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Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Feb 17;16:9470. doi: 10.1038/s41598-026-38035-3 Search in PMC Search in PubMed View in NLM Catalog Add to search Blockchain-driven smart contract with key exchange protocol for secure device-to-device communication using verkle tree K-ary structures A Simbu A Simbu 1 School of Electronic Engineering, Vellore Institute of Technology, Vellore, 632014 India Find articles by A Simbu 1 , S Nandakumar S Nandakumar 1 School of Electronic Engineering, Vellore Institute of Technology, Vellore, 632014 India Find articles by S Nandakumar 1, ✉ , K Saravanan K Saravanan 1 School of Electronic Engineering, Vellore Institute of Technology, Vellore, 632014 India Find articles by K Saravanan 1 Author information Article notes Copyright and License information 1 School of Electronic Engineering, Vellore Institute of Technology, Vellore, 632014 India ✉ Corresponding author. Received 2025 Oct 16; Accepted 2026 Jan 28; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ . PMC Copyright notice PMCID: PMC13004948 PMID: 41703014 Abstract In the rapidly evolving landscape of wireless communication, the traditional model of data exchange predominantly relies on a centralized infrastructure, where all communications, even between nearby devices, are routed through a base station (BS) and potentially the core network. Device-to-device (D2D) communication emerges as a transformative paradigm that challenges this conventional model. The concept of D2D communication has gained considerable traction, especially with the advent of 4G LTE and its crucial role in 5G and beyond. D2D aims to unlock numerous benefits, including improved spectral efficiency, increased throughput, reduced latency, enhanced energy efficiency, and better network offloading. In this paper, we focus on secure D2D communication using D2D-ECDH key exchange protocol with blockchain smart contracts along with blockchain Verkle tree data structure. This approach helps to improve secure communication between IoT devices and avoids Man-in-the-Middle (MITM) attacks, replay attacks, and central points of failure. The Verkle tree approach provides a smaller proof size to verify the root commitment value compared to the traditional Merkle tree data structure. The simulation has been executed in both Python and Solidity coding. Python has executed in VS Code generator, and Solidity code has executed in Remix IDE, Ethereum network V0.65.0. The Remix IDE was developed in Ganache V2.7.1 for blockchain smart contracts. Compared to the traditional Merkle tree approach, the Verkle tree provides less proof size up to 33 times. Supplementary Information The online version contains supplementary material available at 10.1038/s41598-026-38035-3. Keywords: ECDH, D2D, Communication, Key exchange, Blockchain, Smart contract, Merkle tree, Verkle tree Subject terms: Engineering, Mathematics and computing Introduction Wireless communication has gained popularity in the last two decades. In the last decades, there has been a vast number of growths in mobile users and broadband users. Due to the growth of huge users, it creates heavy traffic, and we need faster data access. Applications of wireless communication include Mobile phones, Wi-Fi, Bluetooth, GPS, Remote control access, Wireless charging. Due to the nature of man-made disasters and central base station failure, it creates big issues during communication. The solution for the central point of failure and huge traffic load on the base station is device-to-device (D2D) communication. D2D communication is a fundamental aspect of 5G and the future cellular network. D2D is also one of the emerging technologies in wireless communication. It allows devices to communicate with each other without needing a base station or central network. It’s a decentralized network for wireless communication. D2D communication provides secure communication between devices, helping protect against man-in-the-middle (MITM) attacks 1 . For secure communication, we use D2D using the ECDH (Elliptic Curve Diffie–Hellman) key exchange protocol, which is the most promising technology. ECDH is a cryptographic technique used for secure key exchange among two communicating devices over an untrusted network. It enables both devices to autonomously generate a common secret key without transmitting it directly. The method relies on E lliptic Curve Cryptography (ECC), which offers comparable security to the traditional Diffie–Hellman method but achieves this with much shorter key lengths, resulting in improved efficiency and performance. compare to ECC 2 and RSA, D2D-ECDH provides strong security, less key size, security and faster signing. Blockchain decentralized network technology 3 uses a traditional tree data structure named Merkle tree (M-tree) data structure. A Merkle tree data structure has a very long proof