Meaning of the bit precision


I have a beginner’s question about the meaning of bit precision. In OpenFHE, when using the CKKS scheme, the decryption results include a statement like “Estimated precision: xx bits.” Could you explain what this means and how to interpret the results?

Thank you for your help.

Roughly it corresponds to the [scaling factor] - [log2 of the average L1 norm of the difference between approximate FHE result and floating-point result in the clear] (if the message is close to unity in norm). This precision refers to the fixed-point precision.

This estimate is computed using the imaginary component, which is not used for messages in the OpenFHE CKKS implementation (only the real component is used, i.e., only real numbers are currently supported). See Section 5.1 of Securing Approximate Homomorphic Encryption Using Differential Privacy for a more detailed description of the procedure based on the imaginary component.

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