메뉴 건너뛰기




Volumn 39, Issue 1, 2009, Pages 25-58

Zero-knowledge against quantum attacks

Author keywords

Interactive proof systems; Quantum cryptography; Zero knowledge

Indexed keywords

3-COLORING; COMMITMENT SCHEME; COMMON REFERENCE STRING MODELS; COMPLETE PROBLEMS; COMPLEXITY CLASS; GRAPH ISOMORPHISM; INTERACTIVE PROOF SYSTEM; INTERACTIVE PROOF SYSTEMS; OF QUANTUM-INFORMATION; QUANTUM INTERACTIVE PROOF SYSTEMS; ZERO KNOWLEDGE PROOF; ZERO-KNOWLEDGE; ZERO-KNOWLEDGE PROTOCOLS;

EID: 67650135522     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/060670997     Document Type: Conference Paper
Times cited : (169)

References (46)
  • 1
    • 84937413657 scopus 로고    scopus 로고
    • A quantum Goldreich-Levin theorem with cryptographic applications
    • Proceedings of the 19th International Symposium on Theoretical Aspects of Computer Science, Springer-Verlag, New York
    • M. ADCOCK AND R. CLEVE, A quantum Goldreich-Levin theorem with cryptographic applications, in Proceedings of the 19th International Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Comput. Sci. 2285, Springer-Verlag, New York, 2002, pp. 323-334.
    • (2002) Lecture Notes in Comput. Sci , vol.2285 , pp. 323-334
    • ADCOCK, M.1    CLEVE, R.2
  • 5
    • 0004151496 scopus 로고    scopus 로고
    • Springer-Verlag, New York
    • R. BHATIA, Matrix Analysis, Springer-Verlag, New York, 1997.
    • (1997) Matrix Analysis
    • BHATIA, R.1
  • 8
    • 67650143292 scopus 로고    scopus 로고
    • G. BRASSARD, P. Høyer, M. MOSCA, AND A. TAPP, Quantum amplitude amplification and estimation, in Quantum Computation and Quantum Information: A Millennium Contemp. Math. 305, AMS, Providence, RI, 2002, pp. 53-74.
    • G. BRASSARD, P. Høyer, M. MOSCA, AND A. TAPP, Quantum amplitude amplification and estimation, in Quantum Computation and Quantum Information: A Millennium Volume, Contemp. Math. 305, AMS, Providence, RI, 2002, pp. 53-74.
  • 9
    • 35048864318 scopus 로고    scopus 로고
    • Zero-knowledge proofs and string commitments withstanding quantum attacks
    • Advances in Cryptology, CRYPTO 2004: 24th Annual International Cryptology Conference, Springer-Verlag, New York
    • I. DAMGÅRD, S. FEHR, AND L. SALVAIL, Zero-knowledge proofs and string commitments withstanding quantum attacks, in Advances in Cryptology - CRYPTO 2004: 24th Annual International Cryptology Conference, Lecture Notes in Comput. Sci. 3152, Springer-Verlag, New York, 2004, pp. 254-272.
    • (2004) Lecture Notes in Comput. Sci , vol.3152 , pp. 254-272
    • DAMGÅRD, I.1    FEHR, S.2    SALVAIL, L.3
  • 10
    • 0021420540 scopus 로고
    • The complexity of promise problems with applications to public-key cryptography
    • S. EVEN, A. SELMAN, AND Y. YACOBI, The complexity of promise problems with applications to public-key cryptography, Inform. and Control, 61 (1984), pp. 159-173.
    • (1984) Inform. and Control , vol.61 , pp. 159-173
    • EVEN, S.1    SELMAN, A.2    YACOBI, Y.3
  • 11
    • 0001328001 scopus 로고    scopus 로고
    • Quantum-state disturbance versus information gain: Uncertainty relations for quantum information
    • C. FUCHS AND A. PERES, Quantum-state disturbance versus information gain: Uncertainty relations for quantum information, Phys. Rev. A (3), 53 (1996), pp. 2038-2045.
    • (1996) Phys. Rev. A , vol.53 , Issue.3 , pp. 2038-2045
    • FUCHS, C.1    PERES, A.2
  • 12
    • 0032667067 scopus 로고    scopus 로고
    • Cryptographic distinguishability measures for quantum-mechanical states
    • C. FUCHS AND J. VAN DE GRAAF, Cryptographic distinguishability measures for quantum-mechanical states, IEEE Trans. Inform. Theory, 45 (1999), pp. 1216-1227.
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 1216-1227
    • FUCHS, C.1    VAN DE GRAAF, J.2
  • 14
    • 67650106960 scopus 로고
    • On Promise Problems (a Survey in Memory of Shimon Even
