SGDID: A Privacy-Enhanced Supervised Distributed Identity Model for Smart Grid and Electric Vehicle Integration

Abstract

The rapidly growing number of electric vehicles and the large-scale user privacy management in smart grids have led to a symmetrical phenomenon. While decentralized identifiers (DIDs) offer a promising solution for users to better control their private data, the frequent interactions between vehicles and the grid require a vast number of identities. Existing methods, while focusing on efficiency, often neglect privacy protection, especially in Vehicle-to-Grid (V2G) scenarios. They also overlook fundamental features such as resistance to Sybil attacks and the ability to supervise malicious identities, which may seem contradictory to privacy protection. In this paper, we propose an identity authentication scheme based on decentralized identifiers (DIDs) that allow massive numbers of electric vehicle users to autonomously control the disclosure of their information. We also introduce a mechanism that simultaneously protects privacy while resisting Sybil attacks and strengthening privacy in V2G scenarios. Furthermore, our scheme enables anonymity while maintaining supervisory capabilities. Experimental results and formal proofs demonstrate that the proposed scheme performs well in terms of authentication efficiency and security, making it suitable for large-scale V2G deployments.

1. Introduction

The adoption of Electric Vehicles (EVs) as replacements for fossil fuel-powered vehicles contributes to global efforts in reducing greenhouse gas emissions, mitigating air pollution, and decreasing noise pollution in urban environments [1]. As the automotive sector transitions towards electrification and intelligent systems, both private companies and governments are accelerating research and development efforts [2]. With an increasing variety of EV brands and models across different regions, managing vehicle user identities efficiently and securely has become an emerging challenge. Although traditional Public Key Infrastructure (PKI) systems could be deployed in large-scale EV ecosystems, they are vulnerable to single points of failure due to their reliance on a centralized Root Certificate Authority (Root CA). A compromise or failure of the Root CA could invalidate numerous digital certificates and CA signatures, potentially triggering cascading security breaches with catastrophic consequences [3].

In contrast, the advent of Decentralized Identifiers (DIDs) offers a solution to centralized identity management issues, while simultaneously enhancing user control over their identity. DIDs are designed for creating, managing, and verifying identities based on decentralized networks, often leveraging blockchain technology. This allows users to selectively disclose personal data, improving privacy control. In this paper, we adopt the DID identity model to efficiently manage large-scale vehicle identities and to enable decentralized authentication between smart grid devices, ensuring the integrity and security of device identities through cryptographic proofs and distributed trust mechanisms.

The rapid development of electric vehicle (EV) and Smart Grid (SG) technologies is reshaping energy systems globally. Unlike traditional grids, smart grids integrate power, information, and business flows, facilitating optimized resource management and reliable green energy supply—key elements for achieving sustainability goals. However, the increasing number of EVs [4] poses significant challenges to the power grid, especially in terms of load management. According to McKinsey, by 2050, EV charging in Germany is expected to increase the peak daily load by 1% to 5%, with local peak loads possibly rising by as much as 30% under high EV penetration. Similarly, the Brookings Institution predicts that by 2030, EV charging loads in India may account for 28% to 50% of peak daily loads [5], potentially adding pressure to power generation, transmission, and distribution systems.

Despite these challenges, EVs offer considerable potential for load regulation compared to traditional electricity consumption. With flexible charging times and power capabilities, EVs can serve as distributed energy storage units, discharging power back to the grid. This bidirectional energy flow forms the core of V2G technology. In V2G networks, EVs not only consume energy but also supply energy during peak demand hours, charging during off-peak hours. Given that vehicles are stationary for approximately 95% [6] of the time, they present significant potential as “mobile energy resources” for peak load leveling.

However, V2G systems also introduce significant privacy concerns. The data generated during interactions—such as location, charge/discharge volume, and state of charge—could expose sensitive user information, including personal schedules, financial status, and social relationships. Such data leakage raises the risks of targeted advertising, identity theft, or exploitation of personal details. While the exchange of information and energy between vehicles and the grid is essential for V2G system functionality, robust privacy protection is equally crucial. Without proper safeguards, public trust in smart grids could be eroded, potentially hindering the adoption of V2G technologies.

At the same time, international regulations, such as the UN R155 regulation by WP.29 [7] and ISO/SAE 21434 [8], emphasize the importance of cybersecurity and the protection of vehicle component information. These regulations highlight the increasing demand for secure, privacy-preserving solutions within V2G networks. Specifically, privacy protection is critical during data aggregation, where sensitive user information must be collected and processed without disclosing personal details. Moreover, with the increasing diversity of EV brands and the charging infrastructure, managing large-scale user identities is becoming more complex [9]. Furthermore, authentication methods must be adapted to specific scenarios, balancing security and efficiency. Lightweight solutions may suffice for routine charging, but high-risk interactions—such as payments or V2G feedback—demand more robust security measures.

Given the growing privacy concerns in V2G systems [10], it is essential to implement strong security and privacy-preserving mechanisms to ensure user trust and foster the widespread adoption of V2G technologies. To address these challenges, this paper proposes a decentralized identity (DID) and Zero-Knowledge Proof (ZKP)-based authentication framework. By leveraging decentralized identity management, our framework reduces reliance on centralized systems, mitigates single points of failure, and enhances scalability and security. Moreover, a layered ZKP mechanism is introduced to optimize authentication processes based on varying risk levels, ensuring a balance between efficiency and security across different application scenarios. To further enhance usability and contextual security, this framework also integrates automotive microcontroller applications [11], with experiments conducted on vehicle chips to validate our approach.

