Stream privacy amplification for quantum cryptography

Privacy amplification is the key step to guarantee the security of quantum communication. The existing security proofs require accumulating a large number of raw key bits for privacy amplification. This is similar to block ciphers in classical cryptography that would delay the final key generation since an entire block must be accumulated before privacy amplification. Moreover, any leftover errors after information reconciliation would corrupt the entire block. By modifying the security proof based on quantum error correction, we develop a stream privacy amplification scheme, which resembles the classical stream cipher. This scheme can output the final key in a stream way, prevent error from spreading, and hence can put privacy amplification before information reconciliation. The stream scheme can also help to enhance the security of trusted-relay quantum networks. Inspired by the connection between stream ciphers and quantum error correction in our security analysis, we further develop a generic information-theoretic tool to study the security of classical encryption algorithms.