Threshold Signature Scheme Research Articles

Simple Three-Round Multiparty Schnorr Signing with Full Simulatability

In a multiparty signing protocol, also known as a threshold signature scheme, the private signing key is shared amongst a set of parties and only a quorum of those parties can generate a signature. Research on multiparty signing has been growing in popularity recently due to its application to cryptocurrencies. Most work has focused on reducing the number of rounds to two, and as a result: (a) are not fully simulatable in the sense of MPC real/ideal security definitions, and/or (b) are not secure under concurrent composition, and/or (c) utilize non-standard assumptions of different types in their proofs of security. In this paper, we describe a simple three-round multiparty protocol for Schnorr signatures that is secure for any number of corrupted parties; i.e., in the setting of a dishonest majority. The protocol is fully simulatable, secure under concurrent composition, and proven secure in the standard model or random-oracle model (depending on the instantiations of the commitment and zero-knowledge primitives). The protocol realizes an ideal Schnorr signing functionality with perfect security in the ideal commitment and zero-knowledge hybrid model (and thus the only assumptions needed are for realizing these functionalities). In our presentation, we do not assume that all parties begin with the message to be signed, the identities of the participating parties and a unique common session identifier, since this is often not the case in practice. Rather, the parties achieve consensus on these parameters as the protocol progresses.

Non-interactive SM2 threshold signature scheme with identifiable abort

Non-interactive SM2 threshold signature scheme with identifiable abort

Threshold Lattice-Based Signature Scheme for Authentication by Wearable Devices

This paper presents a new threshold signature scheme based on Damgaard’s work. The proposed scheme allows for changing the message signature threshold, thereby improving the flexibility of the original Damgaard scheme. This scheme can be applied as a user authentication system using wearable devices. Based on the hardness of lattice problems, this scheme is resistant to attacks on a quantum computer, which is an advantage over the currently used multi-factor authentication schemes. The scheme’s security relies on the computational complexity of the Module-LWE and Module-SIS problems, as well as the Shamir secret sharing scheme’s security.

Blockchain-Based Medical Cyber Physical Systems With Decentralized Threshold signature Scheme

Medical cyber physical systems are information applications of medical industry.A lagrge amount of medical data is stored in MCPS,and there are many challenges in the secure store and data sharing.Using blockchain technology into medical Cyber Physical system has become popular.Blockchain has remarkable features such as tamper proof and privacy protection, and has the function of protecting data in the medical Cyber Physical system.In this paper,we propose a hybrid blockchain,which applied private blockchain and consortium blockchain, After the medical source data is hashed, a hash tree is generated and stored in the private chain of the hospital. The hospital server extracts information to build a new transaction on the consortium chain.the system ensure the secure storage and fast access of data.Still,a threshold signature system is proposed.Aiming at the situation that medical accidents are easy to occur in multidisciplinary joint consultation in the medical process, this paper proposes to use threshold signature for joint consultation.Using the security and tamper-proof of the threshold signature, when the consensus is reached,treatment can be carried out and the medical data is uploaded to the consortium blockchain. The security analysis and performance analysis show that the scheme has advantages in safety and performance and is suitable for the medical environment.

Improved Threshold Signature Scheme CSI-FiSh with Fast Secret Recovery

The paper presents an improved version of the CSI-FiSh threshold signature offered by L. De Feo and M. Meyer in 2020. In the proposed scheme, public and private keys are additionally updated avoiding the case of compromising a dealer. It is also proposed to eliminate the sequential information transfer between participants when signing and replace it with an assembly with the participation of the dealer. Experimental results showing the effectiveness of the proposed approach and the assessment of the resulting scheme safety are presented.

Improved quantum (t, n) threshold group signature

Threshold signature is an important branch of the digital signature scheme, which can distribute signature rights and avoid the abuse of signature rights. With the continuous development of quantum computation and quantum information, quantum threshold signatures are gradually becoming more popular. Recently, a quantum (t, n) threshold group signature scheme was analyzed that uses techniques such as quantum-controlled-not operation and quantum teleportation. However, this scheme cannot resist forgery attack and does not conform to the design of a threshold signature in the signing phase. Based on the original scheme, we propose an improved quantum (t, n) threshold signature scheme using quantum (t, n) threshold secret sharing technology. The analysis proves that the improved scheme can resist forgery attack and collusion attack, and it is undeniable. At the same time, this scheme reduces the level of trust in the arbitrator during the signature phase.

