{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T23:29:03Z","timestamp":1784676543735,"version":"3.55.0"},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540345466","type":"print"},{"value":"9783540345473","type":"electronic"}],"license":[{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11761679_1","type":"book-chapter","created":{"date-parts":[[2006,7,4]],"date-time":"2006-07-04T10:11:19Z","timestamp":1152007879000},"page":"1-11","source":"Crossref","is-referenced-by-count":170,"title":["Security Analysis of the Strong Diffie-Hellman Problem"],"prefix":"10.1007","author":[{"given":"Jung Hee","family":"Cheon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"1_CR1","unstructured":"Abdalla, M., Bellare, M., Rogaway, P.: DHAES: An encryption scheme based on Diffie-Hellman problem. IEEE P1363a Submission (1998), available at: http:\/\/grouper.ieee.org\/groups\/1363\/addendum.html"},{"key":"1_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/978-3-540-24676-3_14","volume-title":"Advances in Cryptology - EUROCRYPT 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X.: Efficient Selective-ID Secure Identity-Based Encryption Without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 223\u2013238. Springer, Heidelberg (2004)"},{"key":"1_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1007\/978-3-540-24676-3_4","volume-title":"Advances in Cryptology - EUROCRYPT 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X.: Short Signatures Without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 56\u201373. Springer, Heidelberg (2004)"},{"key":"1_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1007\/11426639_26","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2005","author":"D. Boneh","year":"2005","unstructured":"Boneh, D., Boyen, X., Goh, E.: Hierarchical Identity Based Encryption with Constant Size Ciphertext. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol.\u00a03494, pp. 440\u2013456. Springer, Heidelberg (2005)"},{"key":"1_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/978-3-540-28628-8_3","volume-title":"Advances in Cryptology \u2013 CRYPTO 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Boyen, X., Shacham, H.: Short Group Signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol.\u00a03152, pp. 41\u201355. Springer, Heidelberg (2004)"},{"key":"1_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1007\/BFb0053443","volume-title":"Advances in Cryptology - EUROCRYPT \u201994","author":"M. Burmester","year":"1995","unstructured":"Burmester, M., Desmedt, Y.: A Secure and Efficient Conference Key Distribution System (Extended Abstract). In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol.\u00a0950, pp. 275\u2013286. Springer, Heidelberg (1995)"},{"key":"1_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1007\/11535218_16","volume-title":"Advances in Cryptology \u2013 CRYPTO 2005","author":"D. Boneh","year":"2005","unstructured":"Boneh, D., Gentry, C., Waters, B.: Collution Resistant Broadcast Encryption with Short Ciphertexts and Private Keys. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol.\u00a03621, pp. 258\u2013275. Springer, Heidelberg (2005)"},{"key":"#cr-split#-1_CR8.1","doi-asserted-by":"crossref","unstructured":"Boneh, D., Lynn, B., Shacham, H.: Short Signatures from the Weil Pairing. ASIACRYPT 2001??17(4), 297???319 (2004);","DOI":"10.1007\/s00145-004-0314-9"},{"key":"#cr-split#-1_CR8.2","unstructured":"Extended abstract in proceedings of Asiacrypt 2001. LNCS, vol. 2248, pp. 514???532. Springer, Heidelberg (2001)"},{"key":"1_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1007\/0-387-34799-2_38","volume-title":"Advances in Cryptology - CRYPTO \u201988","author":"B. Boer den","year":"1990","unstructured":"den Boer, B.: Diffie-Hellman is as Strong as Discrete Log for Certain Primes. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol.\u00a0403, pp. 530\u2013539. Springer, Heidelberg (1990)"},{"key":"1_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/3-540-36288-6_3","volume-title":"Public Key Cryptography - PKC 2003","author":"A. Boldyreva","year":"2002","unstructured":"Boldyreva, A.: Threshold Signatures, Multisignatures and Blind Signatures Based on the Gap-Diffie-Hellman-Group Signature Scheme. