Threshold ECDSA Presigning for Multi-Key Batch Signatures
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Solution Overview
Problem
Existing threshold Elliptic Curve Digital Signature Algorithm (ECDSA) schemes do not consider multiple private keys held by signing devices and lack efficient protocols for secure batch generation of signatures in an honest-majority setting.
Innovation Solution
A signing and presigning protocol that allows batch generation of presignatures independent of multiple private keys, using a coordinating system to manage the process and ensure security, with signing devices computing and storing presignatures before interacting to generate final signatures.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing threshold ECDSA schemes are used with single key sharing, then security against malicious behavior is maintained, but computational overhead is high and batch processing is not supported
Solution Approach 1:
The patent implements a presigning phase where signing devices precompute and share presignature components (including shares of k^-1 and F(g^k)) before the actual signing operation. This preliminary computation enables batch processing and reduces computational overhead during the actual signing phase, directly addressing the contradiction between productivity and complexity by separating preparation work from execution work.
Solution Approach 2:
The patent divides the signature generation process into distinct phases: a presigning phase for precomputation and a signing phase for final signature generation. It also segments the computational tasks across multiple signing devices, where each device holds shares of multiple private keys and contributes to batch presignature generation. This segmentation enables parallel processing and reduces the computational burden on any single device.
2Adaptability or versatility
If signing devices hold shares of multiple private keys, then versatility is improved, but security management complexity increases
Solution Approach 1:
The patent enables each signing device to hold shares of multiple private keys and use the same presignature generation protocol for all keys. The presignatures are generated independently of specific keys, allowing a single set of presignature components to be reused across multiple private keys. This universal approach maintains security while improving versatility, as each device can participate in signing operations for any key it holds shares of.
Solution Approach 2:
By precomputing and sharing presignature components before the actual signing operation, the system prepares all necessary cryptographic materials in advance. This eliminates the need for complex key-specific precomputation during the signing phase, simplifying key management while enabling multi-key support. The presigning phase handles all key-specific computations upfront, allowing subsequent signing operations to proceed efficiently regardless of which key is being used.
3Productivity
If traditional ECDSA signing is performed for each message individually, then security is maintained, but computational overhead is high
Solution Approach 1:
The patent implements a presigning phase where signing devices precompute and share presignature components (including shares of k^-1 and F(g^k)) before the actual signing operation. This preliminary computation enables batch processing and reduces computational overhead during the actual signing phase, directly addressing the contradiction between productivity and complexity by separating preparation work from execution work.
Solution Approach 2:
The patent merges multiple individual signing operations into a single batch processing operation. Multiple presignatures are generated and processed simultaneously across different signing devices, and the final signatures are combined using the threshold protocol. This merging approach achieves significant computational savings compared to performing signing operations individually, reducing overall computational overhead by at least 10-20%.
Data Source
AI summary
Some embodiments are directed to a system and methods for presignature and signature generation, the system comprising a plurality of signing devices and a coordinating system. Each signing device stores a share of each of multiple private keys, and is configured to compute one or more presignatures, independent of the multiple private keys; locally store the one or more presignatures; upon receiving from the coordinating system a selection for a private key, generate a share of a signature for a message, using a presignature out of the one or more presignatures computed and stored in the presigning phase; and to send the generated share of the signature for the message to the coordinating system. The coordinating system is configured to send the selection for a private key to one or more of the signing devices, and combine the generated shares of the signature for the message into a signature.