A Quantum Signature Validation Algorithm for Efficient Detection of Tampered Transactions in Blockchain

TL;DR

QSVA addresses the need for fast tampering detection in blockchain by leveraging a PageRank-guided quantum walk on the Bitcoin transaction graph to rank and identify fraudulent transactions. The approach compares Quantum SearchRank and Randomized SearchRank, finding that Randomized aligns better with Classical PageRank and maintains high success probabilities, yielding a practical $O(\sqrt{N})$ runtime. Simulations on the Elliptic Bitcoin dataset with the SQUWALS simulator demonstrate the method’s potential to identify tampered transactions more rapidly than classical search methods. These results suggest quantum-enabled transaction-security tools could be integrated into future distributed ledger technologies as quantum hardware matures.

Abstract

The Quantum Signature Validation Algorithm (QSVA) is introduced as a novel quantum-based approach designed to enhance the detection of tampered transactions in blockchain systems. Leveraging the powerful capabilities of quantum computing, especially within the framework of transaction-based blockchains, the QSVA aims to surpass classical methods in both speed and efficiency. By utilizing a quantum walk approach integrated with PageRank-based search algorithms, QSVA provides a robust mechanism for identifying fraudulent transactions. Our adaptation of the transaction graph representation efficiently verifies transactions by maintaining a current set of unspent transaction outputs (UTXOs) characteristic of models like Bitcoin. The QSVA not only amplifies detection efficacy through a quadratic speedup but also incorporates two competing quantum search algorithms$-$Quantum SearchRank and Randomized SearchRank$-$to explore their effectiveness as foundational components. Our results indicate that Randomized SearchRank, in particular, outperforms its counterpart in aligning with transaction rankings based on the Classical PageRank algorithm, ensuring more consistent detection probabilities. These findings highlight the potential for quantum algorithms to revolutionize blockchain security by improving detection times to $O(\sqrt{N})$. Progress in Distributed Ledger Technologies (DLTs) could facilitate future integration of quantum solutions into more general distributed systems. As quantum technology continues to evolve, the QSVA stands as a promising strategy offering significant advancements in blockchain efficiency and security.

Figures (9)

• Figure 1: Digital Signature Processes: In the signature generation process, a hash function is applied to a message or data to obtain a message digest or hashed message. Then, a signature generation algorithm uses the hashed message and the signatory's secret key as inputs to create a digital signature. For signature verification, the hashed message and the digital signature generated during the signing process are used, along with the signatory's public key, in a signature verification algorithm to produce a boolean value indicating whether the message has been altered (invalid) or not (valid).
• Figure 2: Schematic representation of the blockchain structure. Each block consists of a collection of digitally signed transactions, according to the protocol described in Section \ref{['subsec:cryptography']}, as well as the hash derived from the solved Proof-of-Work (PoW) required to add the block to the blockchain and the hash of the PoW from the preceding block.
• Figure 3: Schematic representation of the blockchain protocol. The starting point is highlighted in green. The diagram illustrates the sequential steps involved in the protocol, including transaction validation, block formation, Proof-of-Work mechanism, and block propagation across the network. Each step ensures the integrity, security, and decentralization of the distributed ledger system.
• Figure 4: a) Schematic representation of Bitcoin's UTXO-based ledger. Outputs specify the amounts of BTC sent to specific addresses, while inputs reference the outputs of previous transactions. If an input is empty, it indicates the creation of new BTC, such as through the mining process of a block. b) Example of an address graph and its associated transaction graph. The transaction graph can be constructed from the UTXO-based ledger following the process described in Section \ref{['subsec:graph_representation']}.
• Figure 5: Transaction graph of the filtered dataset. Fraudulent transactions are represented in red, while licit transactions are shown in blue. The nodes in the graph are arranged in concentric circles based on their in-degree. Nodes with an in-degree of 0 are positioned in the outermost circle; nodes in the second and third circles have in-degrees of 1 and between 2 and 9, respectively; and the innermost circle consists of nodes with an in-degree of 10 or higher. The size of each node is proportional to its Classical PageRank value, scaled logarithmically. Edges are color-coded based on the type of transactions they connect: blue edges represent connections from a fraudulent transaction (origin) to a licit transaction (destination); orange edges represent connections from a licit transaction (origin) to a fraudulent transaction (destination); and red edges indicate connections where both the origin and destination are fraudulent transactions. Finally, the top five fraudulent transactions listed in Table \ref{['tab:Fraudulent_table_t37']} are labeled in the graph.