size for computing the root hash value and also it takes more time to verify the root hash value. So, we address the issues in the traditional Merkle tree; to overcome these issues we use Verkle tree data structure. The verkle tree structure is also one of the data structures like the traditional Merkle tree but the verkle tree provides less proof size and quick validation for root commitment value. Merkle tree root hash value is in the cryptographic hash value. In verkle tree, vector commitment is used for validating the root commitment. Compared to the Merkle tree, the verkle tree data structure has less proof size and less execution of root values. Along with D2D-ECDH, blockchain smart contracts 4 and blockchain verkle tree data structures are the most emerging technology in secure data communication. Figure 1 shows the secure D2D communication for the authorized devices share the data through a smart contract using blockchain verkle tree and the unauthorized devices are restricted for the data access. Fig. 1. Open in a new tab D2D communication using a blockchain network. Literature review A robust and secure architecture for device-to-device communication in emergency situations, RESCUE offers complete defense against common attacks such flooding, impersonation, routing manipulations, dropping, message manipulations, blackholing, and Sybil assaults 5 . a new resource allocation technique based on bee fly patterns for D2D communication in cellular networks to enhance experience and quality of service 6 . In order to facilitate mutual authentication and guarantee message integrity, this article suggested a blockchain-based framework for safe device-to-device communication in Internet of Things networks, utilizing smart contracts and ECC 7 . a novel key generation strategy for D2D communication that enhances the key generation rate and entropy by altering the channel gains through artificial jamming 8 . proves that dynamic group management using a distributed ledger-based hierarchical architecture is quicker and more flexible without sacrificing security or performance. lowering the possibility of a single point of failure in the process 9 . The BAN logic formal security analysis shows how effective it is against a variety of cyberattacks. The research findings make it clear that the suggested plan can guarantee the security of apps in smart cities 10 . CAKA- D2D is a new authentication mechanism for D2D group communications in 5G cellular networks. It is confirmed to be capable of implementing mutual authentication among group users and fending off potential harmful attacks. The CAKA-D2D protocol is the first to tackle the problem of secure D2D group communications in the 3GPP-specified 5G architecture 11 . To improve security and efficiency over earlier solutions, the study suggests a safe two-factor authentication and key agreement approach for cloud computing that makes use of elliptic curve cryptography, a fuzzy verifier, and other methods 12 . For Telecare Medical Information Systems (TMIS), a secure ECC-based three-factor mutual authentication protocol with superior security features and reduced transmission costs. Using ECC and a collision-resistant one-way hash function to offer secure device access control and key agreement between IoT devices. LACKA-IoT is a novel certificate-based lightweight access control and key agreement protocol for the IoT context 13 . BIDAPSCA5G is a blockchain-based authentication protocol for 5G-enabled IoT device-to-device communication in smart city applications. It offers location-based authentication, blockchain-based device registration and revocation, and device anonymity, in addition to mutual authentication between IoT devices without the need for a central registration authority 14 . SCAB-IoTA is a blockchain-based secure communication and authentication scheme for Internet of Things applications that employs a hybrid cryptosystem to offer effective data integrity, secure communication, and authentication with less computational, storage, and communication overhead than current approaches 15 . John Kuszmaul (2019) claims that Verkle Trees are a bandwidth-efficient alternative to Merkle Trees. They may be used in consensus protocols, public-key directories, cryptocurrency, and secure file systems. They use Vector Commitments to balance computing power and bandwidth and verkle tree helps to reduce the computational power required and compared to the Merkle tree, verkle tree is approximately 13 times faster. For Verle tree proof size is 10 times lesser compared to the Merkle tree data structure 16 . This study suggests a new post-quantum digital signature method based on k-ary Verkle trees and lattice-based vector commitments. In addition to offering strong protection against both traditional and quantum threats, it increases efficiency and scalability 17 . The study presents a novel post-quantum digital signature