Insecurity of imperfect quantum bit seal

Chau, H. F.

doi:10.1016/j.physleta.2006.01.022

Cited by 6 publications

(16 citation statements)

References 7 publications

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“…[8] here is that I replace the classical L 1 distance by the probability of distinguishing two classical probability distributions. The later concept readily extends to the case of N > 2.…”

Section: Discussionmentioning

confidence: 99%

“…In addition, he obtained a lower bound for the fidelity of the resultant quantum state after a measurement. More importantly, this lower bound is greater than 1/2 and is attainable by certain quantum sealing schemes [8].…”

Section: Introductionmentioning

confidence: 89%

“…Moreover, the scheme is perfect if Bob can determine the entire classical message with certainty; otherwise, the scheme is imperfect [8].…”

Section: Quantum Sealmentioning

confidence: 99%

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Quantum string seal is insecure

Chau

2007

Phys. Rev. A

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A quantum string seal encodes the value of a (bit) string as a quantum state in such a way that everyone can extract a non-negligible amount of available information on the string by a suitable measurement. Moreover, such measurement must disturb the quantum state and is likely to be detected by an authorized verifier. In this way, the intactness of the encoded quantum state plays the role of a wax seal in the digital world. Here I analyze the security of quantum string seal by studying the information disturbance tradeoff of a measurement. This information disturbance tradeoff analysis extends the earlier results of Bechmann-Pasquinucci et al. and Chau by concluding that all quantum string seals are insecure. Specifically, I find a way to obtain non-trivial available information on the string that escapes the verifier's detection with at least 50% chance.

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“…[8] here is that I replace the classical L 1 distance by the probability of distinguishing two classical probability distributions. The later concept readily extends to the case of N > 2.…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 89%

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Quantum string seal is insecure

Chau

2007

Phys. Rev. A

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“…(To avoid confusion, it should be noted that there is another quantum cryptographic task that can be found in the literature under the name of a quantum seal. [4,5,6,7,8] The task introduced here is quite distinct from the quantum seal protocols that have been introduced, both in its goal and in its execution. See [9] for further comments.…”

Section: Discussionmentioning

confidence: 99%

Fishing for Eavesdroppers

Lopata,

Bahder

2007

Preprint

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“…[4]). It was claimed that the security bounds of imperfect quantum single bit seal obtained by He [5] are not tight, while Chau proved that all imperfect quantum bit seals are insecure, and obtained a greater lower bound [4]. But in fact, Chau's model of quantum bit seal studied in Ref.…”

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confidence: 99%

Comment on “Quantum string seal is insecure”

2007

Phys. Rev. A

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In a recent paper [1], Chau claimed that all quantum string seals are insecure. The core of Chau's attack strategy is the measurement(see Eq. (29) of that reference). It was claimed that with this measurement, the attacker can obtain non-trivial information on the sealed string while escapes the verifier's detection with at least 50% chance. However, the paper concentrated only on the fidelity of the sealed state corresponding to the attacker's measurement, without providing a detailed evaluation on the amount of information obtained by the attacker. Here it will be shown that for a class of quantum string seal protocols including the one proposed by He [2], this amount of information is only trivial. Therefore in contrast to Chau's claim, quantum string seal can be unconditionally secure. In fact, the general proof on why Chau's attack strategy fails had already been well addressed in Ref. [3]. Briefly, consider a simple model of imperfect quantum string seal, in which the sealed state for the message i ′ is taken aswhere the notation is the same as that in Eq. (1) of Ref.[1]. Applying the measurement Q i0 on it yieldsThus the probability for the message i ′ to be decoded as i by the attacker iswhere ν is defined by Eq. (12) It means that any one of the N possible choices of the message i ′ has at least the probability 1/(2N ) to be decoded as message i, even if its content is completely irrelevant with i. In other words, whenever the attacker obtains a message i via the measurement strategy, there is at less a probability p i = i ′ 1/(2N ) = 1/2 that the original message can be anything, i. e., the amount of information he obtained is zero. Thus it can be seen that the attack strategy is useless. Though at half of the time it can escape the verifier's detection, the amount of information obtained on the sealed message is only trivial. Therefore Chau's claim that all quantum seals are insecure is wrong. Now it will be shown that the protocol proposed in Ref.[2] is indeed such a secure quantum string seal. In this protocol, to seal a stringThus by takingwhere f m (θ m ) is cos θ m (sin θ m ) if the m-th bit of the string j ′ equals to (does not equal to) that of the string i ′ , we can see that the protocol belongs to the class of quantum string seal described by Eq. (2). Therefore as shown above, it cannot be broken by Chau's attack strategy. In Sec. IV of Ref.[1], it was claimed that "the major loophole in He's proof of the security of his quantum string seal in Ref.[2] is that he incorrectly assumed that measuring all the qubits is the only method to obtain a significant portion of information of the sealed message". But this is obviously incorrect. In the paragraph before Eq. (5) of Ref. [2], it was clearly written that the general security proof starts as follows. Let H denotes the 2 n dimensional Hilbert space where the sealed state lives

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Insecurity of imperfect quantum bit seal

Cited by 6 publications

References 7 publications

Quantum string seal is insecure

Quantum string seal is insecure

Fishing for Eavesdroppers

Comment on “Quantum string seal is insecure”

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