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol.\u00a02567, pp. 31\u201346. Springer, Heidelberg (2002)"},{"key":"1_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1007\/978-3-540-30580-4_28","volume-title":"Public Key Cryptography - PKC 2005","author":"Y. Dodis","year":"2005","unstructured":"Dodis, Y., Yampolskiy, A.: A Verifiable Random Function with Short Proofs and Keys. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol.\u00a03386, pp. 416\u2013431. Springer, Heidelberg (2005)"},{"issue":"4","key":"1_CR12","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1109\/TIT.1985.1057074","volume":"31","author":"T. Elgamal","year":"1985","unstructured":"Elgamal, T.: A Public Key Cryptosystem and a Signature Scheme based on Discrete Logarithms. IEEE Transactions on Information Theory\u00a031(4), 469\u2013472 (1985)","journal-title":"IEEE Transactions on Information Theory"},{"key":"1_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1007\/3-540-39757-4_19","volume-title":"Advances in Cryptology","author":"J. Gordon","year":"1985","unstructured":"Gordon, J.: Strong Primes are Easy to Find. In: Beth, T., Cot, N., Ingemarsson, I. (eds.) EUROCRYPT 1984. LNCS, vol.\u00a0209, pp. 216\u2013223. Springer, Heidelberg (1985)"},{"key":"1_CR14","doi-asserted-by":"crossref","unstructured":"Koblitz, N., Menezes, A.: Pairing-based Cryptography at High Security Levels. In: IMA Conference of Cryptography and Coding 2005, pp. 13\u201336 (2005)","DOI":"10.1007\/11586821_2"},{"key":"1_CR15","unstructured":"Scott, M.: Multiprecision Integer and Rational Arithmetic C\/C++ Library, available at: http:\/\/indigo.ie\/~mscott\/"},{"key":"1_CR16","doi-asserted-by":"publisher","DOI":"10.1201\/9781439821916","volume-title":"Handbook of Applied Cryptography","author":"A. Menezes","year":"1996","unstructured":"Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)"},{"issue":"2","key":"1_CR17","first-page":"481","volume":"E85-A","author":"S. Mitsunari","year":"2002","unstructured":"Mitsunari, S., Sakai, R., Kasahara, M.: A New Traitor Tracing. IEICE Trans. Fundamentals\u00a0E85-A(2), 481\u2013484 (2002)","journal-title":"IEICE Trans. Fundamentals"},{"issue":"5","key":"1_CR18","doi-asserted-by":"publisher","first-page":"1689","DOI":"10.1137\/S0097539796302749","volume":"28","author":"U. Maurer","year":"1999","unstructured":"Maurer, U., Wolf, S.: The Relationship Between Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms. SIAM J. Comput.\u00a028(5), 1689\u20131721 (1999)","journal-title":"SIAM J. Comput."},{"key":"1_CR19","unstructured":"Recommended Elliptic Curves for Federal Government Use (1999), available at: http:\/\/csrc.nist.gov\/CryptoToolkit\/dss\/ecdsa\/NISTReCur.pdf"},{"key":"1_CR20","first-page":"918","volume":"32","author":"J. Pollard","year":"1978","unstructured":"Pollard, J.: Monte Carlo Methods for Index Computation ( $\\bmod p$ ). Mathematics of Computation\u00a032, 918\u2013924 (1978)","journal-title":"Mathematics of Computation"},{"key":"1_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1007\/3-540-69053-0_18","volume-title":"Advances in Cryptology - EUROCRYPT \u201997","author":"V. Shoup","year":"1997","unstructured":"Shoup, V.: Lower bounds for Discrete Logarithms and Related Problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol.\u00a01233, pp. 256\u2013266. Springer, Heidelberg (1997)"},{"key":"1_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/BFb0054891","volume-title":"Algorithmic Number Theory","author":"E. Teske","year":"1998","unstructured":"Teske, E.: Speeding up Pollard\u2019s Rho Method for Computing Discrete Logarithms. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol.\u00a01423, pp. 541\u2013554. Springer, Heidelberg (1998)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology - EUROCRYPT 2006"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11761679_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,19]],"date-time":"2019-04-19T15:49:55Z","timestamp":1555688995000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11761679_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540345466","9783540345473"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/11761679_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006]]}}}