The primary contributions of this paper are as follows:

• We propose a distributed identity verification framework for smart grid and electric vehicle scenarios, enabling user identity autonomy and control, while ensuring the unlinkability of identities.
• We propose a method combining ZKP and challenge-based Pedersen commitments to verify masterID ownership and support anonymous identities in V2G settings, thereby enhancing the system’s practical applicability.
• We introduce a revocation mechanism using AND ZKP during registration to allow authorized supervisors to verify the mapping between userID and masterID, ensuring the traceability and effective management of malicious activities.
• Wed demonstrate the efficiency and scalability of the proposed framework through experimental results, comparing it with existing solutions in large-scale user scenarios.

This section provides an overview of the background and motivation for the research presented in this paper. Section 2 reviews related research in similar scenarios or relevant fields. Section 3 outlines the necessary background knowledge required to understand the proposed solution. In Section 4, the detailed structure and components of the proposed framework are described. Section 5 presents a security analysis and experimental evaluation of the solution. Finally, Section 6 summarizes the conclusions of the paper and provides directions for future research.

2. Related Work

Most traditional identity systems for smart grids do not safeguard anonymity and privacy, in addition to not providing users with the ability to disclose information on their own. Work related to our system is as follows: identity management in smart grids; application of distributed identity; security and efficiency of zero-knowledge proofs.

Smart grid identity management: The evolution of smart grids has driven significant advancements in identity authentication, security, and privacy. Chaudhry et al. [12] proposed a lightweight authentication scheme (LAS-SG) based on elliptic curve cryptography, which efficiently secures the communication between smart meters and neighborhood area networks (NANs) with minimal computational overhead. However, their scheme predominantly addresses single-identity authentication and fails to consider privacy challenges in dynamic multi-identity scenarios such as vehicle-to-grid interactions. Faheem et al. [13] developed a blockchain-based framework for Distributed Energy Resources (DERs), utilizing lightweight smart contracts to ensure secure communication and real-time control. While effective in enhancing the resilience and efficiency of DER integration, this approach lacks support for decentralized identity management and advanced privacy-preserving techniques, such as ZKPs. Khalid et al. [14] provided a comprehensive review of security and privacy challenges in smart grids, emphasizing interoperability and renewable energy integration. Nevertheless, their study remains largely theoretical, offering limited practical solutions for identity management. Collectively, these works provide a foundational understanding of secure communication in smart grids but leave critical gaps in addressing privacy-preserving identity management and decentralized credential validation.

Distributed identity applications: Distributed identity mechanisms have advanced identity management by addressing the limitations of centralized systems, particularly in enhancing privacy, security, and interoperability. Sadique et al. [15] proposed a DLT-based architecture for edge IoT devices, enabling secure communication in resource-constrained environments, but this remains narrowly focused on IoT without broader applicability to smart grids. Ferdous et al. [16] introduced a self-sovereign identity (SSI) framework for renewable energy certificate (REC) ecosystems, integrating SSI and DLT to address standardization and verification challenges, yet their reliance on predefined threat models limits adaptability in dynamic identity scenarios. Yuan et al. [17] leveraged lattice-based cryptography for quantum-resistant identity authentication, offering improved efficiency and security, though its practical applicability to classical smart grid systems is underexplored. These studies underscore the potential of DID systems but reveal gaps in supporting privacy-preserving multi-identity management and decentralized credential validation in smart grid environments.

Zero-knowledge proofs: Zero-knowledge proofs (ZKPs) [18] have proven to be essential for enhancing privacy and security across various domains by enabling verifiable computations without disclosing sensitive data. Koulianos et al. [19] employed zk-SNARKs for UAV authentication and location proofing, successfully balancing computational efficiency and privacy in resource-constrained environments. However, their reliance on public blockchains introduces scalability and performance limitations, particularly in high-frequency scenarios. Yin [20] proposed a Schnorr-based ZKP framework to secure sensitive student data in educational systems, incorporating matrix factorization to improve both accuracy and privacy. While effective in preserving data integrity, its scalability and applicability in real-time distributed systems remain constrained. Noteworthy zk-SNARK and blockchain-based solutions have also been developed by Guan et al. [21] and Hu et al. [22]. These studies highlight the significant potential of ZKPs in privacy-preserving solutions but also emphasize the challenges related to efficiency and scalability, particularly in dynamic, large-scale systems such as smart grids.

3. Preliminaries

Zero-knowledge proofs (ZKPs): Zero-knowledge proofs are cryptographic protocols that enable a prover to demonstrate the truth of a statement to a verifier without revealing any additional information [23] beyond the validity of the statement itself. Formally, a ZKP allows the prover to convince the verifier that they possess certain knowledge, such as a secret key, without disclosing the knowledge itself. This property is essential for maintaining privacy and security in various applications [24], ensuring that sensitive information remains confidential while providing verifiable proof of authenticity.

Pedersen commitment: The Pedersen commitment is a cryptographic commitment scheme [25] that allows a party to commit to a chosen value while keeping it hidden, possessing the ability to reveal the committed value later. The scheme is defined by the following two algorithms: commitment and opening. Given a value x and a random nonce r, the commitment C is computed as $C=g^x{h}^{r}modp$, where g and h are generators of a cyclic group G of prime order q, and p is a large prime. Pedersen commitments are both perfectly hiding and computationally binding [26], meaning that the commitment conceals the value x completely and it is computationally infeasible to find another pair $(x^{\prime },r^{\prime })$ such that $C=g^{x^{\prime }}{h}^{r^{\prime }}modp$.

