Digital Signature Subkey Derivation for Secure Threshold Signing
Solution Overview
Problem
Existing digital signature schemes using additive key derivation and presignatures introduce potential security weaknesses and inefficiencies, particularly in distributed settings involving threshold signatures.
Innovation Solution
A method for deriving public and secret subkeys from a master key pair using algebraic operations, combined with precomputed presignatures and re-randomization, to enhance security and efficiency in digital signature processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If additive key derivation is used to reduce storage costs, then storage requirements are reduced, but security weaknesses are introduced
Solution Approach 1:
The secret key is segmented into multiple shares using secret sharing schemes, where no single share reveals information about the original key. This allows distributed storage across multiple parties or locations without compromising security, as the key material is divided and protected through cryptographic thresholds.
Solution Approach 2:
A trusted intermediary or threshold mechanism is introduced to manage key derivation and reconstruction. The intermediary enables secure key sharing and recovery without requiring all parties to be simultaneously present, using cryptographic protocols that mediate between storage efficiency and security requirements.
2Productivity
If presignatures are precomputed to accelerate signing, then signing speed is improved, but security vulnerabilities are introduced
Solution Approach 1:
Presignatures are precomputed and stored in advance, but their security is enhanced through binding them to specific contexts or messages using cryptographic commitments. This allows the beneficial precomputation to occur while preventing misuse through additional verification steps that ensure the presignature is applied only to its intended purpose.
Solution Approach 2:
The security parameters of presignatures are dynamically adjusted based on the specific signing context. Different levels of verification strictness or additional cryptographic parameters are applied depending on the message importance or context, allowing fast signing for routine operations while maintaining high security for critical operations.
3Device complexity
If additive key derivation is used to derive multiple public keys from one master key, then key management is simplified, but security levels degrade
Solution Approach 1:
The key hierarchy is extended into additional dimensions beyond simple additive derivation. Multiple independent derivation paths or layers are introduced, where keys can be derived through different cryptographic transformations. This maintains the simplification of having a master key while preventing security degradation by ensuring that compromise in one derivation path does not affect others.
Data Source
AI summary
Embodiments of the invention relate to a computer-implemented method for performing a digital signature according to a public key signature scheme. The method comprises a step of computing a presignature. The method comprises further steps of providing a master secret key pair, the master secret key pair comprising a first master secret key and a second master secret key, and providing a master public key pair, the master public key pair comprising a first master public key and a second master public key. The method comprises further steps of deriving a secret subkey from the master secret key pair and deriving a public subkey from the master public key pair. The method further comprises performing the digital signature by means of the secret subkey and the computed presignature.