Noise tolerance of the BB84 protocol with random privacy amplification

Watanabe, Shun; Matsumoto, Ryutaroh; Uyematsu, R.

doi:10.1109/isit.2005.1523492

Cited by 7 publications

(16 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a result, Alice and Bob obtains sifted key k A , k B ∈ F n 2 , respectively. 2) Alice picks a random number r A ∈ F l 2 , and By using the widely used proof technique due to Shor and Preskill [37], [13], [41], [18], the unconditonal security of this protocol has been shown for the case where F consists of the completely random linear functions [41], [18]. On the other hand, by using the quantum de Finneti representation theorem, Renner proved the unconditional security of the BB84 protocol using universal 2 hash functions for privacy amplification [35].…”

Section: Quantum Key Distributionmentioning

confidence: 99%

“…In Section VI, we apply these results to the security proof of a QKD protocol called the Bennett-Brassard 1984 (BB84) protocol [2]. We use the proof technique of the Shor-Preskilltype, which reduces the security of a secret key to the error correcting property of the Calderbank-Shor-Steane (CSS) quantum error correcting code (e.g., [37], [13], [41], [18]). This proof technique is elegant and widely used, but also has a drawback.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dual Universality of Hash Functions and Its Applications to Quantum Cryptography

Tsurumaru

Hayashi

2013

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

In this paper, we introduce the concept of dual universality of hash functions and present its applications to quantum cryptography. We begin by establishing the one-toone correspondence between a linear function family F and a code family C, and thereby defining ε-almost dual universal2 hash functions, as a generalization of the conventional universal2 hash functions. Then we show that this generalized (and thus broader) class of hash functions is in fact sufficient for the security of quantum cryptography. This result can be explained in two different formalisms. First, by noting its relation to the δ-biased family introduced by Dodis and Smith, we demonstrate that Renner's two-universal hashing lemma is generalized to our class of hash functions. Next, we prove that the proof technique by Shor and Preskill can be applied to quantum key distribution (QKD) systems that use our generalized class of hash functions for privacy amplification. While Shor-Preskill formalism requires an implementer of a QKD system to explicitly construct a linear code of the Calderbank-Shor-Steane type, this result removes the existing difficulty of the construction a linear code of CSS code by replacing it by the combination of an ordinary classical error correcting code and our proposed hash function. We also show that a similar result applies to the quantum wire-tap channel.Finally we compare our results in the two formalisms and show that, in typical QKD scenarios, the Shor-Preskill-type argument gives better security bounds in terms of the trace distance and Holevo information, than the method based on the δ-biased family.

show abstract

Section: Quantum Key Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dual Universality of Hash Functions and Its Applications to Quantum Cryptography

Tsurumaru

Hayashi

2013

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…Hence, the security level of a real system is also finite and needs to be precisely quantified. This problem has been theoretically addressed in a few security proofs [11][12][13][14][15][16][17][18], some of which also guarantee composable security [19,20]. Most of them consider a QKD setup running with the BB84 protocol [2] and making use of an ideal single-photon source.…”

Section: Introductionmentioning

confidence: 99%

Efficient decoy-state quantum key distribution with quantified security

et al. 2013

View full text Add to dashboard Cite

show abstract

“…It is stated in [12] and proved in [14] that random choice of [n − nh(q Z )]-dimensional subspace C 2 in C 1 almost always gives the low phase error decoding probability in the standard CSS decoding procedure. This implies that randomly chosen [n − nh(q Z )]-dimensional subspace C 2 in C 1 can almost always correct HZ errors on Γ.…”

Section: Security Proof and Analysis Of The Key Ratementioning

confidence: 99%

Key Rate Available from Mismatched Measurements in the BB84 Protocol and the Uncertainty Principle

Matsumoto

Watanabe

2008

IEICE Transactions on Fundamentals of Electronics, Communicatio

Self Cite

View full text Add to dashboard Cite

We consider the mismatched measurements in the BB84 quantum key distribution protocol, in which measuring bases are different from transmitting bases. We give a lower bound on the amount of a secret key that can be extracted from the mismatched measurements. Our lower bound shows that we can extract a secret key from the mismatched measurements with certain quantum channels, such as the channel over which the Hadamard matrix is applied to each qubit with high probability. Moreover, the entropic uncertainty principle implies that one cannot extract the secret key from both matched measurements and mismatched ones simultaneously, when we use the standard information reconciliation and privacy amplification procedure. key words: BB84, mismatched measurement, quantum key distribution

show abstract

Noise tolerance of the BB84 protocol with random privacy amplification

Cited by 7 publications

References 23 publications

Dual Universality of Hash Functions and Its Applications to Quantum Cryptography

Dual Universality of Hash Functions and Its Applications to Quantum Cryptography

Efficient decoy-state quantum key distribution with quantified security

Key Rate Available from Mismatched Measurements in the BB84 Protocol and the Uncertainty Principle

Contact Info

Product

Resources

About