{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T18:06:05Z","timestamp":1773511565597,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":40,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540354581","type":"print"},{"value":"9783540354598","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11780656_22","type":"book-chapter","created":{"date-parts":[[2006,6,23]],"date-time":"2006-06-23T10:08:16Z","timestamp":1151057296000},"page":"259-270","source":"Crossref","is-referenced-by-count":4,"title":["Efficient Primitives from Exponentiation in \u2124 p"],"prefix":"10.1007","author":[{"given":"Shaoquan","family":"Jiang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"22_CR1","doi-asserted-by":"crossref","unstructured":"Adleman, L.M.: A Subexponential Algorithm for the Discrete Logarithm Problem with Applications to Cryptography (Abstract). In: FOCS 1979, pp. 55\u201360 (1979)","DOI":"10.1109\/SFCS.1979.2"},{"key":"22_CR2","doi-asserted-by":"crossref","unstructured":"Alexi, W., Chor, B., Goldreich, O., Schnorr, C.: RSA\/Rabin Bits are 1\/2 + 1\/poly(log N) Secure. In: FOCS 1984, pp. 449\u2013457 (1984)","DOI":"10.1109\/SFCS.1984.715947"},{"key":"22_CR3","doi-asserted-by":"crossref","unstructured":"Bellare, M., Goldwasser, S.: Verifiable Partial Key Escrow. In: ACM CCS 1997, pp. 78\u201391 (1997)","DOI":"10.1145\/266420.266439"},{"key":"22_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1007\/3-540-69053-0_13","volume-title":"Advances in Cryptology - EUROCRYPT \u201997","author":"M. Bellare","year":"1997","unstructured":"Bellare, M., Micciancio, D.: A New Paradigm for Collision-Free Hashing: Incrementality at Reduced Cost. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol.\u00a01233, pp. 163\u2013192. Springer, Heidelberg (1997)"},{"issue":"2","key":"22_CR5","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1137\/0215025","volume":"15","author":"L. Blum","year":"1986","unstructured":"Blum, L., Blum, M., Shub, M.: A Simple Unpredictable Pseudo-Random Number Generator. SIAM J. Comput.\u00a015(2), 364\u2013383 (1986)","journal-title":"SIAM J. Comput."},{"key":"22_CR6","doi-asserted-by":"crossref","unstructured":"Blum, M., Micali, S.: How to Generate Cryptographically Strong Sequences of Pseudo Random Bits. In: FOCS 1982, pp. 112\u2013117 (1982)","DOI":"10.1109\/SFCS.1982.72"},{"issue":"1","key":"22_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01840433","volume":"1","author":"D. Coppersmith","year":"1986","unstructured":"Coppersmith, D., Odlyzko, A.M., Schroeppel, R.: Discrete Logarithms in GF(p). Algorithmica\u00a01(1), 1\u201315 (1986)","journal-title":"Algorithmica"},{"key":"22_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/3-540-45708-9_10","volume-title":"Advances in Cryptology-CRYPTO 2002","author":"R. Canetti","year":"2002","unstructured":"Canetti, R., Krawczyk, H.: Analysis of key-exchange protocols and their use for building secure channels. Canetti, R., Krawczyk, H.: Analysis of key-exchange protocols and their use for building secure channels. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol.\u00a02045, pp. 453\u2013474. Springer, Heidelberg (2001); In: Knudsen, L.R. (ed.) EUROCRYPT 2001. LNCS, vol.\u00a02332, pp. 337\u2013351. Springer, Heidelberg (2002); signature-based key-exchange protocol. In: Yung, M. (ed.) EUROCRYPT 2001. LNCS, vol.\u00a02442, pp. 143\u2013161. Springer, Heidelberg (2002)"},{"key":"22_CR9","doi-asserted-by":"crossref","unstructured":"Contini, S., Lenstra, A.K., Steinfeld, R.: VSH: an Efficient and Provable Collision Resistant Hash Function. In: NIST Cryptographic Hash Workshop 2005, Maryland, USA (2005)","DOI":"10.1007\/11761679_11"},{"key":"22_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BFb0055717","volume-title":"Advances in Cryptology - CRYPTO \u201998","author":"R. Cramer","year":"1998","unstructured":"Cramer, R., Shoup, V.: A practical public- key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol.\u00a01462, pp. 13\u201325. Springer, Heidelberg (1998)"},{"key":"22_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/3-540-39118-5_19","volume-title":"Advances in Cryptology - EUROCRYPT \u201987","author":"I.B. Damg\u00e5rd","year":"1988","unstructured":"Damg\u00e5rd, I.B.: Collision Free Hash Functions and Public Key Signature Schemes. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol.\u00a0304, pp. 203\u2013216. Springer, Heidelberg (1988)"},{"key":"22_CR12","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"IT-22","author":"W. Diffie","year":"1976","unstructured":"Diffie, W., Hellman, M.E.: New Directions in Cryptography. IEEE Transactions on Information Theory\u00a0IT-22, 644\u2013654 (1976)","journal-title":"IEEE Transactions on Information Theory"},{"key":"22_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1007\/3-540-36413-7_7","volume-title":"Security in Communication Networks","author":"N. Dedi\u0107","year":"2003","unstructured":"Dedi\u0107, N., Reyzin, L., Vadhan, S.P.: An Improved Pseudorandom Generator Based on Hardness of Factoring. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol.\u00a02576, pp. 88\u2013101. Springer, Heidelberg (2003)"},{"issue":"4","key":"22_CR14","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1109\/TIT.1985.1057074","volume":"31","author":"T. Gamal El","year":"1985","unstructured":"El Gamal, 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":"22_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/3-540-44598-6_29","volume-title":"Advances in Cryptology - CRYPTO 2000","author":"R. Gennaro","year":"2000","unstructured":"Gennaro, R.: An Improved Pseudo-random Generator Based on Discrete Log. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol.\u00a01880, pp. 91\u2013110. Springer, Heidelberg (2000)"},{"key":"22_CR16","doi-asserted-by":"crossref","unstructured":"Goldwasser, S., Micali, S., Tong, P.: Why and how to establish a private code on a public network. In: FOCS 1982, pp. 134\u2013144 (1982)","DOI":"10.1109\/SFCS.1982.100"},{"issue":"2","key":"22_CR17","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1137\/0217017","volume":"17","author":"S. Goldwasser","year":"1988","unstructured":"Goldwasser, S., Micali, S., Rivest, R.L.: A Digital Signature Scheme Secure Against Adaptive Chosen-Message Attacks. SIAM J. Comput.\u00a017(2), 281\u2013308 (1988)","journal-title":"SIAM J. Comput."},{"key":"22_CR18","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546891","volume-title":"Foundations of Cryptography: Basic Tools","author":"O. Goldreich","year":"2001","unstructured":"Goldreich, O.: Foundations of Cryptography: Basic Tools. Cambridge University Press, Cambridge (2001)"},{"issue":"4","key":"22_CR19","doi-asserted-by":"publisher","first-page":"792","DOI":"10.1145\/6490.6503","volume":"33","author":"O. Goldreich","year":"1986","unstructured":"Goldreich, O., Goldwasse amd, S., Micali, S.: How to Construct Random Functions