Characterizing the Sensitivity to Individual Bit Flips in Client-Side Operations of the CKKS Scheme

2025-07-28

AI Summary

This work investigates the sensitivity of CKKS homomorphic encryption client-side operations—namely encoding, encryption, decryption, and decoding—to single-bit flip faults, with particular emphasis on how performance optimizations such as Residue Number System (RNS) arithmetic and the Number-Theoretic Transform (NTT) exacerbate error propagation. Using theoretical modeling and bit-level fault injection experiments, we demonstrate that while vanilla CKKS exhibits limited fault tolerance, RNS and NTT optimizations drastically increase vulnerability: a single-bit fault can induce catastrophic precision loss across the entire output. We develop a fine-grained error propagation model that identifies RNS base conversion and NTT butterfly operations as critical fault-amplification stages. Our results provide the first quantitative vulnerability map for CKKS under soft errors, pinpointing key protection targets for fault-resilient design and filling a fundamental gap in the robustness analysis of CKKS against transient hardware faults.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Constraint Satisfaction and Optimization: Satisfiability
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Homomorphic Encryption (HE) enables computation on encrypted data without decryption, making it a cornerstone of privacy-preserving computation in untrusted environments. As HE sees growing adoption in sensitive applications such as secure machine learning and confidential data analysis ensuring its robustness against errors becomes critical. Faults (e.g., transmission errors, hardware malfunctions, or synchronization failures) can corrupt encrypted data and compromise the integrity of HE operations. However, the impact of soft errors (such as bit flips) on modern HE schemes remains unexplored. Specifically, the CKKS scheme-one of the most widely used HE schemes for approximate arithmetic-lacks a systematic study of how such errors propagate across its pipeline, particularly under optimizations like the Residue Number System (RNS) and Number Theoretic Transform (NTT). This work bridges that gap by presenting a theoretical and empirical analysis of CKKS's fault tolerance under single bit-flip errors. We focus on client-side operations (encoding, encryption, decryption, and decoding) and demonstrate that while the vanilla CKKS scheme exhibits some resilience, performance optimizations (RNS/NTT) introduce significant fragility, amplifying error sensitivity. By characterizing these failure modes, we lay the groundwork for error-resilient HE designs, ensuring both performance and integrity in privacy-critical applications.

Problem

• Analyzes CKKS scheme's sensitivity to bit-flip errors
• Explores error impact on RNS and NTT optimizations
• Assesses fault tolerance in client-side HE operations

Innovation

• Analyzes CKKS fault tolerance under bit-flip errors
• Focuses on client-side operations with RNS/NTT optimizations
• Identifies error sensitivity in optimized CKKS implementations