system that provides improved security and efficiency against quantum attacks by utilizing Verkle trees and vector commitments based on the SIS lattice problem 18 . The study presents a novel called Verkle tree-based digital signature system. It offers a post-quantum cryptography solution that is resistant to quantum attacks and may be used in place of weak RSA systems by combining vector commitments with hash- based one-way functions 19 . This research proposes VADIA, a Verkle tree-based technique to handle data integrity assaults in opportunistic mobile social networks (OMSN). Comparing it to Merkle tree-based methods, it demonstrates significant improvements in malicious node detection, lower false negative rates, and lower packet dropping/modification/faking rates 20 . The Verkle accumulator-based stateless transaction validation (VA-STV) approach is suggested in this study to reduce the storage load in blockchain-based IoT networks. It provides flexibility by modifying the branching factor and gives advantages in terms of witness size and commitment generation time 21 . The study presents and officially specifies polynomial commitment schemes with constant-size commitments and uses them to lower communication costs in cryptographic protocols like content extraction signatures, zero-knowledge sets, credentials, and verifiable secret sharing 22 . A blockchain based key management basis for IoT-enabled smart grids, enhancing security and efficiency by minimalizing computational difficulty, ensuring conditional anonymity, and attaining seamless forward secrecy. Nevertheless, despite its decentralized and tamper-resistant design, the system remains vulnerable to the quantum attacks due to reliance on elliptic curve cryptography (ECC) 23 . The two blockchain based protocols for anonymous cross-domain communication in the IoD (Internet of Drones), addressing security and trust problems among untrusted regions while ensuring well-organized communication and computation. However, limitations include connectivity challenges between Drones and ground stations also need for multi-hop communication beyond range 24 . A secure and efficient blockchain based authentication framework for multidomain IIoT systems using a hybrid on-chain and off-chain design. It reduces overhead, supports key revocation, and resists DDoS attacks. However, issues remain with unlink ability, confidentiality, scalability, and high on-chain storage and replication overheads 25 . According to the existing works like RSA and ECC, there are a lot of Drawbacks likes slower run time, higher key size and security issues that occur during D2D communication, so we are considering a strong key exchange algorithm over RSA and ECC for the secure data exchange between two IoT devices. For the strong key exchange algorithm, this work focuses on the D2D based Elliptic Curve Diffie-Hellman (D2D-ECDH) key exchange protocol along with blockchain smart contracts and blockchain verkle tree data structure for secure data exchange with the AES encryption standard.The proposed protocol helps to avoid Man-In-The-Middle (MITM), replay attacks, repeat attacks, Sybil attacks, DoS attacks and other types of cyber-attacks also provide less key size, faster runtime. Contribution of the paper Device-to-device (D2D) communication along with Elliptic curve Diffie-Hellman (ECDH) key exchange protocol to secure the exchange of the public keys to protect the data also provides lesser key size and faster runtime. AES encryption and decryption algorithms help to secure the communication data between the devices from the attackers using a shared secret key. A smart contract helps to create a contract between the devices to secure the exchanging data and prevent the data from unauthorized access. Blockchain network to provide a decentralized network to secure the data, private, resilient and efficient communication paradigm in IoT devices and emerging 5G applications. Blockchain Verkle tree data structure to reduce the proof size up to 33 times compared to the traditional Merkle tree data structure. Preliminaries Blockchain A blockchain network is a decentralized network; it’s an unchangeable database. A blockchain network allows for the storage and exchange of almost anything of value, which lowers risk and boosts efficiency for those involved. In every business, information is the backbone. The more accurate and quickly it’s accepted, the better blockchain is the ideal technology for delivering such information since it provides instantaneous, sharable and completely transparent data stored on an immutable ledger that is only accessible by authorized network members 2 , 26 . The characteristics of blockchain technology include decentralized, transparent, secure and dependable. Its features make it the most alluring blockchain, and it’s the focus of all self- level arguments. Applications include file storage, health