Blockchain Papers

Zibin Lin, Taotao Wang, Junhao Lai, Shengli Zhang · 6 authors

No abstract is available for this record.

Yashika Gaidhani

In this age of always-on connection, it is very important to keep data safe while also protecting user privacy. In today's networks, where data travels through many pathways, such as cloud services and IoT devices, cryptographic algorithms are very important for keeping private data safe. But it's still exceptionally difficult to create beyond any doubt that information is secure without putting people's protection at chance. This conversation goes into detail almost privacy-preserving security strategies, looking at their significance, issues, and other ways to solve them. The objective of privacy-preserving cryptographic strategies is to create beyond any doubt that private information is kept secure whereas still permitting secure contact and computation. To keep data secure from individuals who shouldn't have get to to it, these frameworks utilize diverse sorts of cryptography, like encryption, hashing, and secure multi-party computation (SMPC). Information spills and illicit observing are less likely to happen with these methods because they cover up information at diverse steps of exchange and handling. Indeed in spite of the fact that they may well be useful, privacy-preserving cryptographic strategies have a number of issues. Finding a great blend between client security and information security is one of the most issues. Extreme security measures may offer assistance keep information secure, but they frequently include collecting information in ways that are as well intrusive and abuse people's security. On the other hand, putting as well much accentuation on protection might make security weaker, taking off information open to being abused. Finding a cautious adjust between these competing objectives is key to making cryptographic frameworks that work well. A few potential methods that permit secure information taking care of whereas ensuring security are homomorphic encryption, differential protection, and zero-knowledge proofs. Improvements in hardware-accelerated cryptography and distributed computing tools also make it possible to speed up secure processes and make them more scalable.

Veri, Hans Kristjan

The rise of quantum computing threatens to break many of the cryptographic systems that secure today’s digital world. In response, researchers are developing new tools designed to remain secure in a post-quantum future. Most of the promising candidates for post-quantum digital signatures rely on security assumptions based on lattices or properties of hash functions. Another promising approach transforms secure multi-party computation protocols into zero-knowledge proofs, which are then turned into digital signatures. This technique, known as multi-party computation in-the-head (MPCitH), offers strong security properties and flexibility for distributed applications. This thesis investigates whether MPCitH digital signatures can be efficiently adapted for use by two cooperating parties to jointly produce a signature. Here we show how to construct two-party signatures based on syndrome decoding in-the-head (SDitH) signatures. We propose a provably secure scheme that achieves the smallest known communication overhead among two-party MPCitH signatures, while resulting in a signature size approximately double that of a single-prover variant. This result provides a new data point in the design space of multi-party MPCitH signatures and post-quantum digital signatures in general.

Jeremies Enmanuel Chinchay Camargo, Massiel Fiorella Parvina Huaman, Carmen Luz Cuba Cornejo, Cesar Augusto Cabrera Garcia

Digital electoral security has become fundamental to the development of reliable, integrated and available technological systems, driven by the growing demand for transparency and protection against threats. The purpose of this study is to analyze the impact of cryptographic protocols on the security of electoral processes, evaluating their effectiveness against traditional methods. For this purpose, a systematic review of the literature was carried out, considering 50 articles extracted from the Scopus database. The analysis focused on cryptographic techniques applied to blockchain-based environments, such as homomorphic encryption, zero-knowledge proofs and smart contracts, evaluating their contribution to design more secure, auditable and reliable voting systems. The results show that these protocols contribute to prevent recurring vulnerabilities, such as vote tampering, electoral fraud, impersonation and lack of validation, in addition to strengthening auditability and operational reliabilityFinally, the study concludes that the adoption and assessment of cryptographic protocols are essential to reduce risks in electronic voting, and promote more secure, transparent and efficient electoral processes.

