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arXiv:quant-ph/0502179 · Physical Review A

Upper bounds of a class of imperfect quantum sealing protocols

Guang-Ping He

Published May 31, 2005• 10 citations
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Abstract

The model of the quantum protocols sealing a classical bit is studied. It is shown that there exist upper bounds on its security. For any protocol where the bit can be read correctly with the probability $\ensuremath{\alpha}$, and reading the bit can be detected with the probability $\ensuremath{\beta}$, the upper bounds are $\ensuremath{\beta}\ensuremath{\leqslant}1∕2$ and $\ensuremath{\alpha}+\ensuremath{\beta}\ensuremath{\leqslant}9∕8$.

DOI
10.1103/physreva.71.054304

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The model of the quantum protocols sealing a classical bit is studied. It is shown that there exist upper bounds on its security. For any protocol where the bit can be read correctly with the probability \ensuremathα\ensuremath{\alpha}\ensuremathα, and reading the bit can be detected with the probability \ensuremathβ\ensuremath{\beta}\ensuremathβ, the upper bounds are \ensuremathβ\ensuremath⩽1∕2\ensuremath{\beta}\ensuremath{\leqslant}1∕2\ensuremathβ\ensuremath⩽1∕2 and \ensuremathα+\ensuremathβ\ensuremath⩽9∕8\ensuremath{\alpha}+\ensuremath{\beta}\ensuremath{\leqslant}9∕8\ensuremathα+\ensuremathβ\ensuremath⩽9∕8.
Abstract: A quantum sealing protocol is a quantum cryptographic protocol that can detect unsealing of a message. It is known that quantum bit sealing is insecure. However, this does not imply that quantum string sealing is also insecure. So the possibility of quantum string sealing has been studied. In this paper, we propose a quantum sealing protocol and give an information theoretic analysis. We also show that our protocol is almost optimal for uniformly distributed inputs in the sense that the upper bound of information leaks almost matches the trivial lower bound.
Oblivious transfer is a fundamental primitive in cryptography. While perfect information theoretic security is impossible, quantum oblivious transfer protocols can limit the dishonest player's cheating. Finding the optimal security parameters in such protocols is an important open question. In this paper we show that every 1-out-of-2 oblivious transfer protocol allows a dishonest party to cheat with probability bounded below by a constant strictly larger than 1/21/21/2. Alice's cheating is defined as her probability of guessing Bob's index, and Bob's cheating is defined as his probability of guessing both input bits of Alice. In our proof, we relate these cheating probabilities to the cheating probabilities of a bit commitment protocol and conclude by using lower bounds on quantum bit commitment. Then, we present an oblivious transfer protocol with two messages and cheating probabilities at most 3/43/43/4. Last, we extend Kitaev's semidefinite programming formulation to more general primitives, where the security is against a dishonest player trying to force the outcome of the other player, and prove optimal lower and upper bounds for them.
We obtain strict upper bounds on the bit transmission rate for communication of Classical bit codewords over Quantum channels. Albeit previous arguments in arXiv: 1804.01797 which have demonstrated that lower bounds can be shown to hold for the bit transmission rate without the presence of significant noise over the channel shared by Alice and Bob for the purposes of encoding, decoding, transmission and authentication, the author suggests that upper bounding the bit transmission rate could be of use towards classifying paradoxical aspects of communication protocols, as well as constructing error correcting codes which are resilient to noise. The upper bound that is obtained in this work for the bit transmission rate, as a converse result, is dependent upon the natural logarithm of the size of each player's alphabet, as well as smaller alphabets, which can be leveraged for simultaneously realizing Quantum advantage for maximizing error correction and minimizing false acceptance. Crucially, the upper bound to the bit transmission rate is dependent upon a pruning procedure, which seeks to determine whether letters from player's alphabets can be removed so that prospective Quantum advantage, in order for Alice and Bob to implement error correction protocols with high probability, despite the fact that there is more noise over the channel between Alice and Bob in comparison to that between Bob and Eve.
We consider the cryptographic task of bit-string generation. This is a generalization of coin tossing in which two mistrustful parties wish to generate a string of random bits such that an honest party can be sure that the other cannot have biased the string too much. We consider a quantum protocol for this task, originally introduced in Phys. Rev. A 69, 022322 (2004), that is feasible with present day technology. We introduce security conditions based on the average bias of the bits and the Shannon entropy of the string. For each, we prove rigorous security bounds for this protocol in both noiseless and noisy conditions under the most general attacks allowed by quantum mechanics. Roughly speaking, in the absence of noise, a cheater can only bias significantly a vanishing fraction of the bits, whereas in the presence of noise, a cheater can bias a constant fraction, with this fraction depending quantitatively on the level of noise. We also discuss classical protocols for the same task, deriving upper bounds on how well a classical protocol can perform. This enables the determination of how much noise the quantum protocol can tolerate while still outperforming classical protocols. We raise several conjectures concerning both quantum and classical possibilities for large nnn cryptography. An experiment corresponding to the scheme analyzed in this paper has been performed and is reported elsewhere.