care, banking, insurance and the fields, among others 3 . Smart contract A smart contract, known as a self-executed contract, has the terms of agreement between the buyer and seller. Agreement is incorporated using program code such as C++, Python, JavaScript and Solidity. Solidity coding is one of the advanced-level languages used to implement the Ethereum blockchain smart contract. Agreements and program codes are distributed over the decentralized blockchain network. Smart contracts remove the requirement for a centralized authority and legal framework in order to facilitate reliable transactions and agreements amongst distant, anonymous users 2 . The advantages of smart contracts are speed, efficiency and accuracy, trust and transparency, security and cost savings 4 . Figure 2 shows, only authenticated devices only communicate with each other through a smart contract to create a transaction. Which is verified and permanently stored in a blockchain network. Figure 3 illustrate the secure data communication flow between the devices and device registration and public key through the smart contract, exchange encrypted data using public key cryptography. Verify authenticity and decryption data only after the successful validation. Fig. 2. Open in a new tab Smart contract execution in a blockchain network. Fig. 3. Open in a new tab Algorithm flow chart for a smart contract between the devices. The contract begins with the deployment of the D2D Security Communication Contract on the blockchain, which serves as the groundwork for secure communication. Devices produce cryptographic key pairs and register their public keys with the smart contract, assuring that each device has a verifiable identification. To start a contract, a device sends an authentication request to the targeting device, whose identification is verified by on-chain registration. If validated, a secure session token (shared secret) is produced. During communication, the beginning device encrypts data with the session key and adds a cryptographic signature before transmission. The destination device decrypts the package with the shared key, checks its integrity by comparing the original and decrypted hashes, and confirms the sender’s signature. Once the data exchange is complete, the occurrence is recorded on the blockchain, and the session is ended by revoking the session token, guaranteeing there are no remaining security issues. This hierarchical solution ensures authenticity, integrity, and confidentiality throughout decentralized device communication. Elliptic curve cryptography (ECC) ECC is one of the encryption methods of the Elliptic Curve (EC). It is constructed based on the complex arithmetic of elliptic curves over an infinite field. The elliptic curve facilitates the encryption and decryption of the key. Initially, it was employed to produce cryptographic keys that were more efficient, quicker, and smaller. The SECP256K1 curve, a widely used algorithm in Bitcoin cryptography, provides the basis for Eq. 2 . An elliptic curve structure may be produced by choosing values for a and b. SECP256K1, a common elliptic curve, creates an elliptic curve by maintaining the specified parameters for a = 0 and b = 7 ( Y 2 = x 3 + 7). After the curve has been created, choose two points and link them In the elliptic curve, P is the large prime number to be used. 1 2 3 4 5 According to the substitute of x and y values (0 to 10) in mod 11.We get the same combination using the SECP256K1 curve (2,2), (2,9), (3,1), (3,10), (4,4), (4,7), (6,5), (6,6), (7,3), (7,8), (5,0) (self-connected). Using the points, the points create a curve structure like shown in Fig. 4 . Elliptic curves, in contrast to functions, lack a single mathematical formula for G. Rather, G is a specific location on the curve (x, y) that is chosen based on the curve’s characteristics and equation. The public key generation procedure is depicted in Fig. 4 2 , where two points P (large prime number) and G (Generative point) on the curve SECP256K1 are selected. To obtain the points (-P and P) continually up to n times (K times P), where n is a private key and K.P is a public key, draw a straight-line connecting P and G 2 . Choose point P in the curve SECP256K1. The curve will yield the third point 2P; similarly, next time we get 3P. Scalar or point multiplication and sum, which is achieved by multiplying k by P, includes the elliptic curve; here, k times is a private key. For the verification of the secret point using of Eqs. 3 , 4 and 5 to find λ: for P = (x 1 ,y 1 ) and Q = (x 2 ,y 2 ) P = (2,2) and Q = (6,5) for P =11 we get λ = 9, and . Fig. 4. Open in a new tab Proposed D2D -ECDH key exchange protocol using ECC and Shared secret key generation. 