis and simulation results. [ABSTRACT FROM AUTHOR]

The representative collective digital signature, which was suggested by us, is built based on combining the advantages of group digital signature and collective digital signature. This collective digital signature schema helps to create a unique digital signature that deputizes a collective of people representing different groups of signers and may also include personal signers. The advantage of the proposed collective signature is that it can be built based on most of the well-known difficult problems such as the factor analysis, the discrete logarithm and finding modulo roots of large prime numbers and the current digital signature standards of the United States and Russian Federation. In this paper, we use the discrete logarithmic problem on prime finite fields, which has been implemented in the GOST R34.10-1994 digital signature standard, to build the proposed collective signature protocols. These protocols help to create collective signatures: Guaranteed internal integrity and fixed size, independent of the number of members involved in forming the signature. The signature built in this study, consisting of 3 components (U, R, S), stores the information of all relevant signers in the U components, thus tracking the signer and against the "disclaim of liability" of the signer later is possible. The idea of hiding the signer's public key is also applied in the proposed protocols. This makes it easy for the signing group representative to specify which members are authorized to participate in the signature creation process. [ABSTRACT FROM AUTHOR]

Group signatures allow users to sign messages on behalf of a group without revealing authority is capable of identifying the user who generated it. However, the exposure of the user's signing key will severely damage the group signature scheme. In order to reduce the loss caused by signing key leakage, Song proposed the first forward-secure group signature. If a group signing key is revealed at the current time period, the previous signing key will not be affected. This means that the attacker cannot forge group signatures regarding messages signed in the past. To resist quantum attacks, many lattice-based forward-secure group signatures have been proposed. However, their key-update algorithm is expensive since they require some costly computations such as the Hermite normal form (HNF) operations and conversion from a full-rank set of lattice vectors into a basis.In this paper, we propose the group signature with forward security from lattice. In comparison with previous works, we have several advantages: Firstly, our scheme is more effective since we only need to sample some vectors independently from a discrete Gaussian during the key-update algorithm. Secondly, the derived secret key size is linear instead of quadratic with the lattice dimensions, which is more friendly towards lightweight applications. Anonymous authentication plays an increasingly critical role in protecting privacy and security in the environment where private information could be collected for intelligent analysis. Our work contributes to the anonymous authentication in the post-quantum setting, which has wide potential applications in the IoT environment.

Summary: Device identity authentication is the first line of defense for edge computing security mechanisms. Many authentication schemes are often accompanied by high communication and computational overhead. In addition, due to the continuous enhancement of network virtualization and dynamics, the security requirements for logical boundaries of many enterprise information systems "cloudification," and the huge data security challenges faced by enterprise core assets, all make the original "one‐time authentication, all the way" trust model no longer reliable. Therefore, the paper proposes a local identity authentication and roaming identity authentication protocol based on a zero‐trust architecture. First, we propose a revocable group signature scheme, the expiration time is bound to the key of each edge terminal device. According to this solution, since the identity authentication token generated by the expired key is invalid, it does not need to be included in the revocation list, which improves the efficiency of revocation checking. Compared with the current identity authentication protocol, this article not only builds a model based on the zero trust architecture, effectively solves the shortcomings of the network security protection architecture, but also considers the unforgeability of the expiration time, and realizes effective revocation and more efficient identity authentication. [ABSTRACT FROM AUTHOR]

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The representative collective digital signature scheme allows the creation of a unique collective signature on document M that represents an entire signing community consisting of many individual signers and many different signing groups, each signing group is represented by a group leader. On documentM, a collective signature can be created using the representative digital signature scheme that represents an entire community consisting of individual signers and signing groups, each of which is represented by a group leader. The characteristic of this type of letter is that it consists of three elements (U, E, S), one of which (U) is used to store the information of all the signers who participated in the formation of the collective signature on documentM. While storing this information is necessary to identify the signer and resolve disputes later, it greatly increases the size of signatures. This is considered a limitation of the collective signature representing 3 elements. In this paper, we propose and build a new type of collective signature, a collective signature representing 2 elements (E, S). In this case, the signature has been reduced in size, but it contains all the information needed to identify the signer and resolve disputes if necessary. To construct the approved group signature scheme, which is the basic scheme for the proposed representative collective signature schemes, we use the discrete logarithm problem on the prime finite field. At the end of this paper, we present the security analysis of the AGDS scheme and a performance evaluation of the proposed collective signature schemes. [ABSTRACT FROM AUTHOR]

There have been many digital signature schemes were developed based on the discrete logarithm problem on a finite field. In this study, we use the elliptic curve discrete logarithm problem to build new collective signature schemes. The cryptosystem on elliptic curve allows to generate digital signatures with the same level of security as other cryptosystems but with smaller keys. To extend practical applicability and enhance the security level of the group signature protocols, we propose two new types of collective digital signature schemes based on the discrete logarithm problem on the elliptic curve: i) the collective digital signature scheme shared by several signing groups and ii) the collective digital signature scheme shared by several signing groups and several individual signers. These two newtypes of collective signatures have combined the advantages of group digital signatures and collective digital signatures. These signatures have a fixed size and do not depend on the number of members participating in the creation of the final collective signature. One of the advantages of the proposed collective signature protocols is that they can be deployed on top of the available public key infrastructures. [ABSTRACT FROM AUTHOR]