Certificateless threshold signature from lattice

Threshold signature has been widely used in electronic wills, electronic elections, cloud computing, secure multi-party computation and other fields. Until now, certificateless threshold signature schemes are all based on traditional mathematic theory, so they cannot resist quantum computing attacks. In view of this, we combine the advantages of lattice-based cryptosystem and certificateless cryptosystem to construct a certificateless threshold signature from lattice (LCLTS) that is efficient and resistant to quantum algorithm attacks. LCLTS has the threshold characteristics and can resist the quantum computing attacks, and the analysis shows that it is unforgeable against the adaptive Chosen-Message Attacks (UF-CMA) with the difficulty of Inhomogeneous Small Integer Solution (ISIS) problem. In addition, LCLTS solves the problems of the certificate management through key escrow.

Elliptic curve threshold signature scheme for blockchain

Smart contract execution requires the triggering condition. Triggering condition of smart contract is the information outside the blockchain, and thus an oracle is required to provide the data services. For the security of user funds in on-chain aggregation model, each oracle must pay the gas fees to transmit off-chain data to the blockchain and trigger the smart contract, but this way easily causes the network congestion. In view of this, we propose an elliptic curve threshold signature scheme for blockchain (BC-ECTSS) to overcome the above issue. In the random oracle (RO) model, we detailedly show BC-ECTSS satisfies the existential unforgeability against the adaptive chosen-message attacks; in addition, it has the anonymity and its computation cost is relatively low.

A New Code-Based Linkable Threshold Ring Signature Scheme

In this paper, we construct a new code-based linkable threshold signature scheme whose security is based on the hardness of the syndrome decoding problem and general syndrome decoding problem. We show that our scheme is secure in terms of existential unforgeability, anonymity, nonslanderability, and linkability. The complexity of the signature size proposed in this paper is O t . Our method is particularly well suited for large free group voting systems. The greater the number of members in the ring, the more pronounced the advantage of the signature length is when compared to other schemes. That is, our scheme achieves a fixed length signature, independent of the number of ring members. In addition, our scheme has a very short public key, and the size is O N .

A Hierarchical and Location-Aware Consensus Protocol for IoT-Blockchain Applications

Blockchain-based IoT systems can manage IoT devices and achieve a high level of data integrity, security, and provenance. However, incorporating existing consensus protocols in many IoT systems limits scalability and leads to high computational cost and consensus latency. In addition, location-centric characteristics of many IoT applications paired with limited storage and computing power of IoT devices bring about more limitations, primarily due to the location-agnostic designs in blockchains. We propose a hierarchical and location-aware consensus protocol (LH-Raft) for IoT-blockchain applications inspired by the original Raft protocol to address these limitations. The proposed LH-Raft protocol forms local consensus candidate groups based on nodes’ reputation and distance to elect the leaders in each sub-layer blockchain. It utilizes a threshold signature scheme to reach global consensus and the local and global log replication to maintain consistency for blockchain transactions. To evaluate the performance of LH-Raft, we first conduct an extensive numerical analysis based on the proposed reputation mechanism and the candidate group formation model. We then compare the performance of LH-Raft against the classical Raft protocol from both theoretical and experimental perspectives. We evaluate the proposed threshold signature scheme using Hyperledger Ursa cryptography library to measure various consensus nodes’ signing and verification time. Experimental results show that the proposed LH-Raft protocol is scalable for large IoT applications and significantly reduces the communication cost, consensus latency, and agreement time for consensus processing.

Distributed Random Beacon for Blockchain Based on Share Recovery Threshold Signature.

Random beacons play a crucial role in blockchains. Most random beacons in a blockchain are performed in a distributed approach to secure the generation of random numbers. However, blockchain nodes are in an open environment and are vulnerable to adversary reboot attacks. After such an attack, the number of members involved in a random number generation decreases. The random numbers generated by the system become insecure. To solve this problem while guaranteeing fast recovery of capabilities, we designed a threshold signature scheme based on share recovery. A bivariate polynomial was generated among the participants in the distributed key generation phase. While preserving the threshold signature key share, it can also help participants who lost their shares to recover. The same threshold setting for signing and recovery guarantees the security of the system. The results of our scheme show that we take an acceptable time overhead in distributed key generation and simultaneously enrich the share recovery functionality for the threshold signature-based random number generation scheme.

A Novel Undeniable (t, n)-Threshold Signature with Cheater Identification

A digital signature is one of the most widely used cryptographic primitives in asymmetry cryptography. According to the security requirements in different symmetry or asymmetry network models, various digital signatures have been developed in the literature. To protect the right of the signer, Chaum and Antrepen first introduced the concept of an undeniable signature, where interactive protocols are needed for the verification process. Besides, a signer can, also, perform a disavowal protocol to prove that they did not sign the message. On the other hand, threshold cryptography is, usually, used to protect the system from a single point of failure. In a (t,n)-threshold signature scheme, as long as t people in the group of n people participate, the signature can be smoothly signed. By combining these two features, an undeniable threshold signature enjoys the advantages from both sides. After our survey, we found that the existing undeniable threshold signature schemes are either insecure or apply impractical assumptions. Thus, in this manuscript, we aim at designing a novel and provably secure undeniable threshold signature scheme. The proposed scheme is formally proven to be unforgeable and invisible. Besides, our scheme supports cheater identification, which allows one to find the cheater, when a signing protocol fails. Moreover, the proposed scheme can be performed without the help of trusted third parties or secure cryptographic modules, which would be more practical when our scheme is deployed in real-world applications.

