{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T15:22:08Z","timestamp":1768922528409,"version":"3.49.0"},"publisher-location":"Berlin, Heidelberg","reference-count":35,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540573401","type":"print"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/3-540-48071-4_3","type":"book-chapter","created":{"date-parts":[[2007,8,6]],"date-time":"2007-08-06T01:23:49Z","timestamp":1186363429000},"page":"31-53","source":"Crossref","is-referenced-by-count":309,"title":["Provably Secure and Practical Identification Schemes and Corresponding Signature Schemes"],"prefix":"10.1007","author":[{"given":"Tatsuaki","family":"Okamoto","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"3_CR1","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/3-540-45961-8_7","volume-title":"Proceedings of Eurocrypt\u2019 88","author":"T. Beth","year":"1988","unstructured":"T. Beth, \u201cEfficient Zero-Knowledge Identification Scheme for Smart Cards,\u201d Proceedings of Eurocrypt\u2019 88, LNCS 330, Springer-Verlag, pp.77\u201386 (1988)."},{"key":"3_CR2","unstructured":"E.F. Brickell, D.M. Gordon, K.S. McCurley, and D. Wilson, \u201cFast Exponentiation with Precomputation\u201d, to appear in the Proceedings of Eurocrypt\u2019 92."},{"key":"3_CR3","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/BF00191319","volume":"5","author":"E.F. Brickell","year":"1992","unstructured":"E.F. Brickell, and K.S. McCurley, \u201cAn Interactive Identification Scheme Based on Discrete Logarithms and Factoring,\u201d Journal of Cryptology, Vol. 5, No. 1, pp.29\u201339 (1992).","journal-title":"Journal of Cryptology"},{"key":"3_CR4","doi-asserted-by":"crossref","unstructured":"E.F. Brickell, and K.S. McCurley, \u201cInteractive Identification and Digital Signatures,\u201d AT&T Technical Journal, pp.73\u201386, November\/December (1991).","DOI":"10.1002\/j.1538-7305.1991.tb00139.x"},{"key":"3_CR5","doi-asserted-by":"crossref","unstructured":"M. Bellare, S. Micali and R. Ostrovsky, \u201cPerfect Zero-Knowledge in Constant Rounds,\u201d Proceedings of STOC, pp.482\u2013493 (1990).","DOI":"10.1145\/100216.100283"},{"key":"3_CR6","doi-asserted-by":"crossref","unstructured":"M. Bellare, S. Micali and R. Ostrovsky, \u201cThe (True) Complexity of Statistical Zero-Knowledge.\u201d Proceedings of STOC, pp.494\u2013502 (1990).","DOI":"10.1145\/100216.100285"},{"issue":"10","key":"3_CR7","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1145\/4372.4373","volume":"28","author":"D. Chaum","year":"1985","unstructured":"D. Chaum, \u201cSecurity without Identification: Transaction Systems to Make Big Brother Obsolete,\u201d Comm. of the ACM, 28,10, pp.1030\u20131044 (1985).","journal-title":"Comm. of the ACM"},{"key":"3_CR8","unstructured":"L. Chen, I. Damg\u00e5rd, \u201cSecurity Bounds for Parallel Versions of Identification Protocols,\u201d Manuscript (1992)."},{"key":"3_CR9","doi-asserted-by":"crossref","unstructured":"U. Feige and A. Shamir, \u201cWitness Indistinguishable and Witness Hiding Protocols,\u201d Proceedings of STOC, pp.416\u2013426 (1990).","DOI":"10.1145\/100216.100272"},{"key":"3_CR10","series-title":"Lect Notes Comput Sci","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1007\/0-387-34805-0_46","volume-title":"Proceedings of Crypto\u2019 89","author":"U. Feige","year":"1990","unstructured":"U. Feige and A. Shamir, \u201cZero Knowledge Proofs of Knowledge in Two Rounds,\u201d Proceedings of Crypto\u2019 89, LNCS 435, Springer-Verlag, pp.526\u2013544 (1990)."