{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T14:15:55Z","timestamp":1725459355032},"publisher-location":"Berlin\/Heidelberg","reference-count":20,"publisher":"Springer-Verlag","isbn-type":[{"type":"print","value":"3540530002"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/bfb0030368","type":"book-chapter","created":{"date-parts":[[2006,1,25]],"date-time":"2006-01-25T15:24:26Z","timestamp":1138202666000},"page":"273-293","source":"Crossref","is-referenced-by-count":2,"title":["Demonstrating possession without revealing factors and its application"],"prefix":"10.1007","author":[{"given":"Hiroki","family":"Shizuya","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenji","family":"Koyama","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Toshiya","family":"Itoh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"24_CR1","doi-asserted-by":"crossref","unstructured":"Adleman, L. M. and McCurley, K. S., \u201cOpen problems in number theoretic complexity,\u201d Proc. Japan-U.S. Joint Seminar on Discrete Algorithms and Complexity, Academic Press, pp.237\u2013262 (1987).","DOI":"10.1016\/B978-0-12-386870-1.50020-4"},{"key":"24_CR2","unstructured":"Blum, M., \u201cCoin flipping by telephone,\u201d Proc. IEEE COMPCON, pp.133\u2013137 (1982)."},{"key":"24_CR3","unstructured":"Brassard, G. and Cr\u00e9peau C., \u201cNon-Transitive Transfer of Confidence: A Perfect Zero-Knowledge Interactive Protocol for SAT and Beyond,\u201d Proc. of FOCS, pp.188\u2013195 (1986)."},{"key":"24_CR4","doi-asserted-by":"crossref","unstructured":"Blum, M., Feldman, P., and Micali, S., \u201cNon-Interactive Zero-Knowledge and its Applications,\u201d Proc. of STOC, pp.103\u2013112 (1988).","DOI":"10.1145\/62212.62222"},{"key":"24_CR5","doi-asserted-by":"crossref","unstructured":"Brillhart, J., Lehmer, D. H., Selfridge, J. L., Tuckerman, B., and Wagstaff, Jr., S. S., \u201cFactorizations of b n\u00b11, b=2, 3, 5, 6, 7, 10, 11, 12 up to high powers,\u201d Contemporary Mathematics, Vol. 22, (Second Edition) American Mathematical Society (1988).","DOI":"10.1090\/conm\/022"},{"key":"24_CR6","doi-asserted-by":"crossref","unstructured":"Chaum, D., Evertse, J., and van de Graaf, J., \u201cAn improved protocol for demonstrating possession of discrete logarithms and some generalizations,\u201d Proc. EUROCRYPT'87, pp.127\u2013142 (1987).","DOI":"10.1007\/3-540-39118-5_13"},{"key":"24_CR7","doi-asserted-by":"crossref","unstructured":"Chaum, D., Evertse, J., van de Graaf, J., and Peralta, R., \u201cDemonstrating possession of a discrete logarithm without revealing it,\u201d Proc. CRYPTO'86, pp.200\u2013212 (1986).","DOI":"10.1007\/3-540-47721-7_14"},{"issue":"165","key":"24_CR8","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1090\/S0025-5718-1984-0726006-X","volume":"42","author":"H. Cohen","year":"1984","unstructured":"Cohen, H. and Lenstra, Jr., H. W., \u201cPrimality testing and Jacobi sums,\u201d Math. Comp., Vol.42, No.165, pp.297\u2013330 (1984).","journal-title":"Math. Comp."},{"key":"24_CR9","doi-asserted-by":"crossref","unstructured":"Coppersmith, D., Odlyzko, A. M., and Schroeppel, R. \u201cDiscrete logarithms in GF(p),\u201d Algorithmica, pp.1\u201315 (1986).","DOI":"10.1007\/BF01840433"},{"key":"24_CR10","doi-asserted-by":"crossref","unstructured":"Feige, U., Fiat, A. and Shamir, A., \u201cZero knowledge proofs of identity,\u201d Proc. 19th STOC, pp.210\u2013217 (1987).","DOI":"10.1145\/28395.28419"},{"key":"24_CR11","doi-asserted-by":"crossref","unstructured":"Goldwasser, S., Micali, S., and Rackoff, C., \u201cThe zero-knowledge complexity of interactive proof-systems,\u201d Proc. 17th STOC, pp.291\u2013304 (1985).","DOI":"10.1145\/22145.22178"},{"key":"24_CR12","doi-asserted-by":"crossref","unstructured":"Goldreich, O., Micali, S., and Wigderson, A., \u201cProofs that yield nothing but their validity and a methodology of cryptographic protocol design,\u201d Proc. 27th FOCS, pp.174\u2013187 (1986).","DOI":"10.1109\/SFCS.1986.47"},{"key":"24_CR13","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1017\/S0305004100054657","volume":"83","author":"D.R. Heath-Brown","year":"1978","unstructured":"Heath-Brown, D.R., \u201cAlmost-primes in arithmetic progressions and short intervals,\u201d Math. Proc. Cambridge Philos. Soc., 83, pp.357\u2013375 (1978).","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"24_CR14","unstructured":"Itoh, T. and Tsujii, S., \u201cHow to generate a primitive root modulo a prime,\u201d SIG Notes of IPS of Japan, SIGAL9-2 (1989)."},{"key":"24_CR15","doi-asserted-by":"crossref","unstructured":"Kaliski, Jr., B.S., \u201cA pseudo-random bit generator based on elliptic logarithms,\u201d Proc. CRYPTO'86, pp.84\u2013103 (1986).","DOI":"10.1007\/3-540-47721-7_7"},{"key":"24_CR16","unstructured":"Knuth, D.E., \u201cThe art of computer programming\u201d, Vol. 2 Addison-Wesley (1981)."},{"key":"24_CR17","unstructured":"Koyama, K., \u201cSpeeding the elliptic curve method and its examination of factoring\u201d (in Japanese), IEICE Technical Report, ISEC 88-19 (1988)."},{"key":"24_CR18","unstructured":"Kurosaki, M., Zheng, Y. Matsumoto, T. and Imai, H. \u201cSimple Protocol for Showing Membership of Several Groups\u201d (in Japanese), Proc. 11th Symposium on Information Theory and Its applications (SITA'88), pp.585\u2013590 (1988)."},{"key":"24_CR19","unstructured":"Lenstra, Jr. H. W., \u201cElliptic curve factorization and primality testing,\u201d Proc. of Computational Number Theory Conference, (1985)."},{"key":"24_CR20","doi-asserted-by":"crossref","unstructured":"Tompa, M. and Woll, H., \u201cRandom self-reducibility and zero knowledge interactive proofs for possession of information,\u201d Proc. 28th FOCS, pp. 472\u2013482 (1987).","DOI":"10.1109\/SFCS.1987.49"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2014 AUSCRYPT '90"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0030368.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,9]],"date-time":"2020-12-09T22:01:26Z","timestamp":1607551286000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0030368"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["3540530002"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/bfb0030368","relation":{},"subject":[]}}