Decentralized identifiers (DIDs): DIDs [27] enable verifiable, self-sovereign digital identities without relying on central authorities, ensuring secure authentication and privacy. DID, along with their associated DID documents and Verifiable Credentials (VCs) [28], are logically linked for identity identification and verification. In our scheme, we propose a DID format that fits our scenario, with a naming convention that conforms to the W3c standard, as shown in Figure 1. Additionally, both the masterID and userID follow the same format.

The DID syntax can be define as DID = “did:scheme:type of identity:specific-id”, where “did” is a fixed string, “:” is to combine strings, “sg” is our method name, and “type of identity” and “specific-id” are variable names. Each DID corresponds to a DID document, which is used to reveal the user’s public information, such as public key, authentication method, etc.

This structure ensures that the masterID (the unique identity for supervision) and userID (the pseudonymous identities for regular application) are indistinguishable by length or composition. Such uniformity mitigates the risk of Sybil attacks, as external systems cannot differentiate between identities based on their format, preserving privacy and anonymity within the system.

For ease of reference, the main symbols in this paper are listed in

Table 1. Summary of abbreviations and notations.

Notations	Meaning	Notations	Meaning
${auth}_v$	Vehicle authentication data	r	Random nonce for Pedersen commitment
${req}_v$	Vehicle registration request	$p{k}_{vehicle},s{k}_{vehicle}$	Vehicle’s public and private key
$p{k}_{master},s{k}_{master}$	Vehicle’s master public and private key	${\sigma }_{SG}$	Smart grid’s signature on credential
C	Pedersen commitment	$p{k}_{user},s{k}_{user}$	Vehicle user’s public and private key
$Z_r$	Response for nonce in ZKP	${VC}_v$	Vehicle’s verifiable credential
H	Hash function	R	Intermediate value in ZKP for masterID
$h,g$	Two random generators of $\mathbb{G}$	$Z_{master}$	Response for masterID in ZKP
${\mathbb{Z}}_q$	Finite field of order q	$Z_r$	Response for nonce in ZKP
$\mathbb{G}$	A cyclic group of order q	DID	Distributed identifier, $DID=\{masterID,userID\}$
$\mathcal{BL}$	Sanctioned blacklist	$\tau$	Timestamp, $\tau \in \mathbb{T}$ (valid time set)

.

4. Proposed Scheme

4.1. System Model

In our system model, there are four key entities—the supervisor, the smart grid, the holder, and the verifier—all operating within the framework of a blockchain network. We assume the presence of N nodes using a $(t,N)$–Shamir threshold scheme, denoted as $O_1,\dots ,O_N$, where t represents the number of malicious nodes. The consensus method is based on Byzantine fault tolerance, where at least t nodes are required to validate a transaction. The supervisor, in our scheme, is a trusted authority typically composed of a cluster of official institutions. This entity is resistant to single points of failure and is responsible for maintaining a sanction list, which includes malicious users (along with their verifiable credentials) or blockchain nodes. Entities listed in the sanction list will no longer be eligible for legitimate certification. The smart grid, functioning as both the energy provider and the credential issuer in our system, operates as a full node or a cluster of full nodes. The holder is typically an entity or program with a registered identity, such as an electric vehicle user. The verifier, which includes charging station systems and other computational entities, is responsible for validating the legitimacy of credentials and accepting proofs from other entities. Verifiers are generally considered light nodes with limited computational capabilities. For simplicity, we abstract the aggregator model to the charging station system and do not describe it separately.

All four types of entities can perform query operations on the blockchain network to retrieve associated documents and verifiable credentials (VCs) through the use of decentralized identifiers. Each user is assigned a unique master identity (masterID) and multiple anonymous identities (userID). Each identity has its own public–private key pair ($pk,sk$), where $pk=g^{sk}$ and g is a generator of group $\mathbb{G}$.

As shown in Figure 2, our full process workflow, with its simplified model, encompasses the process from DID creation to credential usage to DID cancellation.

Although the detailed architecture of the power grid is outside the scope of this study, it is important to clarify that the “smart grid system” depicted in Figure 3 refers to the grid control center, while the charging stations on the right side represent edge devices, primarily charging piles operated by grid retailers. For clarity, intermediary devices and entities, such as aggregators, have been omitted from the diagram.

4.2. Security Model

The interaction process in our scheme, shown in Figure 3, involves a trusted supervisory institution that can trace and revoke DIDs. Communication with the vehicle occurs over a trusted channel. The adversarial model is based on Byzantine fault tolerance, allowing up to t faulty or malicious nodes, where $t<N/3$. Cryptographic primitives such as hash functions and random number generators are assumed secure.

Furthermore, our scheme ensures the Sybil resistance, unlinkability, anonymity, unforgeability, privacy, and auditability of the credential system as follows:

• Sybil resistance: An adversary cannot forge valid peer identities from authentic identities, nor can they manipulate the system’s operation through fake (anonymous) identities.
• Unlinkability: An adversary cannot link different identities across multiple interactions or transactions to determine whether they belong to the same real-world entity.
• Anonymity: Users can choose to conceal their real identity and conduct transactions under an anonymous identity with specific restrictions.
• Unforgeability: Attackers cannot forge valid credentials using public parameters and information, nor can they fabricate a legitimate proof or claim to be associated with a real identity.
• Privacy: An adversary cannot obtain any private information beyond what the user has explicitly disclosed or made publicly available.
• Auditability: Malicious activities can be traced and sanctioned by a trusted supervisory authority, which maintains a list of sanctioned identities.

