Bootstrapping in FHEW-like Cryptosystems

FHEW and TFHE are fully homomorphic encryption (FHE) cryptosystems that can evaluate arbitrary Boolean circuits on encrypted data by bootstrapping after each gate evaluation. The FHEW cryptosystem was originally designed based on standard (Ring, circular secure) LWE assumptions, and its initial implementation was able to run bootstrapping in less than 1 second. The TFHE cryptosystem used somewhat stronger assumptions, such as (Ring, circular secure) LWE over the torus with binary secret distribution, and applied several other optimizations to reduce the bootstrapping runtime to less than 0.1 second. Up to now, the gap between the underlying security assumptions prevented a fair comparison of the cryptosystems for the same security settings.