Toward Data Authenticity and Integrity for Blockchain-Based Mobile Edge Computing

Blockchain-based mobile edge computing (BMEC) solves the problem of limited computing resources of devices in the Internet of Things (IoT). However, there are some security threats in the blockchain environment, among which the attacks against consensus algorithms are particularly serious, such as double-spending attacks and long-range attacks. These attacks target the block proposal or validation process, which compromise the integrity of the BMEC by overwriting the correct block record with the wrong block record. In this article,we propose a scheme to solve the above problem by using the cooperative threshold signature and group management scheme to protect the block validity. The blockchain process of a single node is controlled in a group cooperative way, and each new block is regarded as a valid block only if it has a valid threshold signature for the group to which it belongs. Concretely, the system is initialized by a cooperative distributed key generation protocol, the device management protocol uses a resident node to ensure the security and efficiency of device join and leave, and the signature issuing protocol can tolerate a certain degree of exceptions of nodes within the group. We analyze the resistance ability of the scheme against consensus attacks, prove the security of the scheme, and analyze the computing and communication efficiency. Experimental evaluations on the protocols of the proposed scheme have been conducted on cloud virtual machines and embedded boards, including Raspberry Pi and UP2 Grove, which indicated that the scheme is efficient in practical scenarios.

Two-Round n-out-of-n and Multi-Signatures and Trapdoor Commitment from Lattices

Although they have been studied for a long time, distributed signature protocols have garnered renewed interest in recent years in view of novel applications to topics like blockchains. Most recent works have focused on distributed versions of ECDSA or variants of Schnorr signatures; however, and in particular, little attention has been given to constructions based on post-quantum secure assumptions like the hardness of lattice problems. A few lattice-based threshold signature and multi-signature schemes have been proposed in the literature, but they either rely on hash-and-sign lattice signatures (which tend to be comparatively inefficient), use expensive generic transformations, or only come with incomplete security proofs. In this paper, we construct several lattice-based distributed signing protocols with low round complexity following the Fiat–Shamir with Aborts (FSwA) paradigm of Lyubashevsky (Asiacrypt 2009). Our protocols can be seen as distributed variants of the fast Dilithium-G signature scheme and the full security proof can be made assuming the hardness of module SIS and LWE problems. A key step to achieving security (unexplained in some earlier papers) is to prevent the leakage that can occur when parties abort after their first message—which can inevitably happen in the Fiat–Shamir with Aborts setting. We manage to do so using homomorphic commitments. Exploiting the similarities between FSwA and Schnorr-style signatures, our approach makes the most of observations from recent advancements in the discrete log setting, such as Drijvers et al.’s seminal work on two-round multi-signatures (S&P 2019). In particular, we observe that the use of commitment not only resolves the subtle issue with aborts, but also makes it possible to realize secure two-round n-out-of-n distributed signing and multi-signature in the plain public key model, by equipping the commitment with a trapdoor feature. The construction of suitable trapdoor commitment from lattices is a side contribution of this paper.

Threshold ECDSA with an Offline Recovery Party

A (t, n)-threshold signature scheme enables distributed signing among n players such that any subset of size at least t can sign, whereas any subset with fewer players cannot. Our goal is to produce digital signatures that are compatible with an existing centralized signature scheme: the key-generation and signature algorithms are replaced by a communication protocol between the players, but the verification algorithm remains identical to that of a signature issued using the centralized algorithm. Starting from the threshold scheme for the ECDSA signature due to Gennaro and Goldfeder, we present the first protocol that supports multiparty signatures with an offline participant during the key-generation phase and that does not rely on a trusted third party. Under standard assumptions on the underlying algebraic and geometric problems (e.g. the Discrete Logarithm Problem for an elliptic curve and the computation of \(e\mathrm{th}\) root on semi-prime residue rings), we prove our scheme secure against adaptive malicious adversaries.