4.3. SGDID Design

4.3.1. Identity Registration Phase

In the proposed SGDID system, EVs, charging stations, supervisors, and the power grid are all part of the SGDID network. The specific interaction process is shown in Figure 3.

(1) MasterID registration request: The vehicle user initiates the registration process by sending a masterID registration request to the SGDID identity system. In this process, the user must provide verifiable identity proof $aut{h}_v\in \mathcal{P}$, where $\mathcal{P}$ is the set of all accepted identity proofs, such as an electronic ID, device MAC address, or other forms of guarantee. Additionally, the user specifies the anonymity flag $\alpha \in \{0,1\}$ to indicate whether the registration request requires anonymity. This flag allows the supervisor to determine whether the application corresponds to a masterID.

The vehicle’s registration request, denoted as ${req}_v$, consists of the authentication data ${auth}_v$ for the proof of identity information and and a public key $p{k}_{vehicle}$, the proposed masterID. The request is given by the following tuple:

$${req}_v=({auth}_v,masterID,\alpha ,p{k}_{vehicle}),$$

If the vehicle’s identity is successfully validated, the system assigns $p{k}_{master}=p{k}_{vehicle}$, and the vehicle user securely stores $s{k}_{master}=s{k}_{vehicle}$.

Subsequently, a corresponding registration request is dispatched to the blockchain network for further processing. If the supervisor does not validate successfully, the registration information and masterID in the release request are discarded.

(2) Supervisor Approval: Firstly, the supervisor checks if the DID identity is renamed to a DID in the blacklist, marked as $DID\notin \mathcal{BL}$, where $\mathcal{BL}$ denotes a sanctioned blacklist.Once the registration request is received, the supervisor evaluates the request and approves it if the vehicle’s identity is verified. The supervisor’s approval message, ${approval}_s$, is then broadcasted to the blockchain network. The approval is represented as follows:

$${approval}_s=(hash\left({req}_v\right),result),$$

where $hash\left({req}_v\right)$ is the hash of the registration request, and $result$ represents the outcome of the identity verification process.

(3) Consensus process using PBFT: The supervisor’s approval message, along with the registration request, enters the consensus phase, which is carried out using the Practical Byzantine Fault Tolerance (PBFT) protocol. The consensus process proceeds as follows:

Preprepare Phase: The primary node receives the registration request and the supervisor’s approval message. It then broadcasts a preprepare message to the backup nodes, which is represented as:

$$preprepare=hash({req}_v,{approval}_s).$$

Prepare phase: Each backup node verifies the preprepare message and, if valid, generates a prepare message. This message is broadcast to the replicas.

Commit phase: Once a replica node has received enough prepare messages, it enters the commit phase. After sufficient commit messages are received, the node commits the block and processes the request in its local cache before sending the final response back to the client.

(4) MasterID storage and confirmation: Upon the successful completion of the consensus process, the client receives a confirmation of the registration. The vehicle’s masterID is securely stored for future use within the SGDID network, and other entities can query the DID and its associated information.

(5) A new round of userID registration: Once the masterID has been successfully registered, the client proceeds with requesting a userID. To ensure that the vehicle user is the legitimate owner of both the masterID and the userID, the user must prove ownership of both identities without revealing any private keys. This is achieved using an AND ZKP (See Appendix A for the specific interactions and proof processes), which allows the user to demonstrate the following:

$$p{k}_{master}=g^{s{k}_{master}}andp{k}_{user}=g^{s{k}_{user}},$$

where g is a generator of a cyclic group, and $s{k}_{master}$ and $s{k}_{user}$ are the private keys corresponding to the masterID and userID, respectively. When the supervisor knows the linkability of the DID, if the $masterID\in \mathcal{BL}$, all associated anonymous identities linked to it will also be revoked. By using this approach, the vehicle user can prove that they possess both the masterID and userID without disclosing their private keys, thus preserving privacy and maintaining security. This method prevents potential Sybil attacks [29], as the user’s private keys remain undisclosed.

4.3.2. Credential Request and Issuance

Credential request: In the context of smart grid services for electric vehicles (EVs), the issuance of credentials plays a crucial role in securing interactions and mitigating potential network threats [30]. To begin the process, a vehicle user submits a credential request, ${\mathcal{R}}_v$, consisting of their smart grid decentralized identifier, ${DID}_V$, and a claim vector ${CL}_V$, which contains key attributes like vehicle identity, registration details, and timestamp. Formally, let $\mathcal{V}=\{V_1,V_2,\dots ,V_n\}$ denote the set of all vehicle users, and let $\mathcal{C}$ represent the set of all possible claim vectors. Each vehicle user $V\in \mathcal{V}$ initiates a credential request ${\mathcal{R}}_V$ by submitting their smart grid decentralized identifier and a claim vector ${CL}_V\in \mathcal{C}$. The credential request is represented as ${\mathcal{R}}_V=({DID}_V,{CL}_V,\tau )$, where ${CL}_V$ represents the vehicle’s claim vector, which includes the service of need use(such as charging access).