    • Electronic Colloquium on Computational Complexity, Report TR05-018, 2005
    • O. GOLDREICH, On Promise Problems (a Survey in Memory of Shimon Even [1935-2004]), Electronic Colloquium on Computational Complexity, Report TR05-018, 2005.
    • (1935)
    • GOLDREICH, O.1
  • 15
    • 0034205405 scopus 로고    scopus 로고
    • On the limits of nonapproximability of lattice problems
    • O. GOLDREICH AND S. GOLDWASSER, On the limits of nonapproximability of lattice problems, J. Comput. System Sci., 60 (2000), pp. 540-563.
    • (2000) J. Comput. System Sci , vol.60 , pp. 540-563
    • GOLDREICH, O.1    GOLDWASSER, S.2
  • 16
    • 0029767165 scopus 로고    scopus 로고
    • On the composition of zero-knowledge proof systems
    • O. GOLDREICH AND H. KRAWCZYK, On the composition of zero-knowledge proof systems, SIAM J. Comput., 25 (1996), pp. 169-192.
    • (1996) SIAM J. Comput , vol.25 , pp. 169-192
    • GOLDREICH, O.1    KRAWCZYK, H.2
  • 17
    • 71149116146 scopus 로고
    • Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems
    • Mach
    • O. GOLDREICH, S. MICALI, AND A. WIGDERSON, Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems, J. Assoc. Comput. Mach., 38 (1991), pp. 691-729.
    • (1991) J. Assoc. Comput , vol.38 , pp. 691-729
    • GOLDREICH, O.1    MICALI, S.2    WIGDERSON, A.3
  • 19
    • 0032691797 scopus 로고    scopus 로고
    • Comparing entropies in statistical zero-knowledge with applications to the structure of SZK
    • IEEE Computer Society, Los Alamitos, CA
    • O. GOLDREICH AND S. VADHAN, Comparing entropies in statistical zero-knowledge with applications to the structure of SZK, in Proceedings of the 14th Annual IEEE Conference on Computational Complexity, IEEE Computer Society, Los Alamitos, CA, 1999, pp. 54-73.
    • (1999) Proceedings of the 14th Annual IEEE Conference on Computational Complexity , pp. 54-73
    • GOLDREICH, O.1    VADHAN, S.2
  • 20
    • 0024611659 scopus 로고
    • The knowledge complexity of interactive proof systems
    • S. GOLDWASSER, S. MICALI, AND C. RACKOFF, The knowledge complexity of interactive proof systems, SIAM J. Comput., 18 (1989), pp. 186-208.
    • (1989) SIAM J. Comput , vol.18 , pp. 186-208
    • GOLDWASSER, S.1    MICALI, S.2    RACKOFF, C.3
  • 23
    • 4243807288 scopus 로고    scopus 로고
    • Quantum mechanics helps in searching for a needle in a haystack
    • L. GROVER, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett., 79 (1997), pp. 325-328.
    • (1997) Phys. Rev. Lett , vol.79 , pp. 325-328
    • GROVER, L.1
  • 24
    • 0345253860 scopus 로고    scopus 로고
    • A pseudorandom generator from any one-way function
    • J. HÅSTAD, R. IMPAGLIAZZO, L. A. LEVIN, AND M. LUBY, A pseudorandom generator from any one-way function, SIAM J. Comput., 28 (1999), pp. 1364-1396.
    • (1999) SIAM J. Comput , vol.28 , pp. 1364-1396
    • HÅSTAD, J.1    IMPAGLIAZZO, R.2    LEVIN, L.A.3    LUBY, M.4
  • 25
    • 0000107375 scopus 로고
    • Essai sur la géométriè a n dimensions
    • C. JORDAN, Essai sur la géométriè a n dimensions, Bull. Soc. Math. France, 3 (1875), pp. 103-174.
    • (1875) Bull. Soc. Math. France , vol.3 , pp. 103-174
    • JORDAN, C.1
  • 26
    • 0040052002 scopus 로고    scopus 로고
    • Quantum computations: Algorithms and error correction
    • A. KITAEV, Quantum computations: Algorithms and error correction, Russian Math. Surveys, 52 (1997), pp. 1191-1249.
    • (1997) Russian Math. Surveys , vol.52 , pp. 1191-1249
    • KITAEV, A.1
  • 28
    • 0033720106 scopus 로고    scopus 로고
    • Parallelization, amplification, and exponential time simulation of quantum interactive proof system
    • ACM, New York
    • A. KITAEV AND J. WATROUS, Parallelization, amplification, and exponential time simulation of quantum interactive proof system, in Proceedings of the 32nd ACM Symposium on Theory of Computing, ACM, New York, 2000, pp. 608-617.