6 Using the above equation to substitute the and in the equ 6 for verify whether both points are same, the selecting any 2 points from the successful combinations using SECP256K1, we choose two point (2,2) and (6,5). its successfully verified the point in ECC we get both the values are same (9 = 9). Applications of ECC are key exchange, digital signature, modern secure message, end to end encryptions (Message, WhatsApp), IoT device authentication, secure file transfer protocol, Cryptocurrency Systems in Blockchain, BLE (Bluetooth Low Energy) and blockchain bitcoin public keys. In a D2D communication setup using the ECDH key exchange, the process starts with device discovery, where nearby devices identify each other through direct communication technologies such as Wi-Fi Direct, Bluetooth, or 5G side link. After discovery, a secure D2D connection is established to allow direct interaction between the devices. Each device then generates its own pair of elliptic curve keys, consisting of a private and a public key. These public keys are swapped over the established D2D link, allowing both devices to compute a common secret key using their private key and the other device’s public key. The shared secret is processed through a Key Derivation Function (KDF) to create a symmetric session key for encryption. Finally, after secure communication, temporary keys are deleted to maintain confidentiality and forward secrecy. Verkle tree Verkle trees are a subset of Merkle trees that use polynomial commitments to greatly improve security and speed. Unlike normal Merkle trees, which use hash functions to generate node values, Verkle trees use polynomial commitments, which offer higher cryptographic guarantees and enable more productive proofs. Reduced overhead, scalability, privacy and security, and efficient data storage and retrieval are just a few benefits of verkle trees for D2D communication. These benefits make Verkle trees a viable option for enabling secure and efficient D2D communication networks. Verkle trees, which use vector commitments to lower proof sizes and increase verification efficiency, are a new development. Verkle trees do not require redundant intermediary nodes as Merkle trees do, which makes They are better suited for applications that need rapid updates and succinct proofs. Additionally, by lowering tree height and further minimizing proof sizes, the advent of k-ary Verkle trees—where each node has ‘k’ children—offers further advantages, making them perfect for high-performance applications like digital signatures and blockchain systems. Verkle trees offer several advantages over Merkle trees: In blockchain data structures, Verkle trees are superior to Merkle trees in several ways. Enhanced Efficiency, Improved Scalability, Reduced Computational Costs and Improved Privacy 16 – 18 . Figure 5 shows our proposed block diagram of a secure D2D communication through a shared secret key using ECDH key exchange protocol using blockchain based smart contract. Fig. 5. Open in a new tab Proposed block diagram for D2D-ECDH key exchange using a smart contract. Merkle vs. verkle tree proof size As per the 18 – 20 , 28 Merkle tree the proofs for transaction Tx 3 are [Hash ( Tx 1 )+Hash ( Tx 2 )+ Hash ( Tx 4,5,6 ) +Hash ( Tx 7,8,9 )]. 7 Verkle tree proof: Verkle tree are [MP -3 + (C1, MP -10 ) + C4]. (MP - Membership Proof) 8 However, this would greatly decrease the computational power required for the Verkle Tree to only 84 milliseconds per leaf, which is approximately 13 times faster compared to the Merkle tree. The Merkle tree data structure has greater versatility. Figure 6 : The traditional Merkle tree needs more hash values to compute the root hash value. On the other hand, Fig. 7 shows that the verkle tree destroys the need for superfluous intermediary nodes 17 . Fig. 6. Open in a new tab Merkle tree-proof size. Fig. 7. Open in a new tab Verkle tree-proof size. Time complexities and comparison Table 1 shows the comparison of both Merkle tree and verkle tree data structures in terms of uploading the file and proof size. It also mentions the k-ary merle and verkle tree data structure. ‘ O . notation looks at how a function, such as the time it takes for a computer program to run, or the amount of memory needed, changes as its input gets bigger. In short, it’s a way to group algorithms based on how much more space or time they need to process the more data they manage 16 – 18 . Table 1. Time complexities and comparison. Scheme/operation Construct Update file Proof size Merkle tree Ο (n) Ο (log 2 n) Ο (log 2 n) k -ary Merkle tree Ο (n) Ο ( k log k n) Ο ( k log k n) (VC) Vector commitment Ο (n 2 ) Ο (n) Ο (1) k -ary Verkle tree Ο ( k n) Ο ( k log k n) Ο (log k n) Open in a new tab Verkle tree height calculation 9 10 11 where c can be any convenient base, like 10 (common logarithm, often denoted as log) 12 Verkle tree in blockchain network In Fig. 8 shows the structure of blockchain technology using verkle tree data structure, in evert transaction it includes the membership proof for every node. In blockchain, the block contains nonce value, timestamp, previous