Credential issuance: Upon receiving the credential request, the smart grid retrieves the relevant public key $p{k}_{vehicle}$ and DID document $DI{D}_V$ from the blockchain network $\mathcal{B}$, which contains the information the vehicle has agreed to disclose. The vehicle’s identity is then validated via the authentication function $Auth:\mathcal{V}\times \mathcal{C}\to \{0,1\}$, where $Auth(V,{\mathcal{C}}_V)=1$ indicates a successful validation. and if the conditions are met, it issues a verifiable credential ${\mathcal{C}}_v^{\prime }=({SGDID}_V,{\mathcal{C}}_V^{SG},{\sigma }_{SG})$, where ${\mathcal{C}}_V^{SG}$ represents the content of the verifiable credentials issued by the smart grid to the vehicle user V, and ${\sigma }_{SG}$ is the digital signature from the smart grid. This credential is then broadcasted to the blockchain, allowing the vehicle user and authorized entities to query and validate it. Furthermore, authorized entities can interact with blockchain nodes to store ${\mathcal{C}}_v^{\prime }$ locally, ensuring the future access to and verification of the credential. Through this process, the system ensures both secure issuance and widespread accessibility for subsequent validation within the smart grid network.

4.3.3. Credential Verify

(1) Common scenarios: In the grid-to-vehicle (G2V) scenario, when an electric vehicle (EV) presents its Smart Grid Decentralized Identifier (SGDID) and associated verifiable credential ${\mathcal{C}}_v^{\prime }$, the charging station initiates the verification process by querying the blockchain network for the credential’s stored hash value $H=Hash\left({\mathcal{C}}_v^{\prime }\right)$. The EV user provides a hash $H^{\prime }$, which is compared with H; if $H\equiv H^{\prime }$, the credential is authentic. The verification mechanism is formally described as

$$Au\left({\mathcal{C}}_v^{\prime }\right)=(Hash\left({\mathcal{C}}_v^{\prime }\right)=H^{\prime })\wedge Ver({\mathcal{C}}_V^{SG},{\sigma }_{SG})$$

When $Au\left({\mathcal{C}}_v^{\prime }\right)$ outputs true, it indicates that the verification has been successful; otherwise, the process returns ⊥. In the verified mathematical equation above, the charging station proceeds by validating the contents of the credential ${\mathcal{C}}_V^{SG}$ and the digital signature ${\sigma }_{SG}$. The verification function $Verify({\mathcal{C}}_V^{SG},{\sigma }_{SG})$ checks whether the signature ${\sigma }_{SG}$ correctly authenticates the claims in ${\mathcal{C}}_V^{SG}$ using the smart grid’s public key $p{k}_{SG}$. If both checks pass, the EV is granted access to charging services. Otherwise, if any validation step fails, access is denied.

(2) V2G scenarios: In situations where the electrical grid requires load balancing, electric vehicles (EVs) can supply electrical energy back to the grid [31]. To protect charging stations from potential malicious attacks by users and to ensure traceability for supervisory authorities, vehicles must prove their ownership of a masterID, even when operating under an anonymous identity. Initially, the vehicle presents its masterID and associated proof parameters to the charging station. Upon receiving the masterID, the charging station queries the blockchain network to retrieve the corresponding public key $p{k}_{master}=g^{s{k}_{master}}modp$, where $s{k}_{master}$ is the vehicle’s private key. Subsequently, the vehicle engages in the proof process as illustrated in Figure 4.

The proof process employs the Pedersen commitment and zero-knowledge proof (ZKP) protocol to demonstrate the ownership of the masterID and the corresponding private key $s{k}_{master}$ without revealing any sensitive information. First, the vehicle generates a Pedersen commitment by selecting a random nonce $r\in {\mathbb{Z}}_q$ and computes $C=p{k}_{master}·h^{r}modp$, where h is another generator in the group G. Simultaneously, the vehicle selects random values w and s from ${\mathbb{Z}}_q$ and computes the intermediate value $R=g^w·h^{s}modp$. Both C and R are then sent to the charging station.

Upon receiving C and R, the charging station generates a random challenge $c\in {\mathbb{Z}}_q$ and sends it back to the vehicle. In response, the vehicle calculates the responses $Z_{master}=w+c·s{k}_{master}modq$ and $Z_r=s+c·rmodq$, which are subsequently sent to the charging station for verification.

The charging station verifies the proof by checking the equation $g^{Z_{master}}·h^{Z_r}=R·C^{c}modp$. If the equation holds true, the charging station confirms that the vehicle indeed possesses a valid masterID and the corresponding private key $s{k}_{master}$, thereby authorizing the vehicle to supply energy to the grid. This protocol ensures that the masterID remains confidential through the Pedersen commitment, while the zero-knowledge proof guarantees secure ownership verification without disclosing the private key, maintaining the integrity and security of the smart grid system.

After the user has successfully demonstrated ownership of the masterID, the protocol proceeds by repeating the steps described in the Common Scenarios section. This repetition enables the charging station to verify whether the (VC) issued by the smart grid is both authentic and valid in its contents.

4.3.4. Revocation Mechanism

Revocation triggers are categorized into active revocation and passive revocation. A revocation process is noted as ${\mathcal{F}}_{Revocation}\in \mathcal{R}$, where

$$\mathcal{R}=\{{\mathcal{R}}_a(U,E),{\mathcal{R}}_a(U_{old},U_{new},E),{\mathcal{R}}_p(T,U,n),{\mathcal{R}}_p\left(A\right)\}$$

In our revocation mechanism, active revocation ($R_a$) is initiated by legitimate entities based on specific events affecting a user’s identity or device. For example, if a user U reports the loss of their device E, the system triggers ${\mathcal{R}}_a(U,E)$. We also define another condition, as follows: when ownership of a vehicle device E transfers from $U_{old}$ to $U_{new}$, an active revocation is initiated, $R_a(U_{old},U_{new},E)$.