Hongguo Zhang, Yun-Ming Sun, Kaiqi Zhang, Zhibo Guan · 6 authors

With the rapid expansion of digital asset trading, the contradiction between data sharing and privacy protection has increasingly become a significant challenge in the Internet environment. To address this issue, this paper proposes a secure multi-party computation scheme based on blockchain technology. Firstly, in response to the risk of data leakage in distributed storage scenarios, a threshold-based encryption algorithm is designed, utilizing a distributed key protection mechanism to effectively prevent single-point failures and data breaches. Secondly, a smart contract system is developed: the ERC721 contract is used to confirm the ownership of data assets, the ERC20 contract facilitates the transfer of usage rights, and the threshold decryption contract ensures secure multi-party computation and compliant incentive distribution. The collaboration of these three types of contracts enables comprehensive on-chain management of data assets, covering the entire process from ownership confirmation and circulation to compliant usage. In addition, this paper integrates non-interactive zero-knowledge proofs into the multi-party interaction process, allowing public verification of data consistency and computational validity on the blockchain. Finally, experiments are conducted to evaluate the impact of computation latency, communication overhead, and encryption parameters on system performance. The proposed scheme demonstrates significant performance improvements over mainstream SMPC protocols, with a 95.4 % reduction in key generation time and a 19.5 % reduction in ciphertext decryption time. Meanwhile, the scheme effectively resists various semi-malicious attacks, ensuring data security and privacy. • A t-out-of-N threshold ElGamal-based MPC scheme is proposed for secure computation in synchronous environments. • A blockchain smart contract framework manages data assets' lifecycle by combining ERC721/ERC20 and threshold decryption. • A method verifies on-chain data consistency and computation validity using non-interactive zero-knowledge proofs.

Aditya Kapoor

No abstract is available for this record.

Carmen Wabartha

The end-to-end verifiable e-voting system Ordinos [26] is primarily characterized by its tally-hiding property, which ensures that only the actual election result, e. g., the winner of the election, is revealed while the full tally consisting of the aggregated votes stays hidden. Ordinos is an abstract model that guarantees tally-hiding, verifiability and vote privacy if the underlying cryptographic primitives satisfy certain requirements. It uses a multi-party-computation protocol over an additively homomorphic encryption scheme and guarantees active security with zero-knowledge proofs. Ordinos has already been instantiated for several election systems using the Paillier [35] encryption scheme, which can be broken by Shor’s algorithm [41]. The aim of this thesis is to instantiate Ordinos post-quantum secure using a variant of Regev’s LWE-based cryptosystem [39], which is adapted to realize an actively secure threshold encryption scheme over an arbitrary plaintext space. Then a noise analysis of the arithmetic and logical components used in the MPC-protocol of the Paillier instantiation is conducted, and the components are slightly adapted to restrict the noise growth. Additionally, valid zero-knowledge proofs are provided and a concrete instantiation achieving a security level of 128 bits is shown.

Assiya Akli, Khalid Chougdali

The Internet of Things (IoT) demands robust mechanisms for secure communication and trust establishment among connected devices. Traditional Public Key Infrastructure (PKI) solutions face limitations in scalability, centralization and single points of failure. These limitations hinder their effectiveness in dynamic IoT environments. To address these challenges, this paper introduces a new decentralized authentication protocol for secure identity management and data exchange in IoT, called ISIF (IOTA-Assisted Self-Sovereign Identity Framework). This framework is based on Self-Sovereign Identity (SSI) principles and leverages Decentralized Identifiers (DIDs) and Verifiable Credentials (VCs) to enable mutual authentication without relying on centralized authorities. DIDs ensure decentralized identity management and VCs provide verifiable context-specific claims. This dual-layer approach enables robust and attribute-based authentication, which reduces the risk of unauthorized access and improving interoperability in decentralized IoT environments. ISIF employs the IOTA Tangle as a distributed ledger to manage and verify DIDs and VCs. This offers a decentralized, immutable record that supports efficient and tamper-resistant identity management. ISIF ensures that all interactions within the IoT network are securely authenticated and resilient to tampering. The experimental results show that the framework maintains efficient DID generation and VC issuance times even as network size scales, overcoming the bottlenecks inherent in PKI-based systems. Experimental results demonstrate that ISIF maintains efficient DID generation and VC issuance, even as network size scales. Experimental results show that DID generation time increases from 1.85 ms (for 50 nodes) to 10.81 ms (for 250 nodes), while VC issuance time ranges from 2.66 ms to 13.21 ms. Similarly, VC verification time increases from 3.54 ms to 22.27 ms as the network scales. Despite these increases, the overall end-to-end (E2E) delay remains low (0.16–0.33 ms), ensuring efficient real-time authentication. These findings confirm ISIF’s feasibility for large-scale IoT authentication without performance degradation. Furthermore, the IOTA Tangle’s performance in handling varied payload sizes affirms its suitability for managing block generation and retrieval in IoT, ensuring practical processing times that uphold security and decentralization.

