Multiparty ECDSA Signing via Distributed Key Segmentation
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Solution Overview
Problem
Existing protocols for threshold signing, particularly with DSA/ECDSA, face challenges in constructing efficient protocols due to difficulties in calculating elliptic curve points without knowing the parameter k used to calculate these points with the generator G of the elliptic curve, which is crucial for secure key protection in multiparty digital signing.
Innovation Solution
A method and system for multiparty digital signing using Elliptic Curve Digital Signature Algorithm (ECDSA) that involves two parties, P1 and P2, who share random values and use an elliptic curve point Q and a group generator of order q to compute points, ensuring secure key protection by utilizing additively homomorphic encryption and zero-knowledge proofs to verify honesty and generate distributed signing keys.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If threshold cryptography is used to protect keys by sharing among multiple devices, then key protection is improved, but the complexity of constructing efficient signing protocols increases
Solution Approach 1:
The private key is segmented into multiple shares distributed among different devices. Each device holds a portion of the key material, and only when sufficient shares are collected can the full private key be reconstructed through threshold cryptography protocols, thereby protecting against single-point failures or compromises.
Solution Approach 2:
A trusted third party or threshold signature protocol acts as an intermediary to coordinate the key sharing and verification process. This intermediary manages the complexity of the threshold protocol, enabling multiple devices to work together securely without requiring direct complex interactions between each device.
2Reliability
If multiple distinct signing keys are used in Bitcoin-style multi-signature, then key protection is improved, but the difficulty of calculating elliptic curve points without knowing parameter k increases
Solution Approach 1:
The threshold cryptography protocol introduces an intermediary verification mechanism that allows devices to collaboratively compute elliptic curve points without requiring direct knowledge of the random parameter k. The protocol uses cryptographic commitments and zero-knowledge proofs as intermediaries to enable secure computation while maintaining the difficulty of reversing the process.
Solution Approach 2:
The protocol changes the approach from direct computation using k to using cryptographic commitments and proofs. By transforming the problem into a protocol-based solution with intermediate verification steps, the system maintains security while enabling the necessary computations.
3Adaptability or versatility
If random shares are shared between parties during signing, then multiparty signing capability is improved, but the risk of exposing random shares in non-encrypted format increases
Solution Approach 1:
Before the actual signing operation, the protocol establishes encrypted communication channels and sets up cryptographic commitments. Random shares are exchanged only after these protective measures are in place, ensuring that even if shares are transmitted over networks, they remain protected by encryption and cannot be exposed in plaintext form.
Data Source
AI summary
Described herein is a method and system for digital signing by utilizing Elliptic Curve Digital Signature Algorithm (ECDSA) with a group generator of an elliptic-curve group of order q, and an elliptic curve point Q. The method may be configured to receive a digital message and associated with a request from a third-party in order to sign the digital message. The system designed to sign such messages may comprise two parties denoted P1 and P2 configured to conduct a multiparty signing procedure by utilizing ECDSA. The digital signing procedure may follow preliminary steps configured to set the system with the necessary conditions for the multiparty signing procedure. Such preliminary steps may set the parties P1, and P2, in accordance with the configuration defined herein.