Passive revocation ($R_p$) is triggered by the detection of malicious or abusive behavior within the network. For instance, if a user U makes n fraudulent requests for userIDs within a time window T, their masterID is added to the blacklist $\mathcal{BL}$. Simultaneously, it triggers the function ${\mathcal{R}}_p(T,U,n)$, where $T\in \mathbb{T}$ is a predefined time interval and $n\in \mathbb{N}$ is the threshold number of fraudulent requests. Additionally, if a user engages in a malicious attack A such as device tampering or a Distributed Denial of Service (DDoS) attack, a passive revocation is triggered as follows: $R_p\left(A\right)$, if $A\in {\mathcal{A}}_{attack}$, where ${\mathcal{A}}_{attack}$ represents the set of recognized malicious activities.

Revocation request involves initiating a revocation process by a user U, a supervisory authority I, or the smart grid G. The revocation request $R_{req}$ comprises a proof of the revocation condition $\sigma$, a timestamp $\tau$, and a unique identifier $ID$ as follows:

$$R_{req}=(S,\sigma ,\tau ,ID),$$

where $S\in \{U,I,G\}$ denotes the initiator, $\sigma$ validates the revocation condition, $\tau \in \mathbb{T}$ marks the initiation time, and $ID\in DID$ ensures the specific request and the revocation ID.

Consensus verification employs a consensus mechanism, $Consensus\left(R_{req}\right)$, to validate the legitimacy of the revocation request. Let $N=\{N_1,N_2,\dots ,N_k\}$ represent the set of blockchain nodes participating in the verification. The verification procedure involves verifying $\sigma$ for all nodes $N_i\in N$, validating $\tau$ and $ID$ for all nodes $N_i\in N$, and reaching consensus with $R_v=Consensus\left(R_{req}\right)$, where $R_v\in \{0,1\}$. A value of $R_v=1$ indicates approval, while $R_v=0$ signifies the rejection of the request.

Revocation confirmation occurs upon successful consensus verification ($R_v=1$). The revocation information $R_{revoke}$ is broadcasted to the blockchain network as follows:

$$R_{revoke}=(S,\sigma ,\tau ,ID,statu{s}_{revoke})$$

where $statu{s}_{revoke}=true$ signifies an active revocation. This broadcast ensures that all nodes $N_i\in N$ update their local state ${State}_{N_i}$, accordingly, as follows:

$$Stat{e}_{N_i}\leftarrow {State}_{N_i}\cup \left\{R_{revoke}\right\}$$

This update guarantees that all future authentication attempts involving the revoked masterID or related entities are blocked, thereby maintaining the system’s integrity and security.

5. Security Analysis

5.1. Sybil Attack Resistance

First, during the registration process, vehicles are required to provide verifiable identity information (such as electronic ID or MAC address), and utilize ZKPs to ensure the integrity of the mapping between the masterID and userID. This ensures that, even when users register multiple anonymous identities, the supervisory authority can verify the linkage between the masterID and userID without revealing any private key information. Furthermore, all registration requests undergo validation via the PBFT consensus protocol, ensuring the system’s decentralization and resistance to tampering. Additionally, if a vehicle’s masterID is blacklisted, all associated identities are revoked, effectively preventing malicious actors from creating numerous fraudulent identities to execute an attack. Through this multi-layered approach, the system not only guarantees the authenticity and uniqueness of identities but also preserves user privacy, thereby effectively preventing Sybil attacks.

5.2. Unlinkability

A legitimate user can possess multiple anonymous userIDs, but transactions between these userIDs cannot be linked to a single real-world identity. The detailed proof of this unlinkability property can be found in Appendix B. Furthermore, the masterID and userID are indistinguishable to adversaries, as we employ a semantically secure hash function in generating the specific-identity. The formal proof of this indistinguishability is presented in Appendix C.

5.3. Conditional Anonymity

Electric vehicle users can perform transactions without revealing their true identity. In general scenarios, our system achieves anonymity by allowing users to register and interact using their userID, instead of their masterID, to access limited services. Additionally, the registration process allows users to specify whether they require anonymity, ensuring that their real identity is only disclosed to the supervisor when absolutely necessary.

5.4. Unforgeability

With regard to user identities, only information verified by a supervisory authority (${auth}_v$) can be further broadcast and validated in the distributed identity blockchain network. Since adversaries do not possess the supervisory authority’s private key, they cannot issue ${auth}_v$ and thus cannot generate legitimate authentication messages. For credential verification, adversaries cannot forge the ${cred}_v$ issued by the smart grid to users as they lack the smart grid’s private key. This guarantees that only legitimate requests can generate valid credentials.

5.5. Privacy Preservation

In the identity registration process, our scheme utilizes an AND ZKP to prove the relationship between userID and masterID to the supervisory authority. This approach ensures the completeness, soundness, and zero-knowledge properties, with the formal proof detailed in Appendix A. In the V2G scenario, while maintaining system availability, we enhance privacy protection by using a combination of Pedersen commitments and zero-knowledge proofs. This method proves that a given userID corresponds to the anonymous identity of the owner of a masterID, thus enabling the provision of services in the V2G scenario while safeguarding user privacy.