Yurii Paslavskyi, Ihor Kroshnyi

An important cryptographic mechanism that guarantees confidentiality (the zero-disclosure property) and ensures that it is impossible to prove a false statement to the verifier is zero-disclosure proofs. A popular implementation of zero-disclosure proofs is short, noninteractive proofs that can be quickly verified and that do not require interaction between the parties after the initial setup. The main direction in the development of modern proof systems is interactive proof, which is built in two steps. The first is sending a confirmation of the polynomial of an interactive oracle proof and the second is creating correct oracles of the polynomial commitment scheme using well-defined cryptographic methods for evaluating polynomials. Verifying the use of the same coefficients in each linear combination requires checking both polynomial consistency and variable consistency. To construct general schemes of concise non-interactive zerodisclosure knowledge argument, an interactive oracle proof polynomial was proposed that models messages as polynomial oracles. All tests are proved using polynomial commitment schemes and then evaluated with zero knowledge at a point specified by the person verifying the information. The reliability and confidentiality of all tests are based on three main categories of interactive oracle proof polynomials, namely polynomial commitment schemes with conjunction, with inner product argument and with code theory. The protocols of concise noninteractive zero-disclosure knowledge arguments are implemented through high-level programs (compilers), which are converted into an intermediate representation, i.e. a scheme defined by a system of constraints. The compilers used are divided into domain-oriented languages, embedded domain-oriented languages, and zero-knowledge virtual machines. Specialized domain-oriented hardware description languages or programming languages offer an adapted syntax for efficiently expressing constraints in arithmetic schemes. Embedded domain-oriented languages are implemented as functions in general-purpose programming languages and are oriented to the overhead schemes inherited from the embedded language. Zero-knowledge virtual machines process the opcode of the fetch-decodeexecute cycle, replicating the computation trace for general programs and generating corresponding zeroknowledge proofs. They are compatible with existing high-level programming languages and can use the features of existing compilers. Compilers are evaluated for cross- or syntactic compatibility. In general, the biggest obstacle to using non-interactive proof libraries is the lack of documentation. Standardization can help developers compare important features across libraries and establish a more consistent performance baseline. Library documentation for these core features is implicit, and developers need to understand the underlying cryptographic techniques to choose an appropriate scheme. Standardization of compiler options is important, making it difficult to reuse existing tools.

Dorsaf Salah, Sami Mnasri, Hanen Idoudi

Protecting user rights and enabling cross-border interoperability require the existence of private and secure management of personal identity data in digital environments. To address this need in the context of electronic health cards for digital identification and healthcare services, this paper proposes a novel architecture that integrates self-sovereign identity (SSI), verifiable credentials (VC), and zero- knowledge proofs (ZKP). With SSI, users maintain full control over their data, storing and sharing identity credentials through digital wallets using decentralized identifiers (DIDs). VC enables trusted organizations to issue authenticated, tamper-proof digital certificates, while ZKPs allow individuals to prove identity-related claims without disclosing unnecessary personal details. The combination of these technologies enables a framework that ensures a tradeoff between user privacy and security processes. The findings of the tests achieved indicate that our framework, compared to conventional models, optimizes the interoperability and privacy of e-health card systems. Additionally, the suggested solution supports recent data protection regulations and demonstrates strong potential for global adoption.

Alaa Alsaeed, Saleh Almowuena, Aasem N. Alyahya

The Internet of Vehicles (IoV) is an emerging area within intelligent transportation systems, enabling real-time communication among vehicles, infrastructure, and pedestrians. While this connectivity enhances traffic management and safety, it also introduces significant security challenges—particularly in authentication, authorization, and data integrity. To address these concerns, blockchain technology is explored to eliminate centralized points of failure and support secure, decentralized communication in IoV environments. A solution titled Blockchain-based Authentication and Authorization in IoV (BAAIoV) is proposed, utilizing smart contracts and a distributed ledger to manage vehicle identities and securely control access to network resources. A simulation environment was established using Simulation of Urban Mobility (SUMO) for traffic modeling and Hyperledger Fabric for blockchain implementation. Python-based middleware facilitated real-time interaction between the simulation and the blockchain system. The results indicate that the BAAIoV model significantly reduces authentication delays, enhances emergency vehicle recognition, and mitigates threats like spoofing and replay attacks. These improvements demonstrate the potential of blockchain to enhance the security, efficiency, and reliability of vehicular networks. This research contributes to the development of secure communication frameworks for IoV. It highlights the potential for future blockchain integration with edge computing, artificial intelligence, and post-quantum cryptography technologies. Such integrations are expected to further strengthen smart transportation infrastructures and advance the capabilities of next-generation intelligent mobility systems.

