Composite Finite Field Multiplier for Three-Operand Speed
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Solution Overview
Problem
Existing technologies lack efficient hardware solutions for multiplying three operands in composite finite fields, which is crucial for cryptographic algorithms and mathematical problem-solving, especially under real-time and speed-sensitive conditions.
Innovation Solution
A composite finite field multiplier is developed, utilizing a controller, GF((2 n< ) 2< ) multiplier, GF(2 n< ) standard basis multiplier, and GF(2 n< ) look-up table multiplier to selectively perform 3-input GF(2 n< ) or GF((2 n< ) 2< ) multiplication, enhancing speed and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If multi-operand multiplication is implemented using separate multipliers in cascade, then multiplication functionality is achieved, but multiplication speed is insufficient for real-time applications
Solution Approach 1:
The patent segments the 3-input multiplication operation into two sequential 2-input multiplication operations. The controller divides the three operands into pairs, performs multiplication on each pair using the GF((2^n)^2) multiplier, and combines the results to achieve the final 3-input multiplication product, thereby improving speed through optimized segmentation
Solution Approach 2:
The patent designs a universal GF((2^n)^2) multiplier that can handle multiple multiplication scenarios including 2-input multiplication, 3-input multiplication, and operations over different finite fields (GF(2^n) and GF((2^n)^2)). This multi-functional design eliminates the need for separate dedicated multipliers for each operation type, improving speed while managing complexity
2Productivity
If 3-input multiplication is implemented using existing 2-operand multipliers, then multiplication functionality is achieved, but operation time is excessive for speed-sensitive applications
Solution Approach 1:
The patent implements preliminary action by pre-organizing the multiplication process into optimized stages. The controller pre-processes the three operands to identify optimal multiplication pairs, pre-configures the GF((2^n)^2) multiplier for the specific operation type, and pre-plans the combination strategy, thereby reducing overall multiplication time
Solution Approach 2:
The patent ensures continuity of useful action by designing a seamless pipeline where the first 2-input multiplication operation feeds directly into the second multiplication operation without idle cycles. The controller maintains continuous data flow between operations, and the GF((2^n)^2) multiplier remains actively engaged throughout the process, minimizing idle time and maximizing productivity
Data Source
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AI summary
A composite finite field multiplier is disclosed. The multiplier includes a controller, an input port, an output port, a GF((2n)2) multiplier, a GF(2n) standard basis multiplier, and a GF(2n) look-up table multiplier; the controller is connected respectively to the input port, the output port, the GF((2n)2) multiplier, the GF(2n) standard basis multiplier and the GF(2n) look-up table multiplier; the GF((2n)2) multiplier is connected respectively to the GF(2n) standard basis multiplier and the GF(2n) look-up table multiplier. By using the GF((2n)2) multiplier, the GF(2n) standard basis multiplier and the GF(2n) look-up table multiplier, the multiplication of three operands is realized. Compared with the existing multiplier, the multiplier of the present invention has significant advantages in the speed of multiplying three operands over GF((2n)m).