Abstract
In a standard quantum key distribution (QKD) scheme such as BB84, twoprocedures, error correction and privacy amplification, areapplied to extract a final secure key from a raw key generatedfrom quantum transmission. To simplify the study of protocols,it is commonly assumed that the two procedures can be decoupledfrom each other. While such a decoupling assumption may be validfor individual attacks, it is actually unproven in the contextof ultimate or unconditional security, which is the HolyGrail of quantum cryptography. In particular, this means thatthe application of standard efficient two-way error-correctionprotocols like Cascade is not proven to be unconditionallysecure. Here, I provide the first proof of such a decouplingprinciple in the context of unconditional security. The methodrequires Alice and Bob to share some initial secret string anduse it to encrypt their communications in the error correctionstage using one-time-pad encryption. Consequently, I prove theunconditional security of the interactive Cascade protocolproposed by Brassard and Salvail for error correction and modifiedby one-time-pad encryption of the error syndrome, followedby the random matrix protocol for privacy amplification. This isan efficient protocol in terms of both computational power andkey generation rate. My proof uses the entanglement purificationapproach to security proofs of QKD. Theproof applies to all adaptive symmetric methods for errorcorrection, which cover all existing methods proposed for BB84.In terms of the net key generation rate, the new method is asefficient as the standard Shor-Preskill proof.
Highlights
An important application of quantum information processing is quantum key distribution (QKD) [1,2]
It was first suggested by Deutsch et al [5] that entanglement purification procotols (EPPs) can correct errors introduced by the eavesdroppers and allow the two communicating parties, Alice and Bob, to obtain perfectly entangled quantum systems, socalled EPR pairs, from which they can generate a secure key
A main contribution of this paper is to show that such a decoupling is, possible for error correction and privacy amplification
Summary
An important application of quantum information processing is quantum key distribution (QKD) [1,2]. The application of entanglement purification approach to QKD implies a non-trivial constraint between the two processes, namely the corresponding measurement operators employed by Alice and Bob must be locally commuting. I propose a novel method to remove this local commutability constraint, allowing us to decouple the error correction process from the privacy amplification process This amounts to much simplification in the study of both processes. I prove the unconditional security of a modified version of the Cascade scheme [12] for error correction invented by Brassard and Salvail, (followed by, for example, a random hashing procedure for privacy amplification [6]). Note that the proposed method can be employed as a sub-routine in concatenated entanglement purification procedures, including those involving two-way classical communications, as studied by [13] and those involving degenerate codes [14]
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