{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,21]],"date-time":"2025-12-21T01:36:41Z","timestamp":1766281001921},"publisher-location":"Berlin, Heidelberg","reference-count":32,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642033551"},{"type":"electronic","value":"9783642033568"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"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":[[2009]]},"DOI":"10.1007\/978-3-642-03356-8_37","type":"book-chapter","created":{"date-parts":[[2009,8,18]],"date-time":"2009-08-18T10:00:39Z","timestamp":1250589639000},"page":"637-653","source":"Crossref","is-referenced-by-count":71,"title":["The Group of Signed Quadratic Residues and Applications"],"prefix":"10.1007","author":[{"given":"Dennis","family":"Hofheinz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eike","family":"Kiltz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"37_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/3-540-45353-9_12","volume-title":"Topics in Cryptology - CT-RSA 2001","author":"M. Abdalla","year":"2001","unstructured":"Abdalla, M., Bellare, M., Rogaway, P.: The oracle Diffie-Hellman assumptions and an analysis of DHIES. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol.\u00a02020, pp. 143\u2013158. Springer, Heidelberg (2001)"},{"key":"37_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1007\/3-540-44448-3_41","volume-title":"Advances in Cryptology - ASIACRYPT 2000","author":"M. Bellare","year":"2000","unstructured":"Bellare, M., Namprempre, C.: Authenticated encryption: Relations among notions and analysis of the generic composition paradigm. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol.\u00a01976, pp. 531\u2013545. Springer, Heidelberg (2000)"},{"key":"37_CR3","volume-title":"ACM CCS 1993","author":"M. Bellare","year":"1993","unstructured":"Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993. ACM Press, New York (1993)"},{"unstructured":"Benaloh, J.C.: Dense probabilistic encryption. In: SAC 1994, pp. 120\u2013128 (1994)","key":"37_CR4"},{"key":"37_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/3-540-39568-7_23","volume-title":"Advances in Cryptology","author":"M. Blum","year":"1985","unstructured":"Blum, M., Goldwasser, S.: An efficient probabilistic public-key encryption scheme which hides all partial information. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol.\u00a0196, pp. 289\u2013299. Springer, Heidelberg (1985)"},{"key":"37_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/11935070_1","volume-title":"Cryptology and Network Security","author":"J. Brown","year":"2006","unstructured":"Brown, J., Nieto, J.M.G., Boyd, C.: Concrete chosen-ciphertext secure encryption from subgroup membership problems. In: Pointcheval, D., Mu, Y., Chen, K. (eds.) CANS 2006. LNCS, vol.\u00a04301, pp. 1\u201318. Springer, Heidelberg (2006)"},{"key":"37_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"402","DOI":"10.1007\/3-540-48910-X_28","volume-title":"Advances in Cryptology - EUROCRYPT \u201999","author":"C. Cachin","year":"1999","unstructured":"Cachin, C., Micali, S., Stadler, M.: Computationally private information retrieval with polylogarithmic communication. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol.\u00a01592, pp. 402\u2013414. Springer, Heidelberg (1999)"},{"key":"37_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/978-3-540-45146-4_8","volume-title":"Advances in Cryptology - CRYPTO 2003","author":"J. Camenisch","year":"2003","unstructured":"Camenisch, J., Shoup, V.: Practical verifiable encryption and decryption of discrete logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol.\u00a02729, pp. 126\u2013144. Springer, Heidelberg (2003)"},{"key":"37_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1007\/978-3-540-78967-3_8","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2008","author":"D. Cash","year":"2008","unstructured":"Cash, D., Kiltz, E., Shoup, V.: The Twin Diffie-Hellman problem and applications. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol.\u00a04965, pp. 127\u2013145. Springer, Heidelberg (2008)"},{"doi-asserted-by":"crossref","unstructured":"Cohen, J.D., Fischer, M.J.: A robust and verifiable cryptographically secure election scheme (extended abstract). In: FOCS, pp. 372\u2013382 (1985)","key":"37_CR10","DOI":"10.1109\/SFCS.1985.2"},{"key":"37_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1007\/3-540-46035-7_4","volume-title":"Advances in Cryptology - EUROCRYPT 2002","author":"R. Cramer","year":"2002","unstructured":"Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol.\u00a02332, pp. 45\u201364. Springer, Heidelberg (2002)"},{"issue":"1","key":"37_CR12","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1137\/S0097539702403773","volume":"33","author":"R. Cramer","year":"2003","unstructured":"Cramer, R., Shoup, V.: Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack. SIAM Journal on Computing\u00a033(1), 167\u2013226 (2003)","journal-title":"SIAM Journal on Computing"},{"issue":"6","key":"37_CR13","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W. Diffie","year":"1976","unstructured":"Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Transactions on Information Theory\u00a022(6), 644\u2013654 (1976)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"2","key":"37_CR14","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1137\/S0097539795291562","volume":"30","author":"D. Dolev","year":"2000","unstructured":"Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM Journal on Computing\u00a030(2), 391\u2013437 (2000)","journal-title":"SIAM Journal on Computing"},{"key":"37_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1007\/3-540-39568-7_2","volume-title":"Advances in Cryptology","author":"T. El Gamal","year":"1985","unstructured":"El Gamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol.\u00a0196, pp. 10\u201318. Springer, Heidelberg (1985)"},{"issue":"2","key":"37_CR16","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s001459910008","volume":"13","author":"R. Fischlin","year":"2000","unstructured":"Fischlin, R., Schnorr, C.