5.6. Auditability

All transactions and interactions are recorded on the blockchain, providing an immutable and transparent ledger. Additionally, our scheme introduces a trusted supervisory authority responsible for maintaining a list of sanctioned identities and monitoring the behavior of system participants. The supervisory authority can trace and sanction malicious activities without infringing upon user privacy. It is capable of maintaining the relationship between masterID and userID and mapping all identities within the system to real-world identities, as users are required to provide relevant identity information during registration to ensure accountability.

Similar solutions to ours can be found in References [32,33,34,35], which present authentication schemes in the context of smart grids or use the same cryptographic tools. A comparison of their security attributes is provided in

Table 2. Comparison of security attributes across similar scheme scenarios.

	Schemes	[32]	[33]	[34]	[35]	SGDID
Security Features
Sybil attack resistance		✓	✓	✓	✓	✓
Unlinkability		✓	✓	×	×	✓
Conditional anonymity		✓	✓	×	✓	✓
Unforgeability		×	✓	✓	✓	✓
Privacy preservation		✓	✓	✓	✓	✓
Auditability		✓	×	×	✓	✓

In this table, “✓” means that the protocol meets a security feature or can resist an attack; otherwise, it is “×”.

.

6. Performance Evaluation

In order to accurately measure the experimental results, we conducted runtime tests of the cryptographic operations involved using the JPBC cryptographic library [36]. Our consortium blockchain system was built using Hyperledger Fabric v2.3.2 [37], with client programs and smart contracts developed based on the fabric-chaincode–java framework. We employed a cyclic group of prime order q with $\left|q\right|=2048$ bits. The generators g and h were randomly selected from $\mathbb{G}$ using a cryptographically secure random number generator, ensuring uniformity and independence. In the Pedersen commitment and the zero-knowledge proof (ZKP) protocol, the random nonce r and the challenge c are generated using the ‘java.security.SecureRandom’ class to ensure cryptographic security. The hash function used was SHA-256.The experimental setup included a computer equipped with an Intel i7 processor (2.5 GHz) and 16 GB of memory, while the device-side computation simulation utilized Infineon’s TC4XX chip [38]. The simulation software used was CANoe16 (version 16.0.145), and the hardware used was Vector’s VN 1640A device.

Our proposed scheme demonstrates clear advantages in storage efficiency compared to existing solutions for smart grid applications, as shown in

Table 3. Storage cost comparison.

Scheme	Storage Cost (bits)
[32]	1183
[33]	1460
[34]	1988
[35]	897
SGDID	913

. When compared to alternatives like the scheme in [34] (1988 bits) and [35] (897 bits), our SGDID scheme incurs a storage cost of 913 bits, which is slightly higher than that of [35] but still competitive. While [35] uses quantum-resistant key structures, transitioning to such a setup provides limited practical benefits for current smart grid applications. In contrast, SGDID strikes a practical balance between storage efficiency and operational feasibility, offering a more viable solution for real-world scenarios. The modest storage overhead enables the efficient utilization of system resources, critical for optimizing smart grid operations, particularly in the context of electric vehicle (EV) integration, where real-time data management and scalability are essential for responsive decision making. Specifically, the 913-bit storage cost of SGDID comprises 160 bits for the user identifier, 256 bits for the cryptographic proof, 160 bits for the nonce r, 256 bits for the hash of the user’s identity, and 81 bits for additional protocol parameters, all contributing to ensuring both functionality and security.

In Figure 5a,b, the computational costs of various authentication schemes are presented, as the number of EVs requesting authentication services increases from 100 to 800. These measurements were conducted on EV devices equipped with Infineon TC4XX automotive-grade chips. In Figure 5a, we compare the performance of SGDID against Zhong et al.’s and Odelu et al.’s schemes. SGDID consistently demonstrates the lowest computational cost across all tested scenarios, starting at 21 ms for 100 EVs, in contrast to 29 ms for Zhong et al.’s and 33 ms for Odelu et al.’s schemes. As the number of EVs grows, SGDID maintains its efficiency, reaching a computational cost of 72 ms at 800 EVs, significantly outperforming Zhong et al.’s 90 ms and Odelu et al.’s 95 ms. These findings underscore SGDID’s enhanced scalability and optimized performance, even under progressively increasing authentication demands.

In Figure 5b, the performance of SGDID is compared to that of Tsai et al.’s and Praetta et al.’s schemes. SGDID again outperforms the alternatives, with an initial computational cost of 21 ms for 100 EVs, compared to 24 ms for Tsai et al.’s and 39 ms for Praetta et al.’s schemes. As the number of EVs increases, SGDID continues to exhibit superior computational efficiency, with a cost of 72 ms at 800 EVs, while Tsai et al.’s and Praetta et al.’s schemes increase to 98 ms and 92 ms, respectively. These results further highlight SGDID’s computational efficiency and scalability, making it particularly suitable for deployment in resource-constrained EV environments that require robust and large-scale authentication services.

In Figure 5c, the time cost for the identity registration process across 100 experiments demonstrates the high efficiency and stability of the SGDID scheme. The recorded time costs range from 2.210 ms to 2.352 ms, with an average of 2.296 ms. The minimal fluctuations, with most data points clustering closely around the mean, indicate the scheme’s consistency. This performance highlights SGDID’s optimization, particularly when deployed on Infineon TC4XX automotive-grade chips, which are designed to effectively handle resource-constrained environments. The narrow spread of results further underscores the system’s robustness in maintaining stable performance across repeated trials, ensuring a reliable and swift registration process.

