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## Computational Collapse of Quantum State with Application to Oblivious Transfer (2003)

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Citations: | 15 - 1 self |

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961 |
Quantum cryptography: Public key distribution and coin tossing
- Bennett, Brassard
- 1984
(Show Context)
Citation Context ...rity proof applies when computionally binding commitments are used. The CK protocol can be seen as a quantum reduction of 1-2 OT to bit commitment. To see how it works, consider the BB84 coding scheme=-=[2,6]-=- for classical 376 C. Crépeau et al. bit b into a random state in { b〉+, b〉×}. θ ∈ {+,×} used to encode b into the quantum state b〉θ, is called the transmission basis. Since only orthogonal quantum s... |

555 |
Theory and application of trapdoor functions
- Yao
- 1982
(Show Context)
Citation Context ...from +n to b ⊕ s ⊕ t using (9). From (18), we follow the evolution through Ẽ†nσZẼn, T⊗θB⊗bCn Φ+n 〉 Ẽ † nσzẼn −→ ∑ s,t,v : tθ vb⊕s⊕t (−1)bt ⊕ sv ⊕ vv √ 2 n+|θ|+|b⊕s⊕t| b ⊕ s ⊕ t〉Θ ψb⊕s⊕t,s⊕v〉 =-=(19)-=- = ∑ x,y,v : v⊕x⊕yθ vθ⊕x (−1)bθ ⊕ bx ⊕ by ⊕ vy √ 2 n+|θ|+|θ⊕x| θ ⊕ x〉Θ ψθ⊕x,b⊕y〉 (20) = ∑ yx (−1)bθ ⊕ bx ⊕ by √ 2 n+|θ|+|θ⊕x|−2|θ∧x̄| θ ⊕ x〉Θ ψθ⊕x,b⊕y〉 = ∑ yx (−1)bθ ⊕ bx ⊕ by √ 2 n+|x| ... |

376 |
How to exchange secrets by oblivious transfer
- Rabin
- 1981
(Show Context)
Citation Context ...hereas a random bit is received when θ̂ = θ. In other words, If Bob announces the transmission basis a the end of the transmission then the BB84 coding scheme implements a Rabin’s oblivious transfer =-=[16]-=- from Bob to Alice provided she is honest. Otherwise, Alice can easily cheat the protocol by postponing the measurement until the basis is announced. In this case she gets the transmitted bit all the ... |

199 | Limits on the provable consequences of one-way permutations
- Impagliazzo, Rudich
- 1989
(Show Context)
Citation Context ...blak-box access to a perfect commitment scheme there exists a secure 1 − 2 quantum oblivious transfer (i.e. 1-2 QOT) scheme[6,3,4]. Classically, it is known that such a reduction is unlikely to exist =-=[10]-=-. By 12 QOT we mean a standard oblivious transfer of two classical messages using quantum communication. In [6], Crépeau and Kilian have shown how 1-2 QOT can be obtained from perfect commitments (i.... |

176 | Unconditionally secure quantum bit commitment is impossible
- Mayers
- 1997
(Show Context)
Citation Context ...of such a generalized 1-2 QOT. If 2-party cryptography in the quantum world seems to rely upon weaker assumptions than its classical counterpart, it also shares some of its limits. As it was shown in =-=[12,14,11]-=-, no statistically binding and concealing quantum bit commitment can exist. On the other hand, quantum commitments can be based upon physical[17] and computational[8,7] assumptions. A natural question... |

133 | Achieving oblivious transfer using weakened security assumptions, white plains, new york
- Crepeau, Kilian
- 1988
(Show Context)
Citation Context ...ting. Our analysis assumes for simplicity that A and B have access to a perfect quantum channel. Nevertheless, noise may be tolerated if we construct 1-2 QOT along the lines of BBCS [3] instead of CK =-=[6]-=-. 7 Open Questions An obvious open problem is how to build Fnm-string commitments from computationally binding bit commitment schemes. In particular, how one can transform the computationally binding ... |

89 | Practical Quantum Oblivious Transfer
- Bennett, Brassard, et al.
- 1992
(Show Context)
Citation Context ... differs from its classical counterpart in at least one important way: Given blak-box access to a perfect commitment scheme there exists a secure 1 − 2 quantum oblivious transfer (i.e. 1-2 QOT) scheme=-=[6,3,4]-=-. Classically, it is known that such a reduction is unlikely to exist [10]. By 12 QOT we mean a standard oblivious transfer of two classical messages using quantum communication. In [6], Crépeau and ... |

70 | Is quantum bit commitment really possible
- Lo, Chau
- 1997
(Show Context)
Citation Context ...of such a generalized 1-2 QOT. If 2-party cryptography in the quantum world seems to rely upon weaker assumptions than its classical counterpart, it also shares some of its limits. As it was shown in =-=[12,14,11]-=-, no statistically binding and concealing quantum bit commitment can exist. On the other hand, quantum commitments can be based upon physical[17] and computational[8,7] assumptions. A natural question... |

