A lattice-based McEliece scheme for encryption and signature

The classical McEliece scheme for combined encryption and coding is based on error-correcting codes. We study a variation where codes are replaced by lattices. Dealing with continuous rather than discrete signals eliminates most classical attacks. Decoding a lattice is known to be NP-complete and an universal decoding algorithm is discussed in low dimensions (≤ 100). Classes of lattices with polynomial time decoding algorithms are explored. Further, by replacing decoding by complete decoding, a scheme is obtained which combines signature and quantizing.