Message Generation for Cryptographic Key Integrity Testing
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Solution Overview
Problem
Current cryptographic key pair generation integrity tests may fail to detect errors, particularly during attacks, leading to vulnerabilities in cryptographic systems.
Innovation Solution
A method for generating messages of order λ(n) to enhance key pair generation integrity tests, involving primality tests and generator searches within the multiplicative group of integers modulo n, ensuring robustness and anomaly detection, along with an alternative method to test electronic devices' resistance to errors in calculating the lowest common multiple.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If standard integrity tests (FIPS 140-2) are used for key pair verification, then the testing process is simple and widely accepted, but the tests may fail to detect certain key generation errors and attacks
Solution Approach 1:
The invention segments the integrity test into multiple independent verification steps: (1) verifying the message order is exactly λ(n), (2) checking the message is in the correct range [1, n-1], (3) verifying encryption/decryption or signing operations, and (4) checking for specific mathematical properties that would be violated by certain attacks. This segmentation allows each step to detect specific types of errors without requiring the entire test to be overly complex.
Solution Approach 2:
The invention performs preliminary verification of the message order being exactly λ(n) before executing the main encryption/decryption or signing verification. This preliminary check ensures the message has the correct mathematical properties to detect certain key generation errors and attacks, without adding significant complexity to the overall test process.
2Reliability
If messages of order λ(n) are generated using generator search during primality testing, then anomaly detection capability is enhanced, but the key generation process becomes more time-consuming
Solution Approach 1:
The invention merges the message generation process with the existing primality testing process. The generator search and message creation are performed during the primality test execution, utilizing the same computational resources and time framework. This integration ensures messages of order λ(n) are generated without requiring separate, additional time-consuming processes.
Solution Approach 2:
The invention changes the parameter used for message generation from random integers to specific generators of the multiplicative group modulo p and q. By using generators with specific mathematical properties (order λ(p) and λ(q) respectively), the system enhances anomaly detection capability while the generation process itself remains efficient through algebraic structure exploitation.
3Reliability
If the lowest common multiple λ(n) is calculated accurately, then key pair generation is secure, but the calculation is computationally intensive and vulnerable to attacks
Solution Approach 1:
The invention implements feedback mechanisms where the generated message of order λ(n) is used to verify the correctness of the key pair generation. The message serves as a feedback indicator that reveals certain types of errors or attacks in the λ(n) calculation, allowing the system to detect and reject incorrect key pairs without requiring repeated complex calculations.
Solution Approach 2:
The invention creates a simplified verification copy of the key pair using the generated message. Instead of repeatedly performing the complex λ(n) calculation, the system creates a verification instance where the message of order λ(n) is encrypted/signed and then verified, providing a less computationally intensive way to confirm key pair correctness while maintaining security.
Data Source
AI summary
Generation of a message m of order λ(n) for a test of the integrity of the generation of a pair of cryptographic keys within the multiplicative group of integers modulo n=p·q, including: —key pair generation including, to generate p and q: a random selection of candidate integers; and a primality test; —a first search of the multiplicative group of integers modulo p for a generator a; —a second search of the multiplicative group of integers modulo q for a generator b; —a third search for a number y, as message m, verifying: 1≤γ≤n−1, where γ=a mod p and γ=b mod q, the first or second search being performed during the primality test.