AI-Guided Grover Search for Simulation-Based Evaluation of Post-Quantum Security in CKKS Homomorphic Encryption
DOI:
https://doi.org/10.66279/jaksw134Keywords:
Fully Homomorphic Encryption, Quantum Cryptanalysis, Grover’s Algorithm, CKKS Scheme, Simulation-Based Security AnalysisAbstract
The emergence of quantum computing poses fundamental challenges to the security assumptions underlying modern cryptographic systems, particularly Fully Homomorphic Encryption (FHE) schemes that enable computation on encrypted data. While Grover's algorithm provides a theoretical framework for quantum attacks on symmetric cryptographic primitives, its practical application to complex parameter spaces like those in CKKS FHE has remained limited.
This paper presents a simulation-based, exploratory hybrid framework that combines deep neural networks with a simplified quantum search model to evaluate the post-quantum security of CKKS bootstrapping parameters under idealised conditions. The AI-enhanced system learns to identify potentially vulnerable parameter configurations through pattern recognition, then uses this knowledge to optimize the quantum oracle construction in a 4-qubit Grover's algorithm simulator. Experiments conducted on 5,000 synthetically generated parameter sets, with evaluation on 100 boundary-region configurations, demonstrate that this hybrid approach achieves a 73.4\% success rate in identifying insecure parameters under the experimental setup, representing a 30.6\% improvement over standard quantum search in the same simulated environment.
Within the experimental model, this analysis indicates that under the experimental model, parameter sets nominally targeting 128-bit quantum security may exhibit effective security levels of only 86–101 bits when subjected to AI-guided search, suggesting that current FHE parameter margins warrant further investigation as quantum capabilities mature. The findings are simulation-based and should not be directly extrapolated to real-world deployments without further validation; however, they indicate that security margins may need to be increased by approximately 2.3 times to maintain true 128-bit quantum resistance against intelligent adversaries. These results have implications for post-quantum cryptographic standards and motivate further study at realistic qubit scales.
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