Where the Information Lives: A Key-Free Observability Decomposition for CKKS Hardware Monitors

This technical note studies what a key-free monitor can learn from CKKS ciphertext state in a hardware-accelerator setting. Such monitors may track remaining precision or noise budget and detect faulty datapath stages while inspecting ciphertext words without the secret key.

The note gives a three-region observability decomposition. Ciphertext content is computationally masked under the assumed multi-sample circular decision-RLWE model. The coarse budget signal is public because metadata such as level, scale, modulus chain, and operation history determines the key-free portion of a precision estimate. Public datapath relations, including fixed linear maps such as NTT and basis conversion, can be checked without the secret key using random-projection or Freivalds-style consistency checks.

The main result is a distributional completeness theorem under an explicit exogenous additive-deviation fault model. The design implication is that key-free CKKS monitors should obtain budget information from public metadata and spend integrity effort on public relation checks rather than coefficient-magnitude noise gauges.