Efficient Lattice-Based Multi-Signature Scheme for Blockchain Transactions with Optimal Communication Round and Quantum Resistance

Core Concepts

The proposed 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme is the first lattice-based multi-signature scheme that simultaneously achieves quantum resistance, single-round communication, and aggregate public key features.

Abstract

The paper presents a new lattice-based multi-signature (MS) scheme called 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 that addresses several challenges in existing MS schemes:

Quantum Resistance: The scheme is designed based on the Module Learning with Error (MLWE) and Module Short Integer Solution (MSIS) lattice-hard problems, making it resistant to quantum attacks.

Optimal Communication Round: The 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme requires only a single round of communication among signers to generate the final multi-signature.

Aggregate Public Key: The scheme has an aggregated public key, which reduces the memory required for key storage and speeds up signature verification. Verifiers can verify the final signature without needing the individual public keys of the signers.

Provable Security: The authors prove that the 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme is secure under the hardness assumptions of MLWE and MSIS.

The paper first introduces the system architecture and threat model, then describes the detailed algorithms for the 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme, including the Setup, Key Generation, Multi-Sign Generation, and Multi-Sign Verification phases. The authors also provide concrete parameter settings and security proofs for the proposed scheme.

Stats

The size of Bitcoin's Blockchain was on the verge of reaching 500 gigabytes in 2023, and its database experiences an increase of approximately one gigabyte every few days.

Quotes

"Blockchain is a distributed and decentralized ledger that allows for secure and transparent transaction record-keeping among a network of computers."
"Storing M signatures individually necessitates additional time for verification and storage memory. Consequently, the reduction of memory usage for storage and the acceleration of verification time are significant considerations."

Key Insights Distilled From

Quantum resistant multi-signature scheme with optimal communication round: A Blockchain-based approach

by Hamidreza Ra... at arxiv.org 04-30-2024

https://arxiv.org/pdf/2404.17787.pdf

Deeper Inquiries

How can the proposed 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme be extended to support more complex multi-signature transactions, such as k-of-n transactions

To extend the 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme to support more complex multi-signature transactions like k-of-n transactions, we can modify the key generation and multi-sign generation phases. In the key generation phase, instead of generating keys for a fixed number of signers, we can allow for a variable number of signers. Each signer would generate their public/private key pair and contribute to the aggregate public key. The multi-sign generation phase would then involve a dynamic selection of k signers out of the total n signers to create the multi-signature. This would require additional logic to handle the selection process and ensure that the required number of signers participate in generating the multi-signature.

What are the potential trade-offs or limitations of the 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme compared to other lattice-based multi-signature schemes in terms of computational efficiency or signature size

The 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme offers several advantages compared to other lattice-based multi-signature schemes, but there are also potential trade-offs and limitations to consider. One trade-off is the computational efficiency of the scheme. While 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 requires only one round of communication among signers, some other schemes may offer faster verification times or lower computational costs. Additionally, the signature size of 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 may be larger compared to other schemes, depending on the specific parameters chosen for the scheme. This could impact storage requirements and overall efficiency in a blockchain network.

How can the 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme be integrated with existing blockchain protocols, such as Bitcoin, to enhance the security and efficiency of multi-signature transactions

Integrating the 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 scheme with existing blockchain protocols like Bitcoin can enhance the security and efficiency of multi-signature transactions. By incorporating 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 into the Bitcoin network, users can benefit from its resistance to quantum attacks, optimal communication round, and aggregate public key feature. This would improve the overall security of multi-signature transactions in Bitcoin, especially in scenarios where multiple parties need to authorize a transaction. Additionally, the efficiency of 𝑅𝑎𝑧ℎ𝑖−𝑚𝑠 in terms of communication rounds and signature size can help streamline the verification process and reduce the computational overhead associated with multi-signature transactions.