},{"key":"3_CR11","doi-asserted-by":"crossref","unstructured":"U. Feige, A. Fiat and A. Shamir, \u201cZero Knowledge Proofs of Identity,\u201d Proceedings of STOC, pp.210\u2013217 (1987).","DOI":"10.1145\/28395.28419"},{"key":"3_CR12","series-title":"Lect Notes Comput Sci","first-page":"186","volume-title":"Proceedings of CRYPTO\u2019 86","author":"A. Fiat","year":"1987","unstructured":"A. Fiat and A. Shamir, \u201cHow to Prove Yourself: Practical Solutions to Identification and Signature Problems\u201d, Proceedings of CRYPTO\u2019 86, LNCS 263, Springer-Verlag, pp.186\u2013194 (1987)."},{"key":"3_CR13","doi-asserted-by":"crossref","unstructured":"O. Goldreich, S. Goldwasser, and S. Micali, \u201cHow to Construct Random Functions,\u201d Journal of the ACM, Vol. 33, No. 4 (1986).","DOI":"10.1145\/6490.6503"},{"key":"3_CR14","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1007\/BFb0032038","volume-title":"Proceedings of ICALP","author":"O. Goldreich","year":"1990","unstructured":"O. Goldreich and H. Krawczyk \u201cOn the Composition of Zero-Knowledge Proof Systems,\u201d Proceedings of ICALP, LNCS 443, Springer-Verlag, pp.268\u2013282 (1990)."},{"issue":"1","key":"3_CR15","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1137\/0218012","volume":"18","author":"S. Goldwasser","year":"1989","unstructured":"S. Goldwasser, S. Micali and C. Rackoff, \u201cThe Knowledge Complexity of Interactive Proofs,\u201d SIAM J. Comput., 18,1, pp.186\u2013208 (1989).","journal-title":"SIAM J. Comput."},{"issue":"2","key":"3_CR16","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1137\/0217017","volume":"17","author":"S. Goldwasser","year":"1988","unstructured":"S. Goldwasser, S. Micali and R. Rivest, \u201cA Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks,\u201d SIAM J. Comput., 17,2, pp.281\u2013308 (1988).","journal-title":"SIAM J. Comput."},{"key":"3_CR17","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/3-540-45961-8_11","volume-title":"Proceedings of Eurocrypt\u2019 88","author":"L.S. Guillou","year":"1988","unstructured":"L.S. Guillou, and J.J. Quisquater, \u201cA Practical Zero-Knowledge Protocol Fitted to Security Microprocessors Minimizing both Transmission and Memory,\u201d Proceedings of Eurocrypt\u2019 88, LNCS 330, Springer-Verlag, pp.123\u2013128 (1988)."},{"key":"3_CR18","unstructured":"G. Harper, A.J. Menezes, S.A. Vanstone, \u201cPublic-Key Cryptosystems with Very Small Key Length\u201d, to appear in the Proceedings of Eurocrypt\u2019 92."},{"key":"3_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4684-0310-7","volume-title":"A Course in Number Theory and Cryptography","author":"N. Koblitz","year":"1987","unstructured":"N. Koblitz, A Course in Number Theory and Cryptography, Berlin: Springer-Verlag, (1987)."},{"key":"3_CR20","unstructured":"N. Koblitz, \u201cCM-Curves with Good Cryptographic Properties,\u201d Proceedings of Crypto\u2019 91 (1992)."},{"key":"3_CR21","unstructured":"D.E. Knuth, The Art of Computer Programming, Vol. 2, 2nd Ed. Addison-Wesley (1981)."},{"key":"3_CR22","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/3-540-39799-X_31","volume-title":"Proceedings of Crypto\u2019 85","author":"V. Miller","year":"1986","unstructured":"V. Miller, \u201cUses of Elliptic Curves in Cryptography,\u201d Proceedings of Crypto\u2019 85, LNCS 218, Springer-Verlag, pp.417\u2013426 (1986)."},{"key":"3_CR23","series-title":"Lect Notes Comput Sci","volume-title":"On Ordinary Elliptic Curve Cryptosystems","author":"A. Miyaji","year":"1991","unstructured":"A. Miyaji, \u201cOn Ordinary Elliptic Curve Cryptosystems,\u201d to appear in the Proceedings of Asiacrypt\u2019 91, LNCS, Springer-Verlag."