RSA Key Generation Integrity Verification
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Solution Overview
Problem
Current integrity tests for cryptographic key pair generation in RSA methods, as defined by standards like FIPS 140-2, may fail to detect errors or malicious attacks that corrupt key pairs, leading to vulnerabilities in cryptographic systems.
Innovation Solution
A method that checks for the congruence of λ(n) modulo (p-1) and modulo (q-1) during key generation, and includes additional steps to test the integrity of generated keys by encrypting and decrypting messages with public and private exponents, and comparing encrypted and decrypted messages to ensure key pair integrity, while also disrupting the calculation of λ(n) to detect vulnerabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If current integrity tests (FIPS 140-2) are used for key pair generation, then the cryptographic system can be implemented with standard procedures, but the tests may fail to detect key pair generation errors or malicious attacks
Solution Approach 1:
The patent applies preliminary action by performing the λ(n) verification check during the key generation process itself, before the keys are deployed. The method checks whether λ(n) is divisible by both (p-1) and (q-1) immediately after generating the key pair, preventing corrupted keys from being used in subsequent cryptographic operations.
Solution Approach 2:
The patent implements feedback by using the results of the λ(n) verification to determine whether to accept or reject the generated key pair. If the verification fails (λ(n) is not divisible by (p-1) or (q-1)), the system detects the error and can trigger key regeneration or error handling procedures.
2Reliability
If additional verification steps are added to check λ(n) congruence, then the reliability of key generation is improved, but the computational time and complexity increase
Solution Approach 1:
The patent applies partial action by performing only the essential λ(n) verification checks needed to detect errors - specifically checking divisibility by (p-1) and (q-1) - rather than performing exhaustive verification of all key properties. This provides sufficient error detection with minimal additional computational overhead.
Solution Approach 2:
The patent changes the verification parameter from checking the full λ(n) value to checking its divisibility properties modulo (p-1) and (q-1). This transformation allows for efficient verification using modular arithmetic operations that are computationally lightweight compared to full λ(n) calculation and verification.
Data Source
AI summary
Method for generating a pair of public and private cryptographic keys in the additive group of integers modulo n, where n is the product of two prime numbers p and q, the method including the following steps:calculating a public exponent e for said public key, andcalculating a private exponent d for said private key from said public exponent and said public modulus, where d·e=1 mod λ(n), λ(n) being the least common multiple between p-1 and q-1, characterized in that the method furthermore comprises a step:of checking to check that λ(n)=0 mod (p-1) and λ(n)=0 mod (q-1).