Figure 5d presents the time cost for the identity verification process conducted in a V2G scenario with enhanced privacy protections for authentication. Despite the additional privacy requirements, SGDID maintains impressive efficiency, with time costs ranging from 2.442 ms to 2.521 ms and an average of 2.472 ms. While slightly higher than the registration process, the verification process remains stable with minimal deviations, demonstrating the scheme’s scalability and practicality. The ability to maintain low time costs under stricter privacy conditions in the V2G setting further demonstrates the effectiveness of SGDID for real-world applications. These results emphasize its capacity to deliver secure, lightweight, and efficient authentication solutions, crucial for modern EV environments.

To evaluate the performance of our distributed identity scheme, we compare SmartDID [39] with CanDID [40] in Figure 6. In our experiments, we configure the distributed identity blockchain network with six nodes, including one malicious node, and both systems operate under the PBFT consensus mechanism. The total number of vehicles is divided such that two-thirds are engaged in regular smart grid operations, while one-third participate in V2G scenarios.

The results show that the performance of SGDID consistently outperforms SmartDID. When the number of validations is below approximately 235,000, the computational cost of our scheme is higher due to the need for masterID ownership proof, making vehicle authentication less efficient than CanDID. However, as the number of validations exceeds 235,763, our scheme surpasses CanDID in terms of computational efficiency. Specifically, when the number of validated transactions reaches 100,000, the computational cost is 47.1 s, and when the number of validations increases to 600,000, the computational cost rises to 70.8 s. Despite these increases, our method’s computational cost improves at scale. Once the number of validated vehicles surpasses 300,000, the computational cost of our method becomes significantly lower than that of CanDID. This is due to the efficiency of the decentralized masterID ownership verification process, which reduces computational complexity and eliminates single points of failure as the number of vehicles grows.

Table 4. Performance comparison.

Performance	CanDID	SmartDID	SGDID
Credentials generation	3.97 s	0.031 s	0.028 s
Proof generation	1.2 s	0.29 s	0.41 s
Proof time	0.006 s	0.023 s	0.016 s
Identity revocation	1.5 s	N/A	0.057 s

compares the performance of the proposed SGDID framework with two state-of-the-art decentralized identity systems, CanDID and SmartDID. SGDID demonstrates competitive efficiency across all metrics. For credential generation, SGDID outperforms both CanDID and SmartDID, with a time of 0.028 s. While the proof generation time for SGDID (0.41 s) is slightly higher than that of SmartDID (0.29 s), it still offers a significant security advantage by proving the linkage between masterID and userID, which is crucial for enhanced privacy and attack resistance. Additionally, SGDID’s proof time (0.016 s) is comparable to or better than the other two schemes. A standout feature of SGDID is its identity revocation performance, achieving a time of 0.057 s, which is much faster than CanDID’s 1.5 s, while SmartDID lacks this functionality (N/A). Overall, SGDID offers a balanced trade-off between performance and security, particularly in scenarios where both fast credential management and strong identity linkage are required.

The efficiency of identity revocation in our proposed scheme is evaluated through the experiments shown in Figure 7. In these experiments, we simulate revocation requests triggered by monitoring scripts under varying workloads, with both active and passive revocation processes being tested simultaneously. In the case of active revocation, we simulate the scenario where users lose their devices, corresponding to the function ${\mathcal{R}}_a(U,E)$. For passive revocation, we simulate malicious users performing repeated registrations to exhaust system resources, corresponding to the function ${\mathcal{R}}_p(T,U,n)$. Experimental results show that our scheme efficiently handles identity revocation with minimal processing times. When 100 concurrent revocation requests are triggered on the server-side, the active revocation process takes only 0.82 s of CPU time, while passive revocation takes 1.33 s. As the number of concurrent revocations increases to 400, the CPU processing times for active and passive revocation are 1.54 s and 1.77 s, respectively. These results confirm that our scheme can effectively handle a large volume of simultaneous revocation requests, with sublinear time growth as the workload increases, demonstrating both the scalability and efficiency of the revocation mechanism.

These findings suggest that our approach can efficiently scale to handle the increasing number of vehicles interacting with the smart grid, providing a practical solution for managing peak electricity demand and enhancing overall system performance. In contrast, CanDID’s performance deteriorates as the network grows due to the centralized verification bottleneck, limiting its scalability in large-scale systems.

7. Conclusions

This paper presents a distributed identity verification framework for smart grids and electric vehicles, focusing on providing anonymous userIDs and ensuring unlinkability to protect user privacy in V2G scenarios. We propose a method combining ZKP and challenge-based Pedersen commitments, enabling masterID ownership verification while supporting anonymous identities in V2G environments, thus enhancing system applicability. Additionally, we introduce a revocation mechanism within our identity framework, incorporating AND ZKP during registration to allow supervisors to verify the mapping between userID and masterID, ensuring the effective management and traceability of malicious activities.

Experimental results show that our solution outperforms existing authentication and DID schemes in large-scale deployments. The identity registration process takes just 2.296 ms on average, and V2G verification requires 2.472 ms, demonstrating efficiency and scalability. Our identity revocation mechanism has a low 0.057-s latency and supports concurrent multi-user processing, making it ideal for high-throughput environments. Validation on automotive-grade hardware further confirms its real-world applicability, especially for next-generation EV ecosystems.

Future work will focus on enhancing the framework’s performance by refining identity management granularity, addressing the growing security needs of large-scale systems. These improvements will establish a robust, scalable framework for digital identity management in the DID ecosystem.