Universal Hash Function Calculation Unit for Efficient Shared-Key Generation
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Solution Overview
Problem
Conventional methods for constructing ε-universal-hash-function families are inefficient in reducing the number of elements, especially when the output set is large, limiting their application in message authentication codes and quantum key distribution.
Innovation Solution
A universal-hash-function-family calculation unit that performs specific operations on input data to derive output data, using techniques such as Galois field multiplication and Toeplitz matrix operations, to achieve a reduced number of elements in the hash function set, enabling efficient shared-key generation between communication devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional methods are used to construct ε-universal-hash-function families, then the hash function can be implemented, but the number of elements in the hash function set is large, reducing efficiency
Solution Approach 1:
The patent transforms the hash function construction from conventional parameter selection to using Galois field multiplication parameters. By changing the mathematical domain to GF(2^m) and using field multiplication operations, the patent achieves a reduced number of hash function elements while maintaining security properties. The parameter transformation from arbitrary function selection to structured field operations enables both efficiency improvement and element reduction.
Solution Approach 2:
The patent replaces conventional hash function construction mechanisms with Galois field arithmetic operations. Instead of using traditional hash function families that require large element sets, the invention substitutes field multiplication and linear transformation operations that inherently provide universal hashing properties with fewer elements. This mechanical substitution of mathematical operations reduces the element count while preserving security.
2Productivity
If the number of elements in the hash function set is reduced, then efficiency improves, but achieving the lower bound is limited to extremely-limited parameters in conventional techniques
Solution Approach 1:
The patent creates a universal hash function construction method based on Galois field operations that works across different parameter settings. The field multiplication approach in GF(2^m) provides a unified framework that achieves the lower bound of hash function elements for various input-output set configurations. This universal method eliminates the limitation of conventional techniques that only work for extremely-limited parameters, making the solution adaptable while maintaining efficiency.
Solution Approach 2:
The patent uses parameter transformation to achieve adaptability across different scenarios. By expressing the hash function in terms of Galois field multiplication parameters and linear transformations, the invention can adapt to different input and output set sizes while consistently achieving the lower bound of elements. The parameter changes from conventional fixed structures to flexible field operations enable both efficiency and versatility.
3Ease of manufacture
If conventional hash function construction methods are used, then implementation is straightforward, but the number of elements cannot be minimized for large output sets
Solution Approach 1:
The patent replaces conventional hash function implementation mechanisms with Galois field arithmetic operations. The substitution of field multiplication and linear transformation for traditional hash function construction provides both implementation simplicity through standardized arithmetic operations and minimization of element count. The mechanical substitution to field operations enables efficient implementation while achieving the lower bound of elements even for large output sets.
Data Source
AI summary
An input data enlarging unit (100) derives a first enlargement unit output and a second enlargement unit output that are uniquely specified by input data (103) to output the same. The first enlargement unit output and the second enlargement unit output are elements of output data set B which forms a group. An ε−Δ hash function calculation unit (101) receives as input the first enlargement unit output to calculate an hΔ function which is specified by hash-function-specifying data (104) and an element of the HΔ function set. The function set HΔ is such that the number of hεH Δ which satisfies h(x)−h(y)=d for an arbitrary element d of the output data set B and two different elements x and y of the output data set B is equal to or smaller than |HΔ|·ε. An adding unit (102) adds together the result of calculation of the function HΔ and the second enlargement unit output to output a result of the addition.