},{"key":"3_CR24","doi-asserted-by":"publisher","first-page":"519","DOI":"10.2307\/2007970","volume":"44","author":"P.L. Montgomery","year":"1985","unstructured":"P.L. Montgomery, \u201cModular Multiplication without Trial Division,\u201d Math. of Computation, Vol. 44, pp.519\u2013521 (1985).","journal-title":"Math. of Computation"},{"key":"3_CR25","doi-asserted-by":"crossref","unstructured":"A.J. Menezes, T. Okamoto, S.A. Vanstone, \u201cReducing Elliptic Curve Logarithms to Logarithms in a Finite Field\u201d, Proceedings of STOC, pp.80\u201389 (1991).","DOI":"10.1145\/103418.103434"},{"key":"3_CR26","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1007\/0-387-34799-2_17","volume-title":"Proceedings of Crypto\u2019 88","author":"K. Ohta","year":"1990","unstructured":"K. Ohta, and T. Okamoto, \u201cA Modification of the Fiat-Shamir Scheme,\u201d Proceedings of Crypto\u2019 88, LNCS 403, Springer-Verlag, pp.232\u2013243 (1990)."},{"key":"3_CR27","unstructured":"K. Ohta, and T. Okamoto, \u201cA Digital Multisignature Scheme Based on the Fiat-Shamir Scheme,\u201d to appear in the Proceedings of Asiacrypt\u2019 91."},{"issue":"10","key":"3_CR28","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1002\/scj.4690181002","volume":"18","author":"T. Okamoto","year":"1987","unstructured":"T. Okamoto, \u201cA Single Public-Key Authentication Scheme for Multiple Users,\u201d Systems and Computers in Japan, 18,10, pp.14\u201324 (1987), Previous version, Technical Report of IECE Japan, IN83\u201392 (1984).","journal-title":"Systems and Computers in Japan"},{"key":"3_CR29","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/3-540-46885-4_16","volume-title":"Proceedings of Eurocrypt\u2019 89","author":"T. Okamoto","year":"1990","unstructured":"T. Okamoto, and K. Ohta, \u201cDivertible Zero-Knowledge Interactive Proofs and Commutative Random Self-Reducible.\u201d Proceedings of Eurocrypt\u2019 89, LNCS 434, Springer-Verlag, pp.134\u2013149 (1990)."},{"key":"3_CR30","doi-asserted-by":"publisher","first-page":"106","DOI":"10.1109\/TIT.1978.1055817","volume":"24","author":"S.C. Pohlig","year":"1978","unstructured":"S.C. Pohlig, and M.E. Hellman, \u201cAn Improved Algorithm for Computing Logarithmsover GF (p) and Its Cryptographic Significance,\u201d IEEE Trans. Inform. Theory, 24, pp.106\u2013110 (1978)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"2","key":"3_CR31","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R. Rivest","year":"1978","unstructured":"R. Rivest, A. Shamir and L. Adleman, \u201cA Method for Obtaining Digital Signatures and Public-Key Cryptosystems\u201d, Communications of the ACM, Vol. 21, No. 2, pp.120\u2013126 (1978).","journal-title":"Communications of the ACM"},{"issue":"3","key":"3_CR32","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/BF00196725","volume":"4","author":"C.P. Schnorr","year":"1991","unstructured":"C.P. Schnorr, \u201cEfficient Signature Generation by Smart Cards,\u201d Journal of Cryptology, Vol. 4, No. 3, pp.161\u2013174 (1991).","journal-title":"Journal of Cryptology"},{"key":"3_CR33","series-title":"Lect Notes Comput Sci","first-page":"47","volume-title":"Proceedings of Crypto\u2019 84","author":"A. Shamir","year":"1986","unstructured":"A. Shamir, \u201cIdentity-Based Cryptosystems and Signature Scheme,\u201d Proceedings of Crypto\u2019 84, LNCS 196. Springer-Verlag, pp.47\u201353 (1986)."},{"key":"3_CR34","unstructured":"K. Sakurai, and T. Itoh, \u201cOn the Discrepancy between Serial and Parallel of Zero-Knowledge Protocols,\u201d These proceedings."},{"key":"3_CR35","doi-asserted-by":"crossref","unstructured":"M. Tompa and H. Woll, \u201cRandom Self-Reducibility and Zero Knowledge Interactive Proofs of Possession of Information,\u201d Proceedings of FOCS, pp.472\u2013482 (1987).","DOI":"10.1109\/SFCS.1987.49"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2014 CRYPTO\u2019 92"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-48071-4_3.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T21:15:17Z","timestamp":1605647717000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-48071-4_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540573401"],"references-count":35,"URL":"https:\/\/doi.org\/10.1007\/3-540-48071-4_3","relation":{},"subject":[]}}