    • (2000) Proceedings of the 32nd ACM Symposium on Theory of Computing , pp. 608-617
    • KITAEV, A.1    WATROUS, J.2
  • 29
    • 35248815564 scopus 로고    scopus 로고
    • Non-interactive quantum perfect and statistical zero-knowledge
    • ISAAC 2003: Proceedings of the 14th International Symposium on Algorithms and Computation, Springer-Verlag, New York
    • H. KOBAYASHI, Non-interactive quantum perfect and statistical zero-knowledge, in ISAAC 2003: Proceedings of the 14th International Symposium on Algorithms and Computation, Lecture Notes in Comput. Sci. 2906, Springer-Verlag, New York, 2003, pp. 178-188.
    • (2003) Lecture Notes in Comput. Sci , vol.2906 , pp. 178-188
    • KOBAYASHI, H.1
  • 30
    • 0001260566 scopus 로고    scopus 로고
    • IS quantum bit commitment really possible?
    • H.-K. LO AND H. F. CHAU, IS quantum bit commitment really possible?, Phys. Rev. Lett., 78 (1997), pp. 3410-3413.
    • (1997) Phys. Rev. Lett , vol.78 , pp. 3410-3413
    • LO, H.-K.1    CHAU, H.F.2
  • 31
    • 21244472246 scopus 로고    scopus 로고
    • Quantum Arthur-Merlin games
    • C. MARRIOTT AND J. WATROUS, Quantum Arthur-Merlin games, Comput. Complexity, 14 (2005), pp. 122-152.
    • (2005) Comput. Complexity , vol.14 , pp. 122-152
    • MARRIOTT, C.1    WATROUS, J.2
  • 33
    • 0001336918 scopus 로고    scopus 로고
    • Unconditionally secure quantum bit commitment is impossible
    • D. MAYERS, Unconditionally secure quantum bit commitment is impossible, Phys. Rev. Lett., 78 (1997), pp. 3414-3417.
    • (1997) Phys. Rev. Lett , vol.78 , pp. 3414-3417
    • MAYERS, D.1
  • 34
    • 3042730516 scopus 로고    scopus 로고
    • Unconditional security in quantum cryptography
    • D. MAYERS, Unconditional security in quantum cryptography, J. ACM, 48 (2001), pp. 351-406.
    • (2001) J. ACM , vol.48 , pp. 351-406
    • MAYERS, D.1
  • 36
    • 0001448484 scopus 로고
    • Bit commitment using pseudorandomness
    • M. NAOR, Bit commitment using pseudorandomness, J. Cryptology, 4 (1991), pp. 151-158.
    • (1991) J. Cryptology , vol.4 , pp. 151-158
    • NAOR, M.1
  • 39
    • 67650179619 scopus 로고    scopus 로고
    • private communication
    • O. REGEV, private communication, 2006.
    • (2006)
    • REGEV, O.1
  • 40
    • 0017930809 scopus 로고
    • A method for obtaining digital signatures and public-key cryptosystems
    • R. L. RIVEST, A. SHAMIR, AND L. ADLEMAN, A method for obtaining digital signatures and public-key cryptosystems, Comm. ACM, 21 (1978), pp. 120-126.
    • (1978) Comm. ACM , vol.21 , pp. 120-126
    • RIVEST, R.L.1    SHAMIR, A.2    ADLEMAN, L.3
  • 41
    • 0344794410 scopus 로고    scopus 로고
    • A complete promise problem for statistical zero-knowledge
    • A. SAHAI AND S. VADHAN, A complete promise problem for statistical zero-knowledge, J. ACM, 50 (2003), pp. 196-249.
    • (2003) J. ACM , vol.50 , pp. 196-249
    • SAHAI, A.1    VADHAN, S.2
  • 42
    • 0142051871 scopus 로고    scopus 로고
    • Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer
    • P. W. SHOR, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput., 26 (1997), pp. 1484-1509.
    • (1997) SIAM J. Comput , vol.26 , pp. 1484-1509
    • SHOR, P.W.1
  • 43
    • 0347090658 scopus 로고    scopus 로고
    • Simple proof of security of the BB84 quantum key distribution protocol
    • P. SHOR AND J. PRESKILL, Simple proof of security of the BB84 quantum key distribution protocol, Phys. Rev. Lett., 85 (2000), pp. 441-444.
    • (2000) Phys. Rev. Lett , vol.85 , pp. 441-444
    • SHOR, P.1    PRESKILL, J.2
  • 46
    • 33746708860 scopus 로고
    • A single quantum cannot be cloned
    • W. WOOTTERS AND W. ZUREK, A single quantum cannot be cloned, Nature, 299 (1982), pp. 802-803.
    • (1982) Nature , vol.299 , pp. 802-803
    • WOOTTERS, W.1    ZUREK, W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.