-P.: Stronger security proofs for RSA and Rabin bits. Journal of Cryptology\u00a013(2), 221\u2013244 (2000)","journal-title":"Journal of Cryptology"},{"key":"37_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1007\/978-3-540-30580-4_8","volume-title":"Public Key Cryptography - PKC 2005","author":"K. Gj\u00f8steen","year":"2005","unstructured":"Gj\u00f8steen, K.: Symmetric subgroup membership problems. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol.\u00a03386, pp. 104\u2013119. Springer, Heidelberg (2005)"},{"issue":"2","key":"37_CR18","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/0022-0000(84)90070-9","volume":"28","author":"S. Goldwasser","year":"1984","unstructured":"Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences\u00a028(2), 270\u2013299 (1984)","journal-title":"Journal of Computer and System Sciences"},{"key":"37_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/978-3-540-30576-7_4","volume-title":"Theory of Cryptography","author":"J. Groth","year":"2005","unstructured":"Groth, J.: Cryptography in subgroups of zn. In: Kilian, J. (ed.) TCC 2005. LNCS, vol.\u00a03378, pp. 50\u201365. Springer, Heidelberg (2005)"},{"key":"37_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1007\/978-3-540-74143-5_31","volume-title":"Advances in Cryptology - CRYPTO 2007","author":"D. Hofheinz","year":"2007","unstructured":"Hofheinz, D., Kiltz, E.: Secure hybrid encryption from weakened key encapsulation. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol.\u00a04622, pp. 553\u2013571. Springer, Heidelberg (2007)"},{"key":"37_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/978-3-642-01001-9_18","volume-title":"EUROCRYPT 2009","author":"D. Hofheinz","year":"2009","unstructured":"Hofheinz, D., Kiltz, E.: Practical chosen ciphertext secure encryption from factoring. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, pp. 313\u2013332. Springer, Heidelberg (2009)"},{"key":"37_CR22","series-title":"Lecture Notes in Computer Science","first-page":"589","volume-title":"EUROCRYPT 2009","author":"E. Kiltz","year":"2009","unstructured":"Kiltz, E., Pietrzak, K., Stam, M., Yung, M.: A new randomness extraction paradigm for hybrid encryption. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, pp. 589\u2013608. Springer, Heidelberg (2009)"},{"key":"37_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1007\/978-3-540-28628-8_26","volume-title":"Advances in Cryptology \u2013 CRYPTO 2004","author":"K. Kurosawa","year":"2004","unstructured":"Kurosawa, K., Desmedt, Y.: A new paradigm of hybrid encryption scheme. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol.\u00a03152, pp. 426\u2013442. Springer, Heidelberg (2004)"},{"key":"37_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"374","DOI":"10.1007\/3-540-46877-3_34","volume-title":"Advances in Cryptology - EUROCRYPT \u201990","author":"K. Kurosawa","year":"1991","unstructured":"Kurosawa, K., Katayama, Y., Ogata, W., Tsujii, S.: General public key residue cryptosystems and mental poker protocols. In: Damg\u00e5rd, I. (ed.) EUROCRYPT 1990. LNCS, vol.\u00a0473, pp. 374\u2013388. Springer, Heidelberg (1991)"},{"key":"37_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"236","DOI":"10.1007\/978-3-540-27800-9_21","volume-title":"Information Security and Privacy","author":"K. Kurosawa","year":"2004","unstructured":"Kurosawa, K., Matsuo, T.: How to remove MAC from DHIES. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol.\u00a03108, pp. 236\u2013247. Springer, Heidelberg (2004)"},{"key":"37_CR26","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1007\/3-540-36178-2_2","volume-title":"Advances in Cryptology - ASIACRYPT 2002","author":"S. Lucks","year":"2002","unstructured":"Lucks, S.: A variant of the cramer-shoup cryptosystem for groups of unknown order. In: Zheng, Y. (ed.) ASIACRYPT 2002, vol.\u00a02501, pp. 27\u201345. Springer, Heidelberg (2002)"},{"issue":"2","key":"37_CR27","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1007\/BF02351718","volume":"1","author":"K.S. McCurley","year":"1988","unstructured":"McCurley, K.S.: A key distribution system equivalent to factoring. Journal of Cryptology\u00a01(2), 95\u2013105 (1988)","journal-title":"Journal of Cryptology"},{"key":"37_CR28","first-page":"59","volume-title":"ACM CCS 1998","author":"D. Naccache","year":"1998","unstructured":"Naccache, D., Stern, J.: A new public key cryptosystem based on higher residues. In: ACM CCS 1998, pp. 59\u201366. ACM Press, New York (1998)"},{"key":"37_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1007\/3-540-44586-2_8","volume-title":"Public Key Cryptography","author":"T. Okamoto","year":"2001","unstructured":"Okamoto, T., Pointcheval, D.: The gap-problems: A new class of problems for the security of cryptographic schemes. In: Kim, K. (ed.) PKC 2001. LNCS, vol.\u00a01992, pp. 104\u2013118. Springer, Heidelberg (2001)"},{"unstructured":"Rabin, M.O.: Digital signatures and public key functions as intractable as factorization. Technical Report MIT\/LCS\/TR-212, Massachusetts Institute of Technology (January 1979)","key":"37_CR30"},{"key":"37_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/3-540-46766-1_35","volume-title":"Advances in Cryptology - CRYPTO 1991","author":"C. Rackoff","year":"1992","unstructured":"Rackoff, C., Simon, D.R.: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol.\u00a0576, pp. 433\u2013444. Springer, Heidelberg (1992)"},{"unstructured":"Shmuely, Z.: Composite diffie-hellman public-key generating systems are hard to break. Technical Report 356, Computer Science Department, Technion, Israel (1985)","key":"37_CR32"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology - CRYPTO 2009"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-03356-8_37","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,21]],"date-time":"2019-05-21T22:09:58Z","timestamp":1558476598000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-03356-8_37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642033551","9783642033568"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-03356-8_37","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2009]]}}}