Yubo Song, Yuxin Lin, Hongyu Zhu, Han Zhao · 8 authors

No abstract is available for this record.

Önder Gürcan

The industrial market continuously needs reliable solutions to secure autonomous systems. Especially as these systems become more complex and interconnected, reliable security solutions are becoming increasingly important. One promising solution to tackle this challenge is using smart contracts designed to meet contractual conditions, avoid malicious errors, secure exchanges, and minimize the need for reliable intermediaries. However, smart contracts are immutable. Moreover, there are different smart contract execution architectures (namely Order-Execute and Execute-Order-Validate) that have different throughputs. In this study, we developed an evaluation model for assessing the security of reliable smart contract execution. We then developed a realistic smart contract enabled IoT energy case study. Finally, we simulate the developed case study to evaluate several smart contract security vulnerabilities reported in the literature. Our results show that the Execute-Order-Validate architecture is more promising regarding reliability and security.

Shi Wang

Traditional identity authentication algorithms that rely on centralized trust authorities and plaintext identity verification often suffer from privacy leakage, key misuse, and single-point-of-failure risks. This study proposes a lightweight, privacy-preserving authentication algorithm based on elliptic curve and zero-knowledge proofs to address these issues. The proposed scheme introduces a random challenge and an anonymous verification mechanism during the authentication process to ensure both identity privacy and authentication security. While maintaining high levels of security and verifiability, the algorithm effectively reduces computational complexity and communication overhead. Experimental results demonstrate that the proposed method significantly outperforms traditional RSA and ECDSA in terms of authentication delay, communication cost, and security robustness. This approach is practical and scalable, offering a promising solution for secure authentication in environments with limited resource.

Shi Wang

As network applications rapidly evolve toward mobile and ubiquitous scenarios, identity authentication protocols face heightened demands for privacy protection and computational efficiency while maintaining security.Traditional authentication schemes often struggle to achieve an effective balance between privacy preservation, computational complexity, and security during design, with performance bottlenecks becoming increasingly prominent in resource-constrained environments.To address these challenges, this study proposes an optimized algebraic curve identity authentication protocol incorporating zero-knowledge proofs.Building upon Elliptic Curve Cryptography (ECC) as its cryptographic foundation, the protocol leverages ECC's inherent advantages of shorter key lengths and higher computational efficiency for equivalent security levels.Simultaneously, it integrates zero-knowledge proof mechanisms to minimize the exposure of user identity information during authentication.Through systematic optimization of the key generation mechanism, zero-knowledge proof interaction flow, and identity verification logic, the proposed protocol effectively reduces computational and communication overhead while ensuring identity anonymity and authentication integrity.Experimental results demonstrate that compared to traditional ECC authentication protocols and classical zero-knowledge proof schemes, the optimized protocol exhibits significant advantages in key generation time, authentication response latency, and communication load.It effectively resists common security threats such as replay attacks and forgery attacks, making it suitable for resource-constrained network environments and privacy-sensitive applications.

Ali Ibrahim Mohamed Ibrahim El-Gamal

Zero-knowledge proofs provide cryptographic guarantees of statement validity without revealing underlying secrets. However, static proofs enable linking attacks where adversaries track the same proof across multiple uses, compromising user privacy. We introduce Time-Based Re-randomization (TBR), a novel protocol that automatically transforms zero-knowledge proofs at fixed time intervals while preserving their validity. Our construction leverages cryptographic randomization combined with deterministic time-slot generation to create temporally unlinkable proofs without user interaction. We provide formal security proofs demonstrating that TBR maintains zero-knowledge and soundness properties while preventing proof-linking attacks. Performance analysis shows TBR incurs only 8-12ms overhead compared to 450-600ms for generating fresh proofs, making it practical for privacy-preserving applications including anonymous authentication, timelimited credentials, and blockchain systems.

