Implicit Certificate Public Key Computation Optimization
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Solution Overview
Problem
Existing implicit certificate schemes, such as ECQV, require a large number of computations to construct public keys, which can be resource-intensive and inefficient in cryptographic systems.
Innovation Solution
The method reduces computational overhead by generating and using a pair of integers (e1, e2) derived from the hash of the implicit certificate, where e1 and e2 have bit lengths less than the original hash value, allowing for the computation of public and private keys with fewer operations, specifically using the truncated Extended Euclidean Algorithm to achieve these reductions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional implicit certificate schemes (ECQV) are used to construct public keys, then public key authentication is achieved, but a large number of computations are required making the process resource-intensive and inefficient
Solution Approach 1:
The patent segments the computation of the public key by introducing an intermediate value 'e' that splits the original computation into two parts: (1) computing e from the implicit certificate components, and (2) using e to compute the final public key. This segmentation allows the system to reduce computational complexity while maintaining authentication reliability.
Solution Approach 2:
The patent changes the parameter used in the public key computation from directly using the full hash value to using a truncated or modified version 'e' derived from the hash. This parameter change reduces the computational burden while still providing sufficient authentication strength.
2Reliability
If the full hash value is used to compute public keys in implicit certificates, then authentication strength is maintained, but computational overhead increases significantly
Solution Approach 1:
The patent extracts only the necessary portion of the hash value (denoted as 'e') to use in public key computation, rather than using the complete hash. This extraction approach maintains sufficient authentication strength while significantly reducing computational time requirements.
Solution Approach 2:
The patent applies partial action by using only a portion of the hash value (e) rather than the full hash in the public key computation. This partial approach is sufficient for authentication purposes and avoids the excessive computational cost of using the complete hash value.
Data Source
AI summary
There are disclosed systems and methods for reducing the number of computations performed by a computing device constructing a public key from an implicit certificate associated with a certificate authority in an implicit certificate scheme. In one embodiment, the device first operates on the implicit certificate to derive an integer e. The device then derives a pair of integers (e1, e2) from the integer e, such that each of the pair of integers (e1, e2) has a bit length less than the bit length of the integer e, and such that the ratio of the pair of integers (e1, e2) corresponds to the integer e. The device then computes the public key by combining the integers e1 and e2 with public key contribution data derived from the implicit certificate and a public key of the certificate authority.