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Volumn 72, Issue 2, 2006, Pages 321-391

Lower bounds for non-black-box zero knowledge

Author keywords

Argument systems; Interactive proof systems; Non black box simulation; Pseudorandom generators; Randomness extractors; Zero knowledge

Indexed keywords

COMPUTATIONAL COMPLEXITY; CRYPTOGRAPHY;

EID: 32844469026     PISSN: 00220000     EISSN: 10902724     Source Type: Journal    
DOI: 10.1016/j.jcss.2005.06.010     Document Type: Article
Times cited : (36)

References (67)
  • 1
    • 0034909808 scopus 로고    scopus 로고
    • On pseudorandomness and resource-bounded measure
    • V. Arvind, and J. Köbler On pseudorandomness and resource-bounded measure Theoret. Comput. Sci. 255 1-2 2001 205 221
    • (2001) Theoret. Comput. Sci. , vol.255 , Issue.1-2 , pp. 205-221
    • Arvind, V.1    Köbler, J.2
  • 2
    • 0023995534 scopus 로고
    • Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes
    • L. Babai, and S. Moran Arthur-Merlin Games: A Randomized Proof System and a Hierarchy of Complexity Classes J. Comput. System Sci. 36 1988 254 276
    • (1988) J. Comput. System Sci. , vol.36 , pp. 254-276
    • Babai, L.1    Moran, S.2
  • 3
    • 0035166072 scopus 로고    scopus 로고
    • How to go beyond the black-box simulation barrier
    • IEEE
    • B. Barak, How to go beyond the black-box simulation barrier, in: Proceedings of the 42nd FOCS, IEEE, 2001, pp. 106-115. (preliminary full version available on http://www.wisdom.weizmann.ac.il/~boaz ).
    • (2001) Proceedings of the 42nd FOCS , pp. 106-115
    • Barak, B.1
  • 4
    • 79960802129 scopus 로고    scopus 로고
    • Universal arguments and their applications
    • Preliminary version appeared in CCC' 2002
    • B. Barak, O. Goldreich, Universal arguments and their applications, Cryptology ePrint Archive, Report 2001/105, 2001 (Preliminary version appeared in CCC' 2002).
    • (2001) Cryptology ePrint Archive, Report , vol.2001 , Issue.105
    • Barak, B.1    Goldreich, O.2
  • 5
    • 0036041101 scopus 로고    scopus 로고
    • Strict polynomial-time in simulation and extraction
    • Extended form appeared in STOC' 02
    • B. Barak, Y. Lindell, Strict polynomial-time in simulation and extraction, Cryptology ePrint Archive, Report 2002/043, 2002. http://eprint.iacr.org/. Extended form appeared in STOC' 02.
    • (2002) Cryptology ePrint Archive, Report , vol.2002 , Issue.43
    • Barak, B.1    Lindell, Y.2
  • 7
    • 33749576517 scopus 로고    scopus 로고
    • Derandomization in cryptography
    • D. Boneh (Ed.), Advances in Cryptology - CRYPTO '03, 17-21 August 2003 Springer, New York
    • B. Barak, S.J. Ong, S. Vadhan, Derandomization in cryptography, in: D. Boneh (Ed.), Advances in Cryptology - CRYPTO '03, 17-21 August 2003, Lecture Notes in Computer Science, vol. 2729, Springer, New York.
    • Lecture Notes in Computer Science , vol.2729
    • Barak, B.1    Ong, S.J.2    Vadhan, S.3
  • 8
    • 2942747407 scopus 로고    scopus 로고
    • A note on negligible functions
    • M. Bellare A note on negligible functions J. Cryptology 15 4 2002 271 284
    • (2002) J. Cryptology , vol.15 , Issue.4 , pp. 271-284
    • Bellare, M.1
  • 10
    • 0035163053 scopus 로고    scopus 로고
    • Resettably-sound zero-knowledge and its applications
    • Record 2001/063, Cryptology ePrint Archive, August Appeared in 2001
    • B. Barak, O. Goldreich, S. Goldwasser, Y. Lindell, Resettably-sound zero-knowledge and its applications, Record 2001/063, Cryptology ePrint Archive, August 2001 (Appeared in 42nd FOCS, 2001).
    • (2001) 42nd FOCS
    • Barak, B.1    Goldreich, O.2    Goldwasser, S.3    Lindell, Y.4
  • 11
    • 26444589620 scopus 로고    scopus 로고
    • The knowledge-of-exponent Assumptions and 3-round zero-knowledge protocols
    • M. Bellare, A. Palacio, The knowledge-of-exponent Assumptions and 3-round zero-knowledge protocols, Cryptology ePrint Archive, Report 2004/008, 2004. http://eprint.iacr.org/.