Siddharth Verma

Proof-of-Context (PoC) protocols aim to ensure fairness and integrity in smart contract execution by cryptographically binding on-chain transactions to verifiable off-chain contextual data. Traditional consensus mechanisms (e.g., Proof-of-Work, Proof-of-Stake) focus on ordering and validation of transactions but do not address whether the contextual conditions that should govern contract execution are satisfied. In this manuscript, we propose a novel PoC framework that leverages decentralized oracles, zero-knowledge proofs, and time-stamped Merkle commitments to provide verifiable evidence that all pre-specified preconditions and environmental parameters were met at execution time. We detail the design of the protocol, implement a prototype on an Ethereum testnet using Chainlink oracles and zk-SNARKs, and conduct a performance evaluation under varying network and workload conditions. Our results show that PoC incurs a modest overhead—on average 5% additional gas cost and 200 ms added latency per proof generation—while dramatically enhancing auditability and reducing the risk of context-based manipulation or dispute. We conclude that PoC protocols offer a practical mechanism for enforcing fairness in a wide range of decentralized applications, from DeFi loans conditioned on real-world data to NFT minting events gated by dynamic criteria. Finally, we discuss the scope, limitations, and future research directions for broader deployment.

Akaki Mamageishvili, Benny Sudakov

We compare the total capital efficiency of secure restaking and Proof-of-Stake (PoS) protocols. First, we consider the sufficient condition for the restaking graph to be secure. The condition implies that it is always possible to transform such a restaking graph into separate secure PoS protocols. Next, we derive two main results: upper and lower bounds on the required extra stakes to add to the validators of the secure restaking graph to be able to transform it into secure PoS protocols. In particular, we show that the restaking savings compared to PoS protocols can be very large and can asymptotically grow as a square root of the number of validators. We also study a complementary question of aggregating secure PoS protocols into a secure restaking graph and provide matching lower and upper bounds on the PoS savings.

Xiangyang Luo, Xingxing Chen, Xiaofeng Chen, Qingfeng Cheng · 6 authors

Abstract With the continuous development of network technology, cryptographic protocols are facing diverse and complex security challenges. Blockchain technology, as a solution incorporating decentralization, traceability, programmability, and immutability, effectively enhances the security, trustworthiness, operational efficiency, and ensures the security and integrity of data storage in traditional cryptographic protocols. Consequently, it has gradually emerged as a focal point of research in cryptographic protocols. This manuscript delves into the ongoing research concerning the application of blockchain technology in cryptographic protocols. First, this manuscript introduces the background of blockchain research in cryptographic protocols and the corresponding basic knowledge. Secondly, we delve into the main concerns of traditional cryptographic protocols, with a particular focus on security and performance. Thirdly, according to the main classification of cryptographic protocols, the latest research results of blockchain in authentication protocols, authentication and key agreement protocols, and e-commerce protocols are presented. Finally, the research directions of blockchain technology in cryptographic protocols are summarized based on the existing research, and the future development trend is also prospected.

Changsong Jiang, Chunxiang Xu, Xinfeng Dong, Kefei Chen · 5 authors

Password-based authentication is widely applied in Internet of Things (IoT). It allows IoT devices to identify users with passwords to resist unauthorized access. However, choices of weak passwords, especially popular ones, might violate users’ privacy and lead to large-scale network attacks. Collection of popular passwords among IoT devices to establish blocklists via a service provider can prevent use of weak passwords. To protect unpopular passwords during collection, existing privacy-preserving schemes rely on expensive cryptographic primitives (e.g., garbled circuits and zero-knowledge proofs), which would impose heavy communication and computation burdens on constrained devices and hinder wide deployment of these schemes. In this paper, we propose EAGER+, an efficient privacy-preserving scheme for weak password collection in IoT against perpetual leakage. EAGER+ is mainly built on secret sharing and symmetric encryption, thereby enabling lightweight computation and communication on IoT devices. In EAGER+, we conceive a password-locked encryption with conditional decryption mechanism to efficiently identify popular passwords, where a password is essentially locked under itself in the encryption to guarantee its security, and the password can be revealed from the ciphertext by the service provider only if a sufficient number of devices exploit it. The mechanism is integrated with a servers-aided password-hardening mechanism to resist offline dictionary guessing attacks. Moreover, EAGER+ uses a key renewal mechanism to periodically update secrets for password hardening on key servers to thwart perpetual leakage towards the secrets. We formally analyze the security of EAGER+, and conduct experimental evaluations to show that EAGER+ is more efficient than existing schemes.