An Efficient Blockchain Consensus Algorithm Based on Post-Quantum Threshold Signature

Blockchain is a distributed and append-only data management system maintained by many nodes from Peer-to-Peer (P2P) networks, where one of the most important and successful applications is Bitcoin. In blockchain P 2 P networks, consensus algorithms are playing a key role and take a lot of time. For example, Bitcoin uses Proof-of-Work (PoW) consensus algorithm, which takes 60 minutes to acknowledge a new transaction. Compared with the traditional data management technology, blockchain systems are very inefficient. Thus, it is very crucial to improve the blockchain consensus. We present threshold digital signature techniques to exploit the blockchain consensus mechanism. First, we propose a threshold signature scheme based on NP-hard problem, i.e., solving quadratic equations in a finite field, which is considered to be secure against quantum computer attacks and traditional attacks. Second, we further propose an efficient blockchain consensus algorithm based on the new threshold signature scheme. Third, we build a new blockchain system based on the consensus algorithm. The analysis of the blockchain system shows that the efficiency and security is must better than current blockchain systems.

DistriTrust: Distributed and low-latency access validation in zero-trust architecture

Enterprise networks typically use perimeter-based security to protect their IT resources from security threats originating from outside the enterprise perimeter. In such networks, connection requests from devices residing inside the perimeter are implicitly assumed to be trusted. However, in practice, a considerable fraction of cyberattacks emanate from inside the enterprise network making the perimeter-based trust assumption unrealistic. Zero-trust architecture (ZTA) is an emerging alternative to perimeter-based security, where each connection request for accessing an enterprise resource goes through stringent security checks and validation irrespective of the location of the requesting device. In ZTA, every connection request is authenticated and authorized by a trusted centralized component called the policy decision point (PDP) and subsequently granted (or denied) access to the requested resource. However, the centralized nature of the PDP often makes it vulnerable to various attacks such as compromise of secret keys, impersonation and denial of service. In this article, we propose DistriTrust which distributes trust across multiple PDPs using the notion of threshold signatures. However, involving multiple PDPs also increases latency. In order to keep latency as low as possible, we study different threshold signature schemes and identify a suitable scheme for DistriTrust. We also discuss the security properties achieved by DistriTrust. Finally, we analyze the asymptotic performance of DistriTrust and report the experimental results as well.

A Fully Adaptively Secure Threshold Signature Scheme Based on Dual-Form Signatures Technology

In t , n threshold signature schemes, any subset of t participants out of n can produce a valid signature, but any fewer than t participants cannot. Meanwhile, a threshold signature scheme should remain robust and unforgeable against up to t − 1 corrupted participants. This nonforgeability property is that even an adversary breaking into up to t − 1 participants should be unable to generate signatures on its own. Existential unforgeability against adaptive chosen message attacks is widely considered as a standard security notion for digital signature, and threshold signature should also follow this accordingly. However, there are two special attack models in a threshold signature scheme: one is the static corruption attack and the other is the adaptive corruption attack. Since the adaptive corruption model appears to better capture real threats, designing and proving threshold signature schemes secure in the adaptive corruption model has been focused on in recent years. If a threshold signature is secure under adaptive chosen message attack and adaptive corruption attack, we say it is fully adaptively secure. In this paper, based on the dual pairing vector spaces technology, we construct a threshold signature scheme and use Gerbush et al.’s dual-form signatures technology to prove our scheme, which is fully adaptively secure in the standard model, and then compare it to other schemes in terms of the efficiency and computation.

An efficient lattice‐based threshold signature scheme using multi‐stage secret sharing

Secret sharing is a cryptographic technique used in many different applications such as cloud computing, multi-party computation and electronic voting. Security concerns in these applications are data privacy, availability, integrity and verifiability, where secret sharing provides proper solutions. The authors address some important features like verifiability and being multi-stage to make it usable in various field of application. Here, the authors propose an anonymous threshold signature scheme based on the trapdoor function introduced by Micciancio and Peikert by sharing the private key using a lattice-based threshold multi-stage secret sharing (TMSSS) scheme. Then, the authors improve the previously proposed TMSSS scheme, in such a way that less public values are required to publish on the bulletin board which makes the scheme more efficient while preserving the security of the scheme based on the lattice hard problems. The proposed scheme inherits the desired features such as anonymity and verifiability from the improved TMSSS scheme. Furthermore, both schemes use simple matrix operations, which additionally increase the efficiency.

An efficient multivariate threshold ring signature scheme

At CRYPTO 2011, Sakumoto et al. introduced the first 3-pass identification protocol with security reduction to the MQ problem and impersonation probability 23. Petzoldt et al. (AAECC 2013) extended that protocol into a threshold ring signature scheme, which later was improved by Zhang and Zhao (NSS 2014). In 2015, Monteiro et al. (IEICE 2015) improved the 3-pass identification protocol of Sakumoto et al. to the one with impersonation probability 12. In this paper, we utilize the previous methods and the protocol by Monteiro et al. (2015)[20] to propose an efficient threshold ring signature. As a result, our scheme is more efficient than all previous multivariate threshold signature schemes in terms of both communication cost and signature length. In particular, the signature length of our scheme is 40% and 22% shorter than that of Petzoldt et al. and Zhang–Zhao respectively.