    • (2004) Cryptology ePrint Archive, Report , vol.2004 , Issue.8
    • Bellare, M.1    Palacio, A.2
  • 12
    • 84968518238 scopus 로고
    • Factoring polynomials over large finite fields
    • E.R. Berlekamp Factoring polynomials over large finite fields Math. Comput. 24 1970
    • (1970) Math. Comput. , vol.24
    • Berlekamp, E.R.1
  • 14
    • 32844471446 scopus 로고
    • (see also SIGACT News 15(1) (1983)).
    • (1983) SIGACT News , vol.15 , Issue.1
  • 16
    • 85032878466 scopus 로고
    • Everything in NP can be argued in perfect zero-knowledge in a bounded number of rounds
    • Eurocrypt '89
    • G. Brassard, C. Crépeau, M. Yung, Everything in NP can be argued in perfect zero-knowledge in a bounded number of rounds, in: Eurocrypt '89, 1989, pp. 192-195, LNCS No. 434.
    • (1989) LNCS No. 434 , vol.434 , pp. 192-195
    • Brassard, G.1    Crépeau, C.2    Yung, M.3
  • 17
    • 0035163054 scopus 로고    scopus 로고
    • Universally composable security, a new paradigm for cryptographic protocols extended abstract
    • IEEE Computer Society Los Alamitos, CA
    • R. Canetti Universally composable security, a new paradigm for cryptographic protocols extended abstract 42nd IEEE Symposium on Foundations of Computer Science, Las Vegas, NV, 2001 2001 IEEE Computer Society Los Alamitos, CA 136 145
    • (2001) 42nd IEEE Symposium on Foundations of Computer Science, Las Vegas, NV, 2001 , pp. 136-145
    • Canetti, R.1
  • 19
    • 0034830279 scopus 로고    scopus 로고
    • Black-box concurrent zero-knowledge requires Ω̃(log n) rounds
    • Record 2001/051, Cryptology ePrint Archive, June Extended abstract appeared
    • R. Canetti, J. Kilian, E. Petrank, A. Rosen, Black-box concurrent zero-knowledge requires Ω̃(log n) rounds, Record 2001/051, Cryptology ePrint Archive, June 2001 (Extended abstract appeared in STOC' 01).
    • (2001) STOC' 01
    • Canetti, R.1    Kilian, J.2    Petrank, E.3    Rosen, A.4
  • 20
    • 35248854495 scopus 로고    scopus 로고
    • On the limitations of universally composable two-party computation without set-up assumptions
    • R. Canetti, E. Kushilevitz, Y. Lindell, On the limitations of universally composable two-party computation without set-up assumptions, in: EUROCRYPT '03, 2003, pp. 68-86.
    • (2003) EUROCRYPT '03 , pp. 68-86
    • Canetti, R.1    Kushilevitz, E.2    Lindell, Y.3
  • 21
    • 1142282343 scopus 로고    scopus 로고
    • Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack
    • R. Cramer, V. Shoup, Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack, Cryptology ePrint Archive, Report 2001/108, 2001. http://eprint.iacr.org/.
    • (2001) Cryptology ePrint Archive, Report , vol.2001 , Issue.108
    • Cramer, R.1    Shoup, V.2
  • 22
    • 32844455626 scopus 로고
    • Proofs of partial knowledge and simplified design of witness hiding protocols
    • R. Cramer, B. Schoenmakers, and I. Damgård Proofs of partial knowledge and simplified design of witness hiding protocols CWI Quart. 8 2 1995 111 127
    • (1995) CWI Quart. , vol.8 , Issue.2 , pp. 111-127
    • Cramer, R.1    Schoenmakers, B.2    Damgård, I.3
  • 23
    • 85029541173 scopus 로고
    • Towards practical public-key cryptosystems provably-secure against chosen-ciphertext attack
    • J. Feigenbaum Springer New York
    • I. Damgård Towards practical public-key cryptosystems provably-secure against chosen-ciphertext attack J. Feigenbaum Advances in Cryptology - CRYPTO '91, Lecture Notes in Computer Science vol. 576 1991 Springer New York 445 456 1991 11-15 August
    • (1991) Advances in Cryptology - CRYPTO '91, Lecture Notes in Computer Science , vol.576 , pp. 445-456
    • Damgård, I.1
  • 27
    • 84976826800 scopus 로고
    • Zero knowledge proofs of knowledge in two rounds
    • Crypto '89 Springer, Berlin
    • U. Feige, A. Shamir, Zero knowledge proofs of knowledge in two rounds, in: Crypto '89, Lecture Notes in Computer Science, vol. 435, Springer, Berlin, 1989, pp. 526-545.
