MAC Tag List Generation Using Group Test Matrix
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Solution Overview
Problem
Existing methods for message authentication, such as those using combinatorial group testing (CGT) and message authentication codes (MAC), face challenges in efficiently identifying tampered positions within messages, particularly when constructing d-disjunct matrices for parameters where d > 1, leading to inefficiencies in tag generation and verification.
Innovation Solution
A MAC tag list generation apparatus and method that employs a nonce-based linear CGT approach, utilizing a t-rows and m-columns group test matrix and pseudorandom functions to generate and verify MAC tags, allowing for efficient identification of tampered positions by reducing the number of tags required and improving authentication efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If MAC is applied to each item of a message consisting of m items, then tampered position can be identified, but the number of tags increases to m causing significant data storage increase
Solution Approach 1:
The message is divided into subseries of items rather than treating each item separately. By grouping items into overlapping subseries and applying MAC to each subseries, the patent reduces the total number of tags needed while maintaining the ability to identify tampered positions through combinatorial analysis of which subseries are affected.
Solution Approach 2:
Each MAC tag on a subseries serves multiple verification purposes simultaneously. A single tag can verify multiple items across different subseries, and the combinatorial pattern of tag verifications provides information about which specific items are tampered, making the tagging system more efficient than one-to-one item tagging.
2Quantity of substance
If combinatorial group testing with d-disjunct matrices is used to reduce the number of tags, then tag quantity decreases, but construction becomes difficult when d > 1
Solution Approach 1:
The patent employs a dynamic construction approach where the test matrix is built incrementally using greedy algorithms rather than requiring static optimal d-disjunct matrices. This allows the system to adaptively construct functional matrices for d > 1 cases without facing the theoretical construction difficulties of traditional d-disjunct matrices, making the solution practical for various parameter sets.
3Reliability
If general message authentication is used, then authentication can be performed, but information about tampered position cannot be obtained
Solution Approach 1:
The patent incorporates feedback mechanisms where the verification results of multiple MAC tags on overlapping subseries are analyzed combinatorially. This feedback loop allows the system to not only detect that tampering occurred but to infer the specific positions of tampered items by examining which subseries failed verification and how they overlap, thereby recovering the lost position information.
Data Source
AI summary
A MAC tag list generation apparatus, on reception of a nonce N unique value to each MAC generation process and a message M, generates a t×m group test matrix H serving as combinatorial group testing parameters for s (a positive integer) which is the number of the MACs to be generated, generates a MAC tag list T=(T[1], . . . , T[t]) by generating a MAC value T[i] corresponding to the i-th test (i=1, . . . , t) using the group test matrix H, the nonce N, and pseudorandom functions F and G with variable length input and fixed length output for the message M, and outputs the MAC tag list.