Dynamic Parameter Selection for CKKS Fully Homomorphic Encryption and Its RNS Variant

In recent years, the Cheon–Kim–Kim–Song (CKKS) scheme has gained widespread popularity among practitioners due to its support for approximate arithmetic on encrypted data. However, the decrypted outputs of CKKS inherently contain approximation errors arising from homomorphic operations. If the error term in the ciphertext grows too large, the decrypted results may no longer satisfy the required precision or correctness. To mitigate this issue, error analysis and parameter selection must be performed in advance. Nevertheless, deriving tight error bounds and selecting efficient parameters while jointly satisfying security, correctness, precision, and efficiency requirements remain challenging. To address this, we propose a distribution-aware error analysis method for CKKS and the residue number system (RNS) CKKS to derive tighter probabilistic bounds under the stated assumptions. The method propagates coefficient means and variances through the computation before estimating the final error bound, rather than propagating intermediate norm bounds. Based on this analysis, we further develop a dynamic parameter selector for CKKS. This evaluator can generate an efficient valid parameter set by comprehensively considering security, correctness, circuit depth, and decryption precision for given computational tasks. Moreover, by employing the dynamic parameter evaluation method, the evaluator produces parameter sets that are more closely tailored to the specified computational requirements. Here, dynamic selection refers to feedback-based parameter adjustment before homomorphic evaluation.