61 | On the reversibility of oblivious transfer
- Crépeau, Sántha
- 1991
(Show Context)
Citation Context ... differs from its classical counterpart in at least one important way: Given blak-box access to a perfect commitment scheme there exists a secure 1 − 2 quantum oblivious transfer (i.e. 1-2 QOT) scheme=-=[6,3,4]-=-. Classically, it is known that such a reduction is unlikely to exist [10]. By 12 QOT we mean a standard oblivious transfer of two classical messages using quantum communication. In [6], Crépeau and ... |

51 | Security of quantum protocols against coherent measurements
- YAO
- 1995
(Show Context)
Citation Context ...ssumption was relaxed in [15] by showing that privacy for the sender is garanteed against any individual measurements applied by the receiver. The security against any receiver was obtained by Yao in =-=[20]-=-. This important paper provides a full proof of security for 1-2 QOT when constructed from perfect commitments under the assumption that the quantum channel is error-free. Yao’s result was then genera... |

50 | Quantum key distribution and string oblivious transfer in noisy channels
- Mayers
- 1996
(Show Context)
Citation Context ...t paper provides a full proof of security for 1-2 QOT when constructed from perfect commitments under the assumption that the quantum channel is error-free. Yao’s result was then generalized by Mayers=-=[13]-=- for the case of noisy quantum channel [3] and where strings are transmitted instead of bits. Mayers then reduced the security of quantum key distribution to the security of such a generalized 1-2 QOT... |

43 | Perfectly concealing quantum bit commitment from any quantum one-way permutation
- Dumais, Mayers, et al.
- 2000
(Show Context)
Citation Context ...An obvious open problem is how to build Fnm-string commitments from computationally binding bit commitment schemes. In particular, how one can transform the computationally binding bit commitments of =-=[8]-=- and [7] into Fnm–binding string commitments? This would show that QMCs and therefore 1-2 QOT can 392 C. Crépeau et al. be based upon any one-way permutation[8] and/or any one-way function[7]. It is ... |

39 | Limits on the power of quantum statistical zero-knowledge
- Watrous
- 2002
(Show Context)
Citation Context ...p(s) is not necessarily able to compute simultaneously the openings of all or even a subset of all strings s. In particular, classical security proof techniques like rewinding have no quantum analogue=-=[9,18]-=-. A committer (to a concealing commitment) can always commit upon any superposition of values for s that will remain such until the opening phase. A honest committer does not necessarily know a single... |

35 | A quantum Goldreich-Levintheorem with cryptographic applications
- Adcock, Cleve
- 2002
(Show Context)
Citation Context ...r) and computationally secure against Alice (i.e. the receiver) provided the string commitment scheme used to construct the QMC is Fnmbinding. As for the quantum version of the Goldreich-Levin theorem=-=[1]-=- and the computationally binding commitments of [8] and [7], our result clearly indicates that 2-party quantum cryptography in the computational setting can be based upon different if not weaker assum... |

20 | Quantum oblivious transfer is secure against all individ- ual measurements
- MAYERS, SALVAIL
- 1994
(Show Context)
Citation Context ...ocol). The security analysis of the CK protocol was provided by Crépeau in [4] with respect to receivers restricted to perform only immediate and complete measurements. The assumption was relaxed in =-=[15]-=- by showing that privacy for the sender is garanteed against any individual measurements applied by the receiver. The security against any receiver was obtained by Yao in [20]. This important paper pr... |

14 | L.: How to convert the flavor of a quantum bit commitment
- Crépeau, Légaré, et al.
- 2001
(Show Context)
Citation Context ...limits. As it was shown in [12,14,11], no statistically binding and concealing quantum bit commitment can exist. On the other hand, quantum commitments can be based upon physical[17] and computational=-=[8,7]-=- assumptions. A natural question arises: What happens to the security of the CK protocol when computationally secure commitments are used instead of perfect ones? It should be stressed that Yao’s proo... |

14 | Quantum Bit Commitment from a Physical Assumption,” CRYPTO
- Salvail
- 1998
(Show Context)
Citation Context ...so shares some of its limits. As it was shown in [12,14,11], no statistically binding and concealing quantum bit commitment can exist. On the other hand, quantum commitments can be based upon physical=-=[17]-=- and computational[8,7] assumptions. A natural question arises: What happens to the security of the CK protocol when computationally secure commitments are used instead of perfect ones? It should be s... |

10 | Towards a Formal Definition of Security for Quantum Protocols
- Graaf
- 1997
(Show Context)
Citation Context ...p(s) is not necessarily able to compute simultaneously the openings of all or even a subset of all strings s. In particular, classical security proof techniques like rewinding have no quantum analogue=-=[9,18]-=-. A committer (to a concealing commitment) can always commit upon any superposition of values for s that will remain such until the opening phase. A honest committer does not necessarily know a single... |

3 |
The Trouble With Quantum Bit Commitment”, available at http://xxx.lanl.gov/abs/quant-ph/9603015
- Mayers
- 1996
(Show Context)
Citation Context ...of such a generalized 1-2 QOT. If 2-party cryptography in the quantum world seems to rely upon weaker assumptions than its classical counterpart, it also shares some of its limits. As it was shown in =-=[12,14,11]-=-, no statistically binding and concealing quantum bit commitment can exist. On the other hand, quantum commitments can be based upon physical[17] and computational[8,7] assumptions. A natural question... |