    • (1989) Lecture Notes in Computer Science , vol.435 , pp. 526-545
    • Feige, U.1    Shamir, A.2
  • 28
    • 84990731886 scopus 로고
    • How to prove yourself: Practical solutions to identification and signature problems
    • Crypto '86
    • A. Fiat, A. Shamir, How to prove yourself: practical solutions to identification and signature problems, in: Crypto '86, Lecture Notes in Computer Science, vol. 263, 1986, pp. 186-194.
    • (1986) Lecture Notes in Computer Science , vol.263 , pp. 186-194
    • Fiat, A.1    Shamir, A.2
  • 29
    • 0027306732 scopus 로고
    • A uniform-complexity treatment of encryption and zero-knowledge
    • O. Goldreich A uniform-complexity treatment of encryption and zero-knowledge J. Cryptology 6 1 1993 21 53
    • (1993) J. Cryptology , vol.6 , Issue.1 , pp. 21-53
    • Goldreich, O.1
  • 33
    • 0000108216 scopus 로고    scopus 로고
    • How to construct constant-round zero-knowledge proof systems for NP
    • O. Goldreich, and A. Kahan How to construct constant-round zero-knowledge proof systems for NP J. Cryptology 9 3 1996 167 189
    • (1996) J. Cryptology , vol.9 , Issue.3 , pp. 167-189
    • Goldreich, O.1    Kahan, A.2
  • 34
    • 0029767165 scopus 로고    scopus 로고
    • On the composition of zero proof systems
    • O. Goldreich, and H. Krawczyk On the composition of zero proof systems SIAM J. Comput. 25 1 1996 169 192 (preliminary version appeared in ICALP' 90)
    • (1996) SIAM J. Comput. , vol.25 , Issue.1 , pp. 169-192
    • Goldreich, O.1    Krawczyk, H.2
  • 35
    • 71149116146 scopus 로고
    • Proofs that yield nothing but their validity or all languages in NP have zero-knowledge proof systems
    • 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. ACM 38 3 1991 691 729
    • (1991) J. ACM , vol.38 , Issue.3 , pp. 691-729
    • Goldreich, O.1    Micali, S.2    Wigderson, A.3
  • 36
    • 0028676264 scopus 로고
    • Definitions and properties of zero-knowledge proof systems
    • O. Goldreich, and Y. Oren Definitions and properties of zero-knowledge proof systems J. Cryptology 7 1 1994 1 32 (preliminary version in FOCS' 87)
    • (1994) J. Cryptology , vol.7 , Issue.1 , pp. 1-32
    • Goldreich, O.1    Oren, Y.2
  • 37
    • 0242381728 scopus 로고    scopus 로고
    • On interactive proofs with a Laconic prover
    • O. Goldreich, S. Vadhan, and A. Wigderson On interactive proofs with a Laconic prover Comput. Complex. 11 2002 1 53 (Extended abstract in ICALP '01)
    • (2002) Comput. Complex. , vol.11 , pp. 1-53
    • Goldreich, O.1    Vadhan, S.2    Wigderson, A.3
  • 38
    • 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 1 1989 186 208 (preliminary version in STOC' 85)
    • (1989) SIAM J. Comput. , vol.18 , Issue.1 , pp. 186-208
    • Goldwasser, S.1    Micali, S.2    Rackoff, C.3
  • 39
    • 32844456747 scopus 로고    scopus 로고
    • On the (In)security of the Fiat-Shamir paradigm
    • Extended abstract appears in these proceedings
    • S. Goldwasser, Y. Tauman, On the (In)security of the Fiat-Shamir paradigm. Cryptology ePrint Archive, Report 2003/034, 2003, Extended abstract appears in these proceedings.
    • (2003) Cryptology ePrint Archive, Report , vol.2003 , Issue.34
    • Goldwasser, S.1    Tauman, Y.2
  • 40
    • 84947558992 scopus 로고
    • A "paradoxical" identity-based signature scheme resulting from zero-knowledge
    • Advances in Cryptology - CRYPTO '88, Santa Barbara, CA, 1988 Springer, Berlin
    • L.C. Guillou, J.-J. Quisquater, A "paradoxical" identity-based signature scheme resulting from zero-knowledge, in: Advances in Cryptology - CRYPTO '88, Santa Barbara, CA, 1988, Lecture Notes in Computer Science, vol. 403, Springer, Berlin, 1990, pp. 216-231.
