vDGHV Key Generation Using Hard-to-Factor Primes
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Solution Overview
Problem
The existing vDGHV key generation method for fully homomorphic public-key encryption is vulnerable to security flaws due to the possibility of factoring the secret key, allowing attackers to decompose the prime factors and compromise the key's security.
Innovation Solution
Generating a secret key SK corresponding to a random prime number or a product of prime numbers that is difficult to factor, making it unachievable for attackers to compute the key, thereby enhancing the security of the key generation process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If a random number p is used as the secret key in the vDGHV key generation method, then the key generation process is simple and efficient, but the security is compromised because the random number can be factored into prime factors
Solution Approach 1:
The patent changes the parameter type of the secret key from a general random number to a specifically constructed number with difficult-to-factor properties. This is achieved by selecting prime numbers p such that p-1 has a large prime factor, making the discrete logarithm problem hard and preventing efficient factoring attacks on the public key components.
2Reliability
If the secret key p is made difficult to factor by using specific prime number properties, then the security is enhanced, but the key generation process becomes more complex
Solution Approach 1:
The patent applies preliminary action by pre-selecting prime numbers with specific properties (where p-1 has a large prime factor) before the actual key generation process. This preliminary selection ensures that subsequent key generation operations remain efficient while maintaining high security, as the difficult-to-factor property is established in advance through careful prime number selection.
Data Source
AI summary
There is proposed a method of generating secret and public keys vDGHV with enhanced security, implemented in a device including at least one microprocessor and a memory. The method includes generating a secret key SK corresponding the generation of a prime random number p or product of prime numbers.