Abstract As the important transmission approach of the perception data, the security and privacy of the perception layer nodes have been paid more and more attention. To evaluate the credibility of the perception nodes and protect autologous identity privacy, a remote attestation mechanism using group signature (GS-RAM) for the perception layer of centralized networking is proposed in this paper. First, a RAM, based on the computational Diffie–Hellman (CDH) problem and GS, is established for the data source of the perception nodes. Second, the specific construction of the proposed GS-RAM is given to identify the trusted state of data sources without exposing the privacy of the perception nodes. Then, a strict security certification was carried out to verify the correctness, unforgeability, anonymity, traceability, unrelatedness, non-framing, anti-joint aggression and forward security of the proposed GS-RAM. Finally, simulation experiments are carried out to verify that the proposed scheme has better security and dynamic adaptability.

With the advent of smart cities, the significance of the Internet of Things (IoT) is gaining greater prominence. At the same time, the safety early warning system in the IoT has a significant impact on real-time monitoring and the response to potential risks. Despite the advancements made in edge-assisted IoT deployments, several challenges and constraints persist. Given the potential threat to life posed by safety-related messages, ensuring the authenticity of messages in the edge-assisted IoT safety warning system is crucial. However, considering the identity privacy of devices participating in the edge-assisted Internet of Things system, directly verifying the identity of the sending device is undesirable. To address this issue, in this work, we design a linkable group signature scheme that allows devices to anonymously send safety-related messages to edge nodes, defending against Sybil attacks while ensuring the traceability of malicious device identities. Then, we present a high-efficiency conditional privacy-preserving authentication (CPPA) scheme based on the designed group signatures for the safety warning system in edge-assisted IoT. This scheme effectively protects device identity privacy while providing a reliable authentication mechanism to ensure the credibility and traceability of alert messages. The proposed scheme contributes to the field of safety warning systems in the context of edge-assisted IoT, providing a robust solution for privacy preservation and authentication.

Group signatures are a leading competing signature technique with a substantial amount of research. With group settings, group signatures provide user anonymity. Any group member with access to the group can generate a signature while remaining anonymous. The group manager, however, has the authority to expose and identify the signer if required. Since the privacy of the sender should be preserved, this is a conflict between privacy and accountability. Concerning high performance on security, we propose a novel, well-balanced security and privacy group signature scheme based on a general linear group over group ring. To the best of our knowledge, our work represents the first comprehensive framework for a group signature scheme that utilizes generic linear groups over group rings. We demonstrate that the competing security goals of message trustworthiness, privacy, and accountability are effectively resolved by our protocol. The results of the performance evaluation and simulation demonstrate that our protocol achieves strong security, system robustness, and high-performance efficiency, making it suitable for practical applications.

Federal learning and privacy protection are inseparable. The participants in federated learning need to be the targets of privacy protection. On the other hand, federated learning can also be used as a tool for privacy attacks. Group signature is regarded as an effective tool for preserving user privacy. Additionally, message recovery is a useful cryptographic primitive that ensures message recovery during the verification phase. In federated learning, message recovery can reduce the transmission of parameters and help protect parameter privacy. In this paper, we propose a lattice-based group signature with message recovery (GS-MR). We then prove that the GS-MR scheme has full anonymity and traceability under the random oracle model, and we reduce anonymity and traceability to the hardness assumptions of ring learning with errors (RLWE) and ring short integer solution (RSIS), respectively. Furthermore, we conduct some experiments to evaluate the sizes of key and signature, and make a performance comparison between three lattice-based group signature schemes and the GS-MR scheme. The results show that the message–signature size of GS-MR is reduced by an average of 39.17% for less than 2000 members.

Mixing is an important way for privacy protection among digital currency such as Bitcoin.However,on the one hand,Bitcoin mixing protects user privacy,on the other hand,it facilitates the transfer of assets for illegal activities such as ransomware and Bitcoin theft.In this paper,we propose a traceable scheme for Bitcoin mixing.The scheme aims to protect the privacy of legi-timate users and can trace the illegal assets.The system is regulated by trusted third party,user anonymity and traceability based on the group signature which is constructed by bilinear groups and strong Diffie-Hellman assumption.When there is a need for tracing,the regulator can determine the signed user through the system private key,so as to determine the illegal asset transfer path.Security analysis shows that the scheme can trace the illegal asset transfer without modifying the current Bitcoin system,meanwhile,the solution provide privacy protection and asset safety for legitimate users.Furthermore,the scheme provides a refe-rence direction for the research on digital currency privacy protection.

Bullens et al. left an open problems in CSI-Fish is to devise a identification protocol that allows for the challenge set to be ZN rather than the small set {-S,···,S}. This paper proposed a zero-knowledge proof scheme based on supersingular isogeny. This scheme addresses the open problem by taking the challenge C as a isogeny, and reduces the soundness error and the size of public key. This scheme can be turned into non-interactive zero-knowledge proof scheme using the Fiat-Shamir transform. Then signature scheme and group signature scheme based on supersingular isogeny can be implemented under the quantum random oracles model. And this paper analyzes the security and correctness of these schemes. [ABSTRACT FROM AUTHOR]