  Entanglement purification provides a unifying framework for proving the
security of quantum key distribution schemes. Nonetheless, up till now, a local
commutability constraint in the CSS code construction means that the error
correction and privacy amplification procedures of BB84 are not fully
decoupled. Here, I provide a method to decouple the two processes completely.
The method requires Alice and Bob to share some initial secret string and use
it to encrypt the bit-flip error syndrome using one-time-pad encryption. As an
application, I prove the unconditional security of the interactive Cascade
protocol, proposed by Brassard and Salvail for error correction, modified by
one-time-pad encryption of the error syndrome, and followed by the random
matrix protocol for privacy amplification. This is an efficient protocol in
terms of both computational power and key generation rate.
