High Precision Noise Cleaning for CKKS with Application to Asynchronous Threshold CKKS

What it is

A preprint (IACR ePrint 2026/2675, approved 31 October 2026) from Zhihao Li, Cheng Hong and Tao Wei, all with contact addresses at antgroup.com. It gives a noise cleaning method for discrete CKKS that targets a stated bound on normalized output noise, such as 2^-300. Noise flooding needs this level of precision so that the added noise hides the secret statistically while the message can still be recovered exactly. The authors use it to build an asynchronous threshold CKKS scheme with strong simulation security in the random oracle model.

How it works

The paper's starting point is that key switching and rescaling can dominate the output error, even when a higher Hermite interpolation order shrinks the polynomial residual. A higher degree alone therefore stops helping. The authors respond in four ways:

• They choose the cleaning polynomials and the evaluation parameters together, against a complete error bound that covers the input noise and the errors added during homomorphic evaluation.
• They compose several lower-degree Hermite polynomials. This reaches the same output bound with a smaller ciphertext modulus and lower evaluation cost than one high-degree polynomial.
• To reduce the ciphertext tensor degree, they use polynomial representations with noisy auxiliary powers, chosen so that selected auxiliary error terms cancel.
• For integer messages, they extract the bits with multi-value functional bootstrapping, clean each bit, and recombine them into one ciphertext.

Results

Both implementations are in OpenFHE.

• Binary messages, 2^-300 normalized output noise target: cleaning time falls from 9.63 s to 1.54 s against a single Hermite evaluation. Input error bound and security requirements are the same in both runs.
• The composition also needs a smaller input ciphertext modulus and less evaluation key storage. The abstract gives no figures for either.
• Integer messages: 8-bit integers packed into all 32,768 slots. The maximum measured normalized output noise is below 2^-300, using either leveled digit extraction or functional bootstrapping.

Caveats

The abstract does not report timings for the 8-bit integer case, the modulus and key storage savings, or the cost of the threshold scheme itself. The strong simulation security claim is in the random oracle model. The 9.63 s to 1.54 s comparison is against a single Hermite evaluation, not against other noise cleaning approaches. No code release is mentioned.