Prime Number Generation for Cryptographic Decryption
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Solution Overview
Problem
Existing cryptographic operations are inefficient due to high processor and memory utilization, and are vulnerable to power analysis attacks, particularly during decryption processes that involve computing inverse values.
Innovation Solution
The method involves optimizing decryption operations by avoiding the computation of inverse values, using intermediate randomization to protect against power analysis attacks, and employing fast prime number generation techniques to enhance security and efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If inverse values are computed during decryption operations, then decryption can be performed, but processor utilization increases and the system becomes vulnerable to power analysis attacks
Solution Approach 1:
The patent extracts and eliminates the computation of inverse values from the decryption process. By using an alternative mathematical approach that computes decryption without requiring inverse calculations, the system removes the vulnerable and computationally expensive operation while maintaining decryption functionality.
Solution Approach 2:
The patent introduces intermediate randomization values as mediators in the decryption process. These random values are introduced before and after the decryption operation to mask the actual computational steps, preventing power analysis attacks while the results are properly unmasked to maintain correctness.
2Reliability
If inverse values are computed during decryption operations, then decryption can be performed, but memory utilization increases
Solution Approach 1:
The patent extracts and eliminates the computation of inverse values from the decryption process. By using an alternative mathematical approach that computes decryption without requiring inverse calculations, the system removes the vulnerable and computationally expensive operation while maintaining decryption functionality.
3Productivity
If fast prime number generation is implemented, then cryptographic key generation efficiency improves, but the complexity of the generation process increases
Solution Approach 1:
The patent applies preliminary filtering actions to eliminate non-prime candidates before performing comprehensive primality testing. By pre-filtering numbers based on simple divisibility rules and mathematical properties, the system reduces the number of candidates requiring expensive primality tests, thereby speeding up prime generation while managing complexity through staged processing.
Data Source
AI summary
Aspects of the present disclosure involve a method, a system and a computer readable memory to generate and use prime numbers in cryptographic operations by determining one or more polynomial functions that have no roots modulo each of a predefined set of prime numbers, selecting one or more input numbers, generating a candidate number by applying one or more instances of the one or more polynomial functions to the one or more input numbers, determining that the candidate number is a prime number, and using the determined prime number to decrypt an input into the cryptographic operation.