block hash value and current node hash value that is the root commitment (C4) values. Fig. 8. Open in a new tab Blockchain-based Verkle tree structure. Results and discussion The proposed system for smart contract execution is established in Remix IDE Ethereum network using Solidity coding, shown in Fig. 9 . An effective, open-source, web-based tool made especially for creating, testing, and implementing smart contracts—mostly for the Ethereum blockchain is Remix IDE (Integrated Development Environment). The solidity code is established through the Ganache network V2.7.1 environment. A particular version of the Ganache UI (Graphical User Interface) program, a personal Ethereum blockchain emulator, is referred to as Ganache v2.7.1. Developers may use this well-liked tool to create, test, and launch Decentralized apps (Dapps) locally without having to communicate with an actual public blockchain. Fig. 9. Open in a new tab Smart contract deployed successfully in Remix IDE Ethereum network. Figure 10 illustrates the Ganache application’s smart contract formation process, which includes both contract creation and contract call, as shown in the code run in Solidity. Based on the solidity code, both devices consent to a mutually beneficial contract for data exchange at gas values of 3,000,000. It is an auto-mining process for the Ethereum blockchain network. each transaction is stored in the Verkle tree leaf nodes as per Fig. 7 . Fig. 10. Open in a new tab Smart contract creation in Ganache V2.7.1. The simulation output for D2D-ECDH employing Verkle tree execution is shown in Fig. 11 . We chose 3-ary for the Verkle tree data structure based on the simulation of ECDH key exchange in the Python VS code generator on the blockchain network. The output displays the shared secret key of the two devices in addition to the public and private keys of each device. Additionally, it displays how the AES method is used to encrypt and decode data that is sent between devices 26 . In simulation, we got 37.93ms for executing ECDH key exchange using AES encryption protocol in Merkle tree data structure in 2-ary. for the same protocol executed in the V-tree structure, it takes 13.48ms. Compared M-tree data structure V-tree is up to 33 times smaller. Fig. 11. Open in a new tab Python execution for D2D-ECDH key exchange for AES, along with device verification and verkle tree root hash. 13 14 The proof sizes of the Verkle and Merkle tree data structures are shown in the equations above. We are utilizing the SHA256 algorithm for the hash size, which is 32 bytes. The elements that aid in calculating the Merkle tree proof size are (k-1) sibling hashes to recompute the parent hash and (log k (n)) to signify the tree’s height. Equation 14 represents the verkle tree proof size calculation, which needs the height (H) of the tree (log k (n) ), opening size of the proof and commitment size. For proof node size, we use KZG (Kate-Zaverucha-Goldberg) based polynomial commitment 22 at the size of approximately 32 bytes to 48 bytes. for both opening proof size and commitment size, we chose a maximum of 48 bytes for the calculations. According to the Table 2 , height calculation, which is (log k (n)), each tree data structure has a branching factor (K) and number of leaves occupied (N) to generate a table. The tree’s height decreases as the branching factor increases. Table 2. Tree height (H) calculation for different K and N values. N 100 200 300 400 500 10 9 K 3 4.19 4.82 5.19 5.45 5.65 18.86 10 2 2.3 2.4 2.6 2.7 9 20 1.53 1.76 1.96 2 2.07 6.91 30 1.35 1.55 1.67 1.76 1.82 6.09 50 1.17 1.35 1.45 1.53 1.58 5.29 100 1 1.15 1.23 1.30 1.34 4.5 Open in a new tab Table 3 shows that the branching factor (K) is 3 to 100 and the leaf nodes are 100 to 10 9 (1 billion) according to the Merkle tree (M-tree) proof size estimate using Eq. 13. For k = 3 and N = 100, the minimal proof size was 268.26 bytes. Table 3. M-tree k-ary data structure (in bytes). K-ary / leaf node( N ) N = 100 N = 200 N = 300 N = 400 N = 500 N = 10 9 K = 3 268.16 308.48 332.16 348.8 361.6 1207.04 K = 10 576 662.4 691.2 748.8 777.6 2592 K = 20 930.24 1070.08 1191.68 1216 1258.56 4201.28 K = 30 1252.8 1438.4 1818.88 1633.28 1688.96 5651.52 K = 50 1834.56 2116.8 2273.6 2399.04 2477.44 8294.72 K = 100 3168 3643.2 3896.64 4118.4 4245.12 14,256 Open in a new tab Similarly, we found that, when received in k = 100 and N = 1 billion (10 9 ), the highest proof size was 14,256 bytes. Table 4 displays the proof size for the Verkle tree (V-tree). The computation was extracted using Eq. 14 to generate the proof size table. The leaf nodes and breaching factor are the same as in the Merkle tree data structure. Calculation Table 4 makes it evident that the proof size has improved in comparison to the Merkle tree proof size. In a Verkle tree, increasing the branching factor k results in a decrease in both the proof size and the overall height of the