Authentication Tag Generation Using Group Testing Matrix Hashing
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
The computational complexity of existing authentication tag generation methods, particularly those using two-layer hash trees and combinatorial group testing, is high due to the linear order of computational complexity with respect to the input length, leading to increased calculation amounts and inefficiencies in alteration detection.
Innovation Solution
An authentication tag generation apparatus and method that computes a hash function for each item in partial strings divided by a group testing matrix, using a combiner to combine individual hash values with a hash value of an empty string as an identity element, reducing the computational burden by employing incremental hash functions and specific combining operations like MuHASH, AdHASH, and LtHASH.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a hash function is applied to each item in a message to generate authentication tags, then alteration detection capability is improved, but the computational complexity increases linearly with the number of items
Solution Approach 1:
The message is divided into partial strings according to a group testing matrix, where each partial string contains a subset of items. Hash functions are applied to these partial strings rather than to every individual item, reducing the total number of hash computations while maintaining alteration detection capability through the combinatorial structure of the matrix.
Solution Approach 2:
The invention changes the parameter of hash function input from individual items to grouped partial strings. By modifying the granularity and grouping of hash function applications based on the group testing matrix structure, the computational complexity is reduced while preserving the ability to detect alterations through verification of the grouped hash values.
2Quantity of substance
If combinatorial group testing is used to divide messages into partial strings, then the number of authentication tags is reduced, but the computational burden per tag increases
Solution Approach 1:
The message is segmented into partial strings based on rows of the group testing matrix, where each partial string represents a group of items. This segmentation reduces the total number of authentication tags needed compared to item-by-item hashing, while the computational burden per tag remains manageable because each partial string hash is computed independently using standard hash functions.
Solution Approach 2:
Multiple items are merged into partial strings for joint hashing. Instead of computing separate hash values for each item, the invention combines items into groups (partial strings) and computes a single hash value for each group, thereby reducing the total number of hash computations while maintaining the ability to identify altered items through the group testing framework.
3Reliability
If two-layer hash trees are used for authentication tag generation, then alteration detection is achieved, but the calculation amount increases significantly
Solution Approach 1:
The invention extracts and eliminates the two-layer hash tree structure, replacing it with a simpler single-layer hashing approach applied to partial strings. By removing the complex two-layer structure and its associated computational overhead, the invention maintains alteration detection capability while significantly improving calculation efficiency through direct hashing of grouped items.
Solution Approach 2:
Instead of using a bottom-up two-layer hash tree approach that accumulates computations through multiple levels, the invention inverts the approach by directly applying hash functions to partial strings in a single layer. This inversion simplifies the computational structure and reduces the total calculation amount while preserving the ability to detect alterations through the group testing matrix framework.
Data Source
AI summary
A hash function is computed for each item of a partial string obtained by dividing a message received according to a group testing matrix representing combinatorial group testing relating to the message, and an authentication tag for the partial string is generated using a value obtained by a combining operation of individual hash values by a combiner, wherein the combiner performs the combining operation of the individual hash values, by using a hash value of an item of an empty string as an identity element of the operation.