The best algorithms for the Learning Parity with Noise (LPN) problem require sub-exponential time and memory. This often makes memory, and not time, the limiting factor for practical attacks, which seem to be out of reach even for relatively small parameters. In this paper, we try to bring the state-of-the-art in solving LPN closer to the practical realm. We improve upon the existing algorithms by modifying the Coded-BKW algorithm to work under various memory constrains. We correct and expand previous analysis and experimentally verify our findings. As a result we were able to mount practical attacks on the largest parameters reported to date using only 239bits of memory.

We present KEMTLS, an alternative to the TLS 1.3 handshake that uses key-encapsulation mechanisms (KEMs) instead of signatures for server authentication. Among existing post-quantum candidates, signature schemes generally have larger public key/signature sizes compared to the public key/ciphertext sizes of KEMs: by using an IND-CCA-secure KEM for server authentication in post-quantum TLS, we obtain multiple benefits. A size-optimized post-quantum instantiation of KEMTLS requires less than half the bandwidth of a size-optimized post-quantum instantiation of TLS 1.3. In a speed-optimized instantiation, KEMTLS reduces the amount of server CPU cycles by almost 90% compared to TLS 1.3, while at the same time reducing communication size, reducing the time until the client can start sending encrypted application data, and eliminating code for signatures from the server's trusted code base.