high_precision

Documentation

Overview

Package main implements an example showcasing high-precision bootstrapping for high-precision fixed- point approximate arithmetic over the reals/complexes. High-precision bootstrapping is achieved by bootstrapping the residual error iteratively until it becomes smaller than the initial ciphertext error. Assume that the bootstrapping circuit has `d` bits of precision and that a ciphertext encrypts a message `m` with `kd` bits of scaling factor. Then the procedure works as follow:

1) Input: ctIn[2^{kd} * m] 2) Bootstrap(ctIn[2^{kd} * m] / 2^{(k-1)d})*2^{(k-1)d} -> ctOut[2^{kd} * m + 2^{(k-1)d} * e0] 3) Bootstrap((ctOut - ctIn)/2^{(k-2)d}) * 2^{(k-2)d} -> ctIn = [2^{(k-1)d} * e0 + 2^{(k-2)d} * e1] 4) ctOut = ctOut - ctIn = [2^{kd} * m + 2^{(k-2)d} * e1] 4) We can repeat this process k-2 additional times to get a bootstrapping of k * d bits of precision.

The method is described in details by Bae et al. in META-BTS: Bootstrapping Precision Beyond the Limit (https://eprint.iacr.org/2022/1167).

This example assumes that the user is already familiar with the bootstrapping and its different steps. See the basic example `lattigo/examples/he/hefloat/bootstrapping/basic` for an introduction into the bootstrapping. Use the flag -short to run the examples fast but with insecure parameters.