Coprime Number Generation Mapping for Cryptography
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Solution Overview
Problem
Cryptographic operations, particularly in public-key cryptography, face inefficiencies in processor and memory utilization due to the computational expense of generating coprime numbers, which are essential for key generation and decryption processes, especially in devices with modest computational capabilities.
Innovation Solution
The method involves generating coprime numbers using a mapping {xi}→x that avoids computation and storage of inverse values, employing iterative procedures and modular operations to produce uniformly random outputs, reducing processing and memory requirements while ensuring the generated numbers are coprime with a set of predefined prime numbers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional methods are used to generate coprime numbers, then the generated numbers can be used for cryptographic operations, but the computational expense and processor utilization are high
Solution Approach 1:
The patent extracts and eliminates the computationally expensive inverse value calculations from the coprime number generation process. By using a mapping approach that avoids computing modular inverses, the method reduces computational expense while maintaining the ability to generate valid coprime numbers for cryptographic operations
Solution Approach 2:
The patent changes the parameters and approach of number generation by using a mapping function {xi}→x that transforms input values into coprime outputs without requiring inverse calculations. This parameter change in the generation methodology directly reduces computational expense and improves efficiency
2Productivity
If traditional methods are used to generate coprime numbers, then the generated numbers can be used for cryptographic operations, but memory utilization is high
Solution Approach 1:
The patent removes the need to store and process inverse values during the coprime number generation process. By eliminating this intermediate computational step, memory utilization is reduced while still producing the required coprime numbers for cryptographic applications
3Productivity
If traditional methods are used to generate coprime numbers, then the generated numbers can be used for cryptographic operations, but the processing requirements are high
Solution Approach 1:
The patent extracts and eliminates complex inverse value computations from the processing requirements. The simplified mapping approach {xi}→x reduces processing complexity while maintaining cryptographic validity, making the system more suitable for devices with modest computational capabilities
Data Source
AI summary
Aspects of the present disclosure involve a method, a system and a computer readable memory to perform a cryptographic operation that includes identifying a first set of mutually coprime numbers, obtaining a second set of input numbers coprime with a corresponding one of the first set of mutually coprime numbers, obtaining an output number that is a weighted sum of the second set of input numbers, each of the second set of input numbers being taken with a weight comprising a product of all of the first set of mutually coprime numbers except the corresponding one of the first set of mutually coprime numbers, and performing the cryptographic operation using the output number.