Joint ECDSA and ECQV Verification via Pre-computed Scalar Multiples
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Solution Overview
Problem
The existing verification processes for digital signatures and implicit certificates in cryptography systems, such as those using Elliptic Curve Digital Signature Algorithm (ECDSA) and Elliptic Curve Qu-Vanstone (ECQV) certificates, require significant computational resources and time, especially when verifying both simultaneously.
Innovation Solution
A joint operation method is introduced to simultaneously verify ECDSA signatures and ECQV certificates, utilizing a combined fast verification technique that reduces total computation time and resources by employing pre-computed scalar multiples and elliptic curve point multiplications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If separate verification processes are used for ECDSA signatures and ECQV certificates, then verification correctness is ensured, but total computation time and resources increase significantly
Solution Approach 1:
The patent combines the verification of ECDSA signatures and ECQV certificates into a single joint verification process. The verification equation integrates both verification requirements: v = u1*G + u2*C1 + u3*P - u4*R, where the first two terms verify the ECDSA signature and the last two terms verify the ECQV certificate simultaneously. This merging eliminates the need for separate verification computations, reducing total computation time while maintaining the correctness of both verifications.
2Ease of operation
If traditional separate verification methods are used, then implementation simplicity is maintained, but computational resources and time consumption increase
Solution Approach 1:
The joint verification equation v = u1*G + u2*C1 + u3*P - u4*R merges multiple verification operations into a single computational process. The method maintains implementation simplicity by using standard elliptic curve point operations that are already familiar to practitioners, while achieving significantly improved verification efficiency through the combined approach.
Solution Approach 2:
The patent performs preliminary computations of scalar multiples (C1 = 2^k*C and G1 = 2^k*G) in advance, where k is the bit length of the signature component. These pre-computed values are then reused in the joint verification equation, reducing the computational burden during the actual verification process and improving overall efficiency without complicating the implementation.
Data Source
AI summary
Methods, systems, and computer programs for verifying a digital signature are disclosed. The verifier accesses an implicit certificate and a digital signature provided by the signer. The implicit certificate includes a first elliptic curve point representing a public key reconstruction value of the signer. The verifier accesses a second elliptic curve point representing a pre-computed multiple of the certificate authority's public key. The verifier uses the first elliptic curve point and the second elliptic curve point to verify the digital signature. The verifier may also use a third elliptic curve point representing a pre-computed multiple of a generator point. Verifying the digital signature may provide verification that the implicit certificate is valid.