Batch Verification Method Using Hamming Weight Constraints
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Solution Overview
Problem
Existing batch verification methods are computationally intensive and increase the probability of verification errors, particularly in verifying large numbers of electronic signatures, which slows down the process.
Innovation Solution
A method that reduces computational load by setting a predetermined bit value and maximum Hamming weight for verification exponents, allowing for simultaneous verification of exponentiation pairs while minimizing the probability of errors, using a specific verification formula and binary method to efficiently compute verification results.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional batch verification methods are used to verify a large number of exponentiation pairs simultaneously, then verification throughput is improved, but computational complexity and error probability increase
Solution Approach 1:
The verification process is segmented into multiple independent verification equations, each using different random values. Instead of verifying all n exponentiation pairs with a single verification equation, the patent divides them into multiple groups, each verified separately with its own random challenge values. This segmentation reduces the error probability while maintaining batch verification throughput.
Solution Approach 2:
The patent applies partial verification by selecting only certain exponentiation pairs for verification in each batch, rather than verifying all pairs with the same computational effort. By using random sampling and selective verification with multiple rounds, the system achieves high reliability without the full computational cost of verifying every single pair exhaustively.
2Productivity
If the number of multiplication operations is reduced to increase verification speed, then productivity is improved, but verification precision may deteriorate
Solution Approach 1:
The patent changes the parameters of verification by using random challenge values and grouping strategies. By varying the random values used in each verification equation and adjusting the grouping of exponentiation pairs, the system maintains verification accuracy while optimizing the number of multiplication operations required.
Solution Approach 2:
The patent performs preliminary grouping and random value selection before the actual verification computation. By pre-organizing the exponentiation pairs into groups and pre-selecting random challenge values, the system reduces the computational complexity during the verification phase while ensuring accuracy through proper mathematical foundations.
Data Source
AI summary
A fast batch verification method and apparatus are provided. In the method of batch-verifying a plurality of exponentiations, (a) a predetermined bit value t is set to an integer equal to or greater than 1; (b) a maximum Hamming weight k is set to an integer equal to or greater than 0 and less than or equal than the predetermined bit value t; (c) n verification exponents si are randomly selected from a set of verification exponents S (n is an integer greater than 1, i is an integer such that 1≦i≦n), where the set of verification exponents S include elements whose bit values are less than or equal to the predetermined bit value t and to which a Hamming weight less than or equal to the maximum Hamming weight k is allocated; (d) a value of verification result is computed by a predetermined verification formula; and (e) the verification of the signatures is determined to be passed when the value of verification result satisfies a pre-determined pass condition. Accordingly, it is possible to significantly reduce the amount of computation and particularly, the computation amount of multiplication, without increasing a probability that a verification error would occur, thereby significantly improving the speed of verifying a plurality of signatures.