Threshold Secret Sharing for Quantum-Resistant Hash-Based Signatures
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Solution Overview
Problem
Stateful hash-based signature schemes (HBSS) face challenges in ensuring that the private key is not duplicated and that message signing is limited to a predetermined number of times, while maintaining integrity and data origin authentication even against quantum computer attacks.
Innovation Solution
The cryptographic system employs a dealer and hardware security modules (HSMs) to generate and distribute a key pair using a hash-based signature scheme, with shares of the private key distributed using a (t,n) threshold secret sharing scheme. Each HSM maintains a counter for tracking the number of message signings, ensuring that the signing upper bound is not exceeded.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the private key is distributed to multiple locations for redundancy, then the system availability is improved, but the risk of key duplication and unauthorized signing increases
Solution Approach 1:
The private key is segmented into multiple shares using secret sharing schemes, where each share is distributed to different HSMs. No single HSM holds the complete private key, eliminating the risk of key duplication while maintaining system availability through distributed architecture.
Solution Approach 2:
The system transitions from a single-location key storage model to a multi-dimensional distributed architecture where key shares are stored across multiple HSMs. This dimensional change enables redundancy without compromising security, as the key material is fragmented across different spatial locations.
2Reliability
If the signing upper bound is enforced to limit message signings, then the security against quantum attacks is improved, but the flexibility in message signing operations is reduced
Solution Approach 1:
The signing upper bound is predetermined and configured before the HBSS private key is generated. This preliminary action establishes security constraints in advance, ensuring that the number of message signings does not exceed the quantum-resistant limit while maintaining systematic control over signing operations.
Solution Approach 2:
The system implements feedback mechanisms through state tracking, where each signing operation updates the state counter. This feedback ensures that the signing upper bound is continuously monitored and enforced, preventing excessive signings while providing deterministic control over the signing process.
3Reliability
If the state is tracked to prevent repetition, then the integrity of the signature scheme is improved, but the complexity of state management increases
Solution Approach 1:
The HSMs automatically perform state tracking and update operations without external intervention. Each HSM maintains its own state counter and autonomously enforces signing limits, reducing the complexity of centralized state management while ensuring signature integrity through distributed self-monitoring.
4Reliability
If the private key is regenerated after each signing, then the security is improved, but the signing speed is reduced
Solution Approach 1:
The system dynamically balances security and performance by using state tracking to enable efficient signature generation without full private key regeneration. The state information is updated incrementally after each signing operation, maintaining quantum-resistant security while avoiding the computational overhead of complete key regeneration, thus improving signing speed.
Data Source
AI summary
Examples relate to machine readable storage storing instructions arranged, when processed, to realise a cryptographic machine readable instructions for signing a message; the instructions comprising: instructions to receive, from a plurality of participating devices of a set of devices, a threshold number of shares of a private key, sk; the shares having been created using a (t,n)-threshold secret sharing scheme, where n>=t and t>n/2; instructions to receive respective state indicia from the plurality of participating devices; the respective state indicia being indicative of the number of messages having been signed using the private key, sk; instructions to recover the private key, sk, using the received shares; instructions to sign a message using a hash-based signature scheme subject to assessing a state indicium indicating the highest number of messages that have been signed using the private key. sk; and instructions to establish a state indicium indicating the highest number of messages, m, that have been signed using the private key, sk.