tree. Based on the Table 3 , we plot a graphical representation based on a proof size between the Merkle and verkle tree data structure its shows in a Fig. 12 . Table 4. V-tree k-ary data structure (in bytes). K-ary / leaf node( N ) N = 100 N = 200 N = 300 N = 400 N = 500 N = 10 9 K = 3 402.24 462.72 498.24 523.2 542.4 1810.56 K = 10 192 220.8 230.4 249.6 259.2 864 K = 20 146.88 168.96 188.16 192 198.72 663.36 K = 30 129.6 148.8 160.32 168.96 174.72 584.64 K = 50 112.32 129.6 139.2 146.88 151.68 507.84 K = 100 96 110.4 118.08 124.8 128.64 432 Open in a new tab Fig. 12. Open in a new tab Proof size comparison between Merkle and Verkle trees. The Verkle tree-proof size is up to 33 times less than the Merkle tree-proof size. In the simulation of root value validation, we select a maximum of K = 100 and N = 10 9 . We achieved 0.106 ms for the Verkle tree root commitment and 0.218 ms for the traditional Merkle tree root hash value, approximately double the time of Verkle tree root commitment validation. The above Table 5 shows the comparison of cryptographic schemes, RSA, ECC and ECDH key exchange protocols provide equal 128-bit security but difference significant in resource using and performance. The RSA relies on large key size of 3072 bits, resulting in higher key exchange time, computational cost and energy consumption. In ECC and our proposed ECDH key exchange protocol achieve same level of security with the compact private key of 256 bits and 512 bits of public keys reducing the communication overhead. ECDH key exchange using SECP256K1 elliptic curve is the most efficient and offering faster key exchange compare to the other curves. ECDHKE provide lower computational time of 4.7ms and minimal energy used. The simulation was executed on an ARM cortex-A53 IoT class device using python coding. For the secure data exchange between the devices used AES-256 for data encryption and decryption. Table 5. Basic comparisons table. Parameter RSA ECC ECDH (SECP256K1) Security equivalence 128-bit 128-bit 128-bit Private key size (bits) 3072 256 256 Public key size (bits) 3072 512 512 Shared secret size (bits) 256 - 256 AES session key size (bits) 256 128 / 256 256 Key exchange time (sec) 0.215432 0.003121 0.004087 Total computation setup time (ms) 28.3 7.7 4.7 Total protocol energy (mJ) 43.8 15.5 11.1 Open in a new tab In Table 6 , For blockchain based secure D2D communication, ECDH provide better than traditional RSA, DH and general ECC key exchange protocol because to its lower communication and computational overhead, higher scalability, low gas cost and high security with Perfect Forward Security. Table 6. Performance metrics comparison. Metric RSA Diffie–Hellman (DH) ECC ECDH (our proposed) Computational overhead High High Medium Low Communication latency High Medium–high Medium Low Key generation time Slow Slow Medium Fast Gas cost (using blockchain) Very high High Medium Low Scalability Poor Limited Good Excellent Security strength Strong but no perfect forward secrecy (PFS) Strong with proper setup Strong Strong with PFS Key Size for ~ 128-bit security 3072 bits 3072 bits 256 bits 256 bits Suitability for D2D communication Low Medium High Very high Open in a new tab Figure 13 shows the comparison of RSA, ECC and ECDH key exchange using SECP256K1 curve protocols, In terms of key size, execution time and energy consumption. RSA used very large keys and highest computational time and energy consumption time. in ECC and ECDH achieve same security with smaller key size, ECDH gives the lowest key exchange time, reduce computational overload and minimum energy consumption makes its suitable for efficient and secure communication system. Fig. 13. Open in a new tab Graph comparison for RSA, ECC and ECDH. In Table 7 shows the consolidate treat mitigation table using Dolev–Yao (DY) threat model, several attacks are considered and mitigated in our proposed D2D-ECDHKE protocol using blockchain network. MITM (man in the middle) assaults using by key substitution are prevented through blockchain verified public keys. The replay attacks caused through reused message are mitigated nonce values along with the timestamps using in blockchain. The cipher text tampering is detected through AES authentication. The eavesdropping is countered by ECDH key exchange protocol combined with the AES encryption impersonation attacks are prevented via on chain public key binding. Ledger root forgery is mitigated through verkle tree root commitment validation while side channel timing attacks are reduced using constant time Elliptic Curve Cryptographic (ECC) implementation. Table 7. Consolidated threat–mitigation table using Dolev–Yao (DY) threat model. Threat Dolev–Yao (DY) attack Mitigation MITM Key substitution Blockchain-verified public keys Replay Reuse old messages Nonce + timestamp Tampering Modify ciphertext AES-GCM authentication Eavesdropping Observe traffic ECDH + AES Impersonation