Lattice-Based Post-Quantum Threshold Signature Scheme
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Solution Overview
Problem
There is a lack of successful implementations of lattice-based post-quantum threshold signature schemes that offer proof of security, primarily due to the difficulty in converting post-quantum signature schemes into threshold schemes.
Innovation Solution
A method for implementing a lattice-based post-quantum threshold signature scheme is provided, which involves generating private and public keys using a polynomial vector threshold secret sharing scheme, computing commitments and partial signatures, and combining these to produce a final signature.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a traditional signature scheme with a unique private key is used, then the signing process is simple, but the system has a single point of failure and lacks fault tolerance
Solution Approach 1:
The private key is segmented into multiple shares distributed among n signers. Each signer holds a portion of the private key, and no single signer can independently generate a valid signature. This segmentation eliminates the single point of failure while maintaining cryptographic security through threshold secret sharing mechanisms.
Solution Approach 2:
The signature scheme transitions from a single-key model to a multi-dimensional distributed model where security and fault tolerance are achieved through spatial distribution of key shares across multiple signers, adding the dimension of distributed participation to the signing process.
2Reliability
If a post-quantum signature scheme is implemented, then security against quantum attacks is improved, but the conversion to a threshold scheme becomes difficult
Solution Approach 1:
The patent introduces lattice-based cryptographic primitives as an intermediary framework that naturally supports both post-quantum security requirements and threshold signature functionality. The lattice structure provides a mathematical foundation that bridges the gap between post-quantum cryptography and distributed secret sharing, enabling seamless integration of both requirements.
Solution Approach 2:
The signature scheme utilizes lattice-based parameters such as error distributions and modulus values that can be adjusted to simultaneously achieve quantum resistance and threshold properties. By carefully selecting and tuning these parameters, the scheme maintains security against quantum attacks while enabling flexible threshold configurations.
3Reliability
If multiple private keys are generated for threshold signing, then fault tolerance is improved, but the key management and signature verification process becomes more complex
Solution Approach 1:
The patent merges the key management processes of multiple signers into a unified threshold signature generation protocol. Instead of managing separate key pairs independently, the system combines key shares and signing operations into a coordinated process where the complexity is abstracted away, and signers interact through standardized messages and verification procedures.
Data Source
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AI summary
A method of performing a threshold digital signature of a message, the method comprising: receiving, at a signing entity, one of a plurality of private signing keys and a public verification key, wherein each of the plurality of private signing keys is associated with the public verification key and the public and private keys are generated using a lattice-based signature scheme; computing a first commitment and transmitting the first commitment to each of a plurality of remote entities; receiving a commitment from each of a subset of the plurality of remote entities; computing a first partial signature using the received commitments and the first commitment, the received private key, and the message, wherein the computation of the first partial signature includes performing a linear transformation using a polynomial vector threshold secret sharing scheme, PVSS, on the commitments and combining the transformed commitments; transmitting the first partial signature to each of the subset of remote entities; receiving a partial signature from each of the subset of the plurality of remote entities; and computing a combined signature using the computed first partial signature and the received partial signatures.