bstract. There is a heavy preference towards instantiating BGV and
BFV homomorphic encryption schemes where the cyclotomic order m is a power of two, as this admits highly efficient fast Fourier transforma tions. Field Instruction Multiple Data (FIMD) was introduced to increase packing capacity in the case of small primes and improve amortised per formance, using reverse multiplication-friendly embeddings (RMFEs) to encode more data into each SIMD slot. However, FIMD currently does not admit bootstrapping. In this work, we achieve bootstrapping for RMFE-packed ciphertexts with low capacity loss. We first adapt the digit extraction algorithm to work over RMFE-packed ciphertexts, by applying the recode map after every evaluation of the lifting polynomial. This allows us to follow the blueprint of thin bootstrapping, performing digit extraction on a single ciphertext. To achieve the low capacity loss, we introduce correction maps to the Halevi-Shoup digit extraction algorithm, to remove all but the final recode of RMFE digit extraction. We implement several workflows for bootstrapping RMFE-packed ci phertexts in HElib, and benchmark them against thin bootstrapping for m =32768. Our experiments show that the basic strategy of recoding multiple times in digit extraction yield better data packing, but result in very low remaining capacity and latencies of up to hundreds of sec onds. On the other hand, using correction maps gives up to 6 additional
