Presignature Re-Randomization for Secure Fast Digital Signatures
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Solution Overview
Problem
Existing digital signature methods, particularly those using presignatures, are vulnerable to security weaknesses such as the 4-sum attack, and there is a need for enhanced security without significant computational or latency overhead.
Innovation Solution
A computer-implemented method involving the re-randomization of presignatures using a non-predictable public re-randomization value, which can be derived from a random beacon or hash function, to enhance security in digital signature processes, especially in distributed settings like threshold ECDSA.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If presignatures are used to accelerate digital signature computation, then signing speed is improved, but security is worsened due to vulnerability to 4-sum attacks
Solution Approach 1:
The patent applies parameter changes by transforming the presignature through re-randomization. Specifically, a random value k' is generated and used to transform the original presignature components (r, s) into new components (r', s') through mathematical operations. This changes the parameters of the presignature while maintaining its functional properties, thereby enhancing security against 4-sum attacks while preserving the acceleration benefit.
Solution Approach 2:
The patent uses preliminary action by precomputing the presignature components (r, s) in advance before the actual signing operation. This allows the computationally intensive parts of the signature generation to be performed beforehand, and only the lighter re-randomization and final signature computation are performed when signing is actually needed, thus achieving speed improvement without compromising security.
2Reliability
If re-randomization is applied to enhance security, then security is improved, but computational overhead increases
Solution Approach 1:
The re-randomization process changes the parameters of the presignature by generating new random values and transforming the original components. This provides enhanced security by ensuring that each signature operation uses unique randomized parameters, preventing replay attacks and 4-sum attacks while adding only moderate computational overhead.
Solution Approach 2:
The patent introduces dynamics by making the presignature transformation adaptive and randomized rather than static. The re-randomization process dynamically generates new parameters based on fresh random values, making each signature operation unique and secure while keeping the computational steps manageable through efficient mathematical operations.
3Reliability
If re-randomization is applied to prevent 4-sum attacks, then security is improved, but latency increases
Solution Approach 1:
The parameter changes through re-randomization transform the presignature components using efficiently computable mathematical operations. While this does add some computational steps compared to using presignatures directly, the operations are designed to be lightweight, minimizing the latency increase while achieving the security goal of preventing 4-sum attacks.
Data Source
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AI summary
Embodiments of the invention relate to a computer-implemented method for performing a digital signature. The embodied method comprises steps of computing a presignature, receiving a signing request to perform the digital signature on a message, re-randomizing the presignature and performing the digital signature on the message with the re-randomized presignature.