MAC Tag List Generation via Group Test Matrix
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Solution Overview
Problem
Existing message authentication techniques using known hash functions or message authentication schemes, such as CMAC, face significant computational overhead when performing combinatorial group testing for identifying falsified items, leading to increased computation time and inefficiency, especially in large datasets like databases, where the number of tests required grows exponentially with the number of items.
Innovation Solution
A MAC tag list generating apparatus that employs a group test matrix and pseudorandom functions to efficiently generate and verify MAC tags, using a pseudorandom permutation to reduce the computational complexity by sharing intermediate results across tests, thereby generating a list of MAC tags that can identify falsified positions with reduced computational effort.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a MAC function is applied to each of m items in a message, then the position of falsification can be identified, but the amount of data to be stored increases significantly due to m tags
Solution Approach 1:
The patent combines multiple MAC tags into a single aggregated tag by applying a MAC function to the concatenation of multiple original tags. This merging approach maintains the ability to detect falsification while significantly reducing the total amount of stored data from m separate tags to a single aggregated tag.
Solution Approach 2:
The patent introduces an intermediate aggregation step where multiple individual tags are combined through a MAC function before final storage. This intermediary process allows the system to preserve detailed verification capability while storing only compact aggregated results.
2Measurement precision
If combinatorial group testing is performed using known hash functions or message authentication schemes, then falsified positions can be identified, but the computational overhead increases significantly
Solution Approach 1:
The patent segments the computation process into two efficient stages: first computing individual MAC tags for each item using a standardized MAC function, then aggregating these tags through a single additional MAC computation. This segmentation avoids the exponential complexity of traditional combinatorial group testing while maintaining precise falsification detection.
Solution Approach 2:
The patent changes the computational parameter from evaluating multiple possible falsification combinations (exponential complexity) to computing individual item MACs and aggregating them (linear complexity). This parameter transformation fundamentally reduces computational overhead while preserving detection accuracy.
3Measurement precision
If the number of tests is increased to identify falsified items in large datasets, then the precision of falsification detection improves, but the computation time increases exponentially
Solution Approach 1:
The patent performs preliminary computation of individual MAC tags for each message item before the aggregation step. These pre-computed tags are then efficiently combined to detect falsification, avoiding the need for time-consuming repeated computations during the verification phase.
Solution Approach 2:
The patent maintains continuous useful computation by processing all message items through the MAC function in a streamlined sequence, then immediately aggregating the results. This continuous processing approach eliminates idle computation time and maintains high productivity throughout the verification process.
Data Source
AI summary
Disclosed is a MAC tag list generating apparatus capable of efficiently performing message authentication through which information pertaining to a falsified position as well as existence of falsification can be obtained. This MAC tag list generating apparatus is provided with: a group test matrix generating means for generating a group test matrix W, which is a parameter of a combined group test, on the basis of a plurality of items obtained by dividing an obtained message M; and a MAC tag list generating means that, while sharing results obtained by applying a pseudo random function to the items forming each row of the generated group test matrix W, sums the results, and then applies the summed results to pseudo random permutation to generate a MAC tag list T, which is a MAC tag list pertaining to the message M.