Fake identity On-chain key binding Root forgery Modify ledger data Verkle root validation Side-channel Timing leakage Constant-time ECC Open in a new tab In above Table 8 The Threat model for D2D communication, assaults exploit the open wireless medium. ECDH protects communication through securely establishing a shared secret key ( ) over an insecure medium, when integrate with blockchain smart contract authentication mechanisms. ECDH protect from eavesdropping, impersonation, replay attacks, key compromise impersonation (KCL), repudiation assaults and Man in the Middle (MiTM) assaults while providing forward security. The passive eavesdropping occurs when an attacker listens the exchange data or message to infer sensitive data. Our proposed protocol mitigates this by using ephemeral elliptic curve (EC) keys, ensuring that captured data don’t reveal session keys. For MiTM assaults where a challenger or attacker intercepts and improved communications or the impersonates genuine devices are prevented through immutable on chain registration of device IDs and public keys which permits authenticated key exchange without trusted intermediaries. Table 8. Security comparison table. Aspect / protocol RSA 29 ECC 2 , 13 CAKE-PUF (PUF-based key exchange) 11 Our protocol (D2D-ECDH with blockchain) Passive eavesdropping No Yes Yes Yes Man-in-the-middle No No Yes Yes Replay attack No No Yes Yes Key compromise impersonation (KCI) No No Yes Yes Forward secrecy No No Yes Yes Side cchannel attacks No No No Yes Physical attack resistance No No Yes Yes Device authentication No No Yes Yes Open in a new tab The replay attacks produced through resending of previously valid messages or data are addressed through smart contract that enforce freshness using nonce value, timestamps and protocol state validation. In KCL process where an attacker compromises a devices private key to impersonate others, the protocol limits impersonation through relying on unchallengeable public key binding and on-chain verification. The repudiation attacks are mitigated through tamper proof blockchain records that provide verifies proof of participation to ensuring accountability and auditability in a D2D communication. The ECDH key exchange uses ephemeral keys to deliver perfect forward security and readily raises to large installations. The PUF based key exchange is more difficult to regulate attest and maintain over the time it depends on a physical characteristic unique to each device and necessitates enrolments and mistake correction. Conclusion and future work Our research begins with the Elliptic Curve Diffie-Hellman (ECDH) key exchange based on secure data exchange between the device-to-device (D2D) communication using the AES algorithm. The blockchain smart contract that were successfully executed on the Ethereum network allowed for the secure data exchange between the devices. A smart contract was deployed using Solidity coding in the Remix IDE Ethereum network. A smart contract was executed by Ganache Provider, and a D2D-ECDH key exchange was executed in VS Code generator using Python coding. Additionally, we used a Verkle tree data structure for adding transactions into the blockchain network. Previous transactions were stored in a traditional Merkle tree data structure, which requires more proof size for root node verifications. The verkle tree provides a smaller proof size to verify the root commitment up to 33 times compared to the traditional Merkle tree data structure. Also, verkle tree data structure provides a smaller tree height compared to the traditional Merkle tree data structure. The Merkle tree takes nearly twice as long as the Verkle tree for root commitment validation under the same conditions. In our future work, we plan to improve the robust hybrid key exchange protocol through the incorporation of optimized post quantum attacks and classic key encapsulation protocol. Rigorous performance evolution and real-world implementation testing. This will additional strengthen secure communication between the D2D communication and ensure robustness against both current and future generation cryptographic attacks. Supplementary Information Below is the link to the electronic supplementary material. Supplementary Material 1 (562KB, pdf) Author contributions Simbu A: Writing the original draft, figures, software, methodology, investigation, validation, formal analysis, and conceptualization. Nandakumar S* and Saravanan K: Writing—review and editing the manuscripts, validation, visualization, supervision, investigation, conceptualization. Funding Open access funding provided by Vellore Institute of Technology. Data availability The data supporting the results and findings of this work/study can be provided by corresponding author upon responsible request. Declarations Competing interests The authors declare no competing interests. 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