João André Monteiro Martins

In the era of decentralized identity management within blockchain ecosystems, ensuring user privacy during authentication processes is a critical concern. This dissertation addresses the challenge of privacypreserving authentication within decentralized identity management systems, specifically on the Algorand blockchain platform. As digital identity solutions become critical in today’s interconnected world, traditional centralized models expose user data to substantial privacy and security risks, such as data breaches, identity theft, and unauthorized access. The research leverages Algorand’s pure proof of stake (PPoS) consensus mechanism, recognized for its scalability and energy efficiency, along with cryptographic techniques such as zero-knowledge proofs (ZKPs) and the Pedersen commitment scheme. The primary contribution of this dissertation is the development of a proof of concept decentralized application (DApp) designed for secure and anonymous voting, designed to balance data protection with usability within the context of Dharma Teams, a decentralized application of Yari Labs. By incorporating cryptographic primitives such as anonymous credentials and secure, decentralized authentication protocols, the DApp demonstrates how user privacy can be maintained even in open blockchain environments. The framework developed within this research not only ensures user anonymity, but also upholds the integrity and transparency of the authentication process. Furthermore, this dissertation explores the applicability of these privacy-preserving methods in various use cases, including decentralized finance, supply chain management, and verification of digital identity. Through a blend of theoretical insights and practical implementation, this work lays a pathway toward more secure and use centric digital ecosystems on Algorand and similar platforms.

Xia Feng, Yaru Wang, Kaiping Cui, Liangmin Wang

The advancement of 6G wireless communication technology has facilitated the integration of Vehicular Ad-hoc Networks (VANETs). However, the messages transmitted over the public channel in the open and dynamic VANETs are vulnerable to malicious attacks. Although numerous researchers have proposed authentication schemes to enhance the security of Vehicle-to-Vehicle (V2V) communication, most existing methodologies face two significant challenges: (1) the majority of the schemes are not lightweight enough to support real-time message interaction among vehicles; (2) the sensitive information like identity and position is at risk of being compromised. To tackle these issues, we propose a lightweight dual authentication protocol for V2V communication based on Physical Unclonable Function (PUF). The proposed scheme accomplishes dual authentication between vehicles by the combination of Zero-Knowledge Proof (ZKP) and MASK function. The security analysis proves that our scheme provides both anonymous authentication and information unlinkability. Additionally, the performance analysis demonstrates that the computation overhead of our scheme is approximately reduced 23.4% compared to the state-of-the-art schemes. The practical simulation conducted in a 6G network environment demonstrates the feasibility of 6G-based VANETs and their potential for future advancements.

Jeyamohan Neera, Xiaomin Chen, Nauman Aslam, Biju Issac

Current mobile payment schemes gather detailed information about purchases customers make. This data can then be used to infer a customer’s spending behaviour, potentially violating their privacy. To tackle this problem, we propose an untraceable mobile payment scheme that strikes a better balance, preserving user privacy while allowing the Third-Party Service Provider (TPSP) to collect necessary information such as card details and transaction amount for regulatory compliance. Our scheme offers untraceability for legitimate users from malicious adversaries and curious TPSPs using cryptographic primitives such as partially blind signatures, zero-knowledge proofs, and identity-based signatures. It also guarantees that only authorised TPSPs can issue valid payment tokens, and even with limited data, the TPSP can still prevent dishonest customers/merchants from double-spending a payment token. We also propose a comprehensive evaluation framework to assess the untraceable payment schemes against seven key criteria such as untraceability, exculpability—merchant double-spending, exculpability—customer double-spending, unforgeability, confidentiality, message authenticity, efficiency, and regulatory compliance. We rigorously benchmark the security and privacy of our proposed payment scheme against this framework and other established schemes. Furthermore, we formally verify these properties using complexity-based analysis and Proverif modelling.

Jing Jiang, Xiaofeng Wang, Qianqian Xing, Jin Tang

Currently, personal information leakage and identity theft have become risks that cannot be ignored. As a robust authentication mechanism, multi-factor authentication (MFA) has gained prominence. However, many existing MFA schemes based on certificate-less public key cryptography amalgamate multiple authentication factors into a single factor for local verification, which fails to achieve independent authentication of each factor and is difficult to resist internal privilege attacks. To address these issues, this paper proposes a certificate-less multi-factor privacy authentication scheme based on elliptic curve cryptography. The proposed scheme divides the full private key into multiple authentication factors and employs the Schnorr zero-knowledge proof technique to independently generate challenge values for each factor, facilitating separate authentication of multiple factors. Notably, this approach eliminates the need to reconstruct the full private key during the authentication process, thereby effectively mitigating the risk of private key leakage.