A Research Report on Threshold Digital Signature Schemes in Cross-Chain Communications
Now public blockchains and alliance blockchains with different technology routes and product highlights are emerging one after another, and the development can be described as a blowout. Blockchains have different characteristics and advantages, and all strive to solve the industry’s pain points in this information age. However, the current blockchains are all in a state of self-isolation, and the boundaries are insurmountable. If you choose to embrace blockchain technology, you can only choose between multiple blockchains.
Facing this bottleneck in blockchain development, and driven by the upsurge of DeFi, many blockchain cross-chain projects have sprung up, trying to build a blockchain system that facilitates the exchange of crypto assets between blockchains. There are various proposals, such as side chain, relay chain, hash lock, threshold digital signature. Among them, according to the adaptability of cross-chain, the solution based on threshold digital signature is particularly eye-catching. At the same time, there is no lack of academic experts in the cryptographic field who are enjoying working on it. This report analyzed several representative threshold digital signature projects and the most updated research of Cryptography with the hope of summarizing the parts to be improved and trying to arrive at a break-through solution.
We believe that in the near future, crypto assets exchange across chains will usher in a new era for DeFi, by connecting community and ecosystem on different blockchains and providing better liquidity for digital assets.
When we talk about a cross-chain solution, there are different approaches we can consider. For example,
For the cross-chain use of assets, proposed solutions typically require that accounts are locked. For example,
In considering 3 possible cross-chain solutions HPB has given special consideration to the following:
- Algorithm Efficiency
- Flexibility of Threshold
- Cross-Chain Adaptation Rate
- Node Computing Performance
- Implementation Difficulty
Wanchain
The proposal of Wanchain is aimed at the vision of the Wanchain interconnection, the relationship between the Internet and the local area network, hoping to create a public chain, private chain and the network chain linked to each other blockchain system. Wanchain and Fusion were the two first project proposals that were based on threshold digital signatures to cross chains and they opened up new categories of cross-chain technology.
1.1 Technology Overview
Locked Account Generation Algorithm
Threshold Digital Signature Algorithm
Notes: For details, please refer to the Wanchain Yellow Paper listed in the References herein.
Locked Account Key Share Updating Algorithm
1.2 Summary
- The calculation speed of threshold digital signature is fast, which greatly improves the cross-chain efficiency.
- The relationship between the threshold t and the number of users n needs to satisfy t<n/2. If the number of thresholds is limited, it may limit its actual application.
- Digital assets supported: blockchains that support ECDSA signature are all covered.
- Nodes that participate in the generation of locked accounts need to pledge assets but are not required to be high-performance computing nodes.
ECDSA Explained: Bitcoin is an example of a blockchain that relies on ECDSA for security. Every Bitcoin address is a cryptographic hash of an ECDSA public key. The ownership of the account is determined by who controls the ECDSA private key. To transfer an amount of Bitcoin to another person, you create a message saying “I give this Bitcoin to address X”, sign it with your private key and submit it to the Bitcoin system. Your ECDSA private key is therefore vital to keeping your Bitcoin secure so only you can transfer it.
Fusion
The Fusion project proposes building a blockchain financial system that is benchmarked against traditional finance. This concept coincides with the DeFi application, but it is nearly a year earlier than the latter. Fusion is also built on the threshold digital signatures, but its advantage over Wanchain is that its threshold scheme is more flexible. The core to achieve this goal is the Paillier threshold key, which makes the relationship between the threshold and the number of users unlimited, and thus more flexible.
2.1 Technology Overview
Paillier Threshold Key Generation Algorithm
Due to its complex process, please refer to 【Threshold Paillier】paper listed in the references herein.
Locked Account Generation Algorithm
Locked Account Signature Algorithm
2.2 Summary
- The calculation speed of threshold digital signature is fast, which greatly improves the cross-chain efficiency.
- There is no special restriction on the relationship between the threshold t and the number of users n. It only needs to satisfy t<n, which is an unlimited multi-party threshold signature.
- Digital assets supported: blockchains that support ECDSA signature are all covered.
- Nodes participating in the generation of locked accounts need to pledge assets and may require high-performance computing nodes for Paillier threshold key generation.
- Nodes that participate in the generation of locked accounts need to pledge assets, and Paillier threshold key generation may require the nodes to be high-performance computing nodes.
GE Threshold Signature Solution
3.1 Technology Overview
Locked Account Generation Algorithm
The sharing of private keys is the same as above.
Locked Account Signature Algorithm
3.2 Summary
- When the paper [GE Paper] was first proposed, it was designed to enhance the distributed ECDSA algorithm, but not to solve the blockchain cross-chain issue. Later, it got widely discussed when its potential as a blockchain cross-chain solution came to everyone’s attention.
- Although this solution is different from the Wanchain architecture, the threshold limit is the same, that is, the relationship between the threshold t and the number of users n must satisfy t<n/2.
Conclusion
We have studied and analyzed the above technical routes of threshold digital signature schemes in different cross-chain solutions. We believe there is still great space to improve on our research. If there are any comments or suggestions, please feel free to let us know. Through the analysis of the above solutions, we evaluate the above cross-chain solutions from different criterias, and the scores (full scores of 5 points) on each criteria are shown in the following table.
References
【Wanchain Yellow Paper】
https://github.com/wanchain/crypto/blob/master/Wanchain%20yellow%20paper%20English%20version.pdf
【Fusion Yellow Paper】
https://docs.wixstatic.com/ugd/76b9ac_4b32719f01374efdbef5f24fe08403e8.pdf
【Threshold Paillier】
Efficient RSA Key Generation and Threshold Paillier in the Two-Party Setting
【GE Paper】
Strength in Numbers Threshold ECDSA to Protect Keys in the Cloud
About HPB
High Performance Blockchain (HPB) is a revolutionary permissionless blockchain architecture that combines HPB’s customized hardware Blockchain Offload Engine (BOE), with high-performance blockchain software, enabling unrivaled scalability.
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