    • (1990) Lecture Notes in Computer Science , vol.403 , pp. 216-231
    • Guillou, L.C.1    Quisquater, J.-J.2
  • 41
    • 84927764036 scopus 로고    scopus 로고
    • On the existence of 3-round zero-knowledge protocols
    • Advances in cryptology - CRYPTO '98 Santa Barbara, CA, 1998, Springer, Berlin
    • S. Hada, T. Tanaka, On the existence of 3-round zero-knowledge protocols, in: Advances in cryptology - CRYPTO '98, Lecture Notes in Computer Science, Santa vol. 1462, Barbara, CA, 1998, Springer, Berlin, 1998, pp. 408-423.
    • (1998) Lecture Notes in Computer Science , vol.1462 , pp. 408-423
    • Hada, S.1    Tanaka, T.2
  • 42
    • 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 4 1999 1364 1396
    • (1999) SIAM J. Comput. , vol.28 , Issue.4 , pp. 1364-1396
    • Håstad, J.1    Impagliazzo, R.2    Levin, L.A.3    Luby, M.4
  • 43
    • 0030706544 scopus 로고    scopus 로고
    • P = BPP if e requires exponential circuits: Derandomizing the XOR lemma
    • ACM New York
    • R. Impagliazzo, and A. Wigderson P = BPP if E Requires Exponential Circuits: Derandomizing the XOR Lemma Proceedings of the 29th STOC 1997 ACM New York 220 229
    • (1997) Proceedings of the 29th STOC , pp. 220-229
    • Impagliazzo, R.1    Wigderson, A.2
  • 44
    • 38249043088 scopus 로고
    • Random generation of combinatorial structures from a uniform distribution
    • M.R. Jerrum, L.G. Valiant, and V.V. Vazirani Random generation of combinatorial structures from a uniform distribution Theoret. Comput. Sci. 43 2-3 1986 169 188
    • (1986) Theoret. Comput. Sci. , vol.43 , Issue.2-3 , pp. 169-188
    • Jerrum, M.R.1    Valiant, L.G.2    Vazirani, V.V.3
  • 45
    • 0026963441 scopus 로고
    • A note on efficient zero-knowledge proofs and arguments (extended abstract)
    • ACM New York
    • J. Kilian A note on efficient zero-knowledge proofs and arguments (extended abstract) Proceedings of the 24th STOC 1992 ACM New York 723 732
    • (1992) Proceedings of the 24th STOC , pp. 723-732
    • Kilian, J.1
  • 46
    • 32844460502 scopus 로고    scopus 로고
    • Concurrent zero-knowledge in poly-logarithmic rounds cryptology
    • preliminary version appeared in STOC'01
    • J. Kilian, E. Petrank, Concurrent zero-knowledge in poly-logarithmic rounds cryptology, ePrint Archive, Report 2000/013, 2000 (preliminary version appeared in STOC' 01).
    • (2000) ePrint Archive, Report , vol.2000 , Issue.13
    • Kilian, J.1    Petrankr, E.2
  • 48
    • 0036588881 scopus 로고    scopus 로고
    • Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses
    • A.R. Klivans, and D. van Melkebeek Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses SIAM J. Comput. 31 5 2002 1501 1526
    • (2002) SIAM J. Comput. , vol.31 , Issue.5 , pp. 1501-1526
    • Klivans, A.R.1    Van Melkebeek, D.2
  • 49
    • 0002602811 scopus 로고
    • Universal search problems
    • L.A. Levin Universal search problems Problemy Peredači Inform. 9 3 1973 115 116
    • (1973) Problemy Peredači Inform. , vol.9 , Issue.3 , pp. 115-116
    • Levin, L.A.1
  • 53
    • 0001448484 scopus 로고
    • Bit Commitment Using Pseudorandomness
    • M. Naor Bit Commitment Using Pseudorandomness J. Cryptology 4 2 1991 151 158 (preliminary version in CRYPTO' 89)
    • (1991) J. Cryptology , vol.4 , Issue.2 , pp. 151-158
    • Naor, M.1
  • 54
    • 35248818856 scopus 로고    scopus 로고
    • On cryptographic assumptions and challenges
    • D. Boneh (Ed.), Advances in Cryptology - CRYPTO '03, 17-21 August Springer, Berlin
    • M. Naor, On cryptographic assumptions and challenges, in: D. Boneh (Ed.), Advances in Cryptology - CRYPTO '03, 17-21 August 2003, Lecture Notes in Computer Science, vol. 2729, Springer, Berlin.
    • (2003) Lecture Notes in Computer Science , vol.2729
    • Naor, M.1
  • 56
    • 84875762817 scopus 로고
    • Provably secure and practical identification schemes and corresponding signature schemes
    • Advances in Cryptology - CRYPTO '92, Santa Barbara, CA, 1992 Springer, Berlin
    • T. Okamoto, Provably secure and practical identification schemes and corresponding signature schemes, in: Advances in Cryptology - CRYPTO '92, Santa Barbara, CA, 1992, Lecture Notes in Computer Science, vol. 740, Springer, Berlin, 1993, pp. 31-53.
    • (1993) Lecture Notes in Computer Science , vol.740 , pp. 31-53
    • Okamoto, T.1
  • 57
    • 84927727752 scopus 로고    scopus 로고
    • Security proofs for signature schemes
    • Advances in Cryptology - EUROCRYPT'96, Saragossa, 1996 Springer, Berlin
    • D. Pointcheval, J. Stern, Security proofs for signature schemes, in: Advances in Cryptology - EUROCRYPT '96, Saragossa, 1996, Lecture Notes in Computer Science, vol. 1070, Springer, Berlin, 1996, pp. 387-398.
    • (1996) Lecture Notes in Computer Science , vol.1070 , pp. 387-398
    • Pointcheval, D.1    Stern, J.2
  • 60
    • 84957621865 scopus 로고    scopus 로고
    • On the concurrent composition of zero-knowledge proofs
    • Springer, Berlin
    • R. Richardson, J. Kilian, On the concurrent composition of zero-knowledge proofs. in: Eurocrypt '99, vol. 1592, Springer, Berlin (1999).
    • (1999) Eurocrypt'99 , vol.1592
    • Richardson, R.1    Kilian, J.2
  • 61
    • 84983126760 scopus 로고    scopus 로고
    • A note on the round-complexity of concurrent zero-knowledge
    • Crypto '00 Springer, Berlin
    • A. Rosen, A note on the round-complexity of concurrent zero-knowledge. in: Crypto '00, Lecture Notes in Computer Science, vol. 1880, Springer, Berlin, 2000.
    • (2000) Lecture Notes in Computer Science , vol.1880
    • Rosen, A.1
  • 62
    • 0344794410 scopus 로고    scopus 로고
    • A complete problem for statistical zero knowledge
    • A. Sahai, and S. Vadhan A complete problem for statistical zero knowledge J. ACM 50 2 2003 196 249 (Extended abstract in FOCS '97)
    • (2003) J. ACM , vol.50 , Issue.2 , pp. 196-249
    • Sahai, A.1    Vadhan, S.2
  • 63
    • 12344258539 scopus 로고
    • Efficient signature generation by smart cards
    • C.P. Schnorr Efficient signature generation by smart cards J. Cryptology 4 3 1991 161 174
    • (1991) J. Cryptology , vol.4 , Issue.3 , pp. 161-174
    • Schnorr, C.P.1
  • 64
    • 0035175916 scopus 로고    scopus 로고
    • Simple extractors for all min-entropies and a new pseudo-random generator
    • IEEE
    • R. Shaltiel, and C. Umans Simple extractors for all min-entropies and a new pseudo-random generator Proceedings of the 42st FOCS 2001 IEEE 648 657
    • (2001) Proceedings of the 42st FOCS , pp. 648-657
    • Shaltiel, R.1    Umans, C.2
  • 66
    • 0032631071 scopus 로고    scopus 로고
    • Computing with very weak random sources
    • A. Srinivasan, and D. Zuckerman Computing with very weak random sources SIAM J. Comput. 28 4 1999 1433 1459 (electronic)
    • (1999) SIAM J. Comput. , vol.28 , Issue.4 , pp. 1433-1459
    • Srinivasan, A.1    Zuckerman, D.2
  • 67
    • 0000787513 scopus 로고
    • On approximation algorithms for #P
    • L. Stockmeyer On approximation algorithms for #P SIAM J. Comput. 14 4 1985 849 861
    • (1985) SIAM J. Comput. , vol.14 , Issue.4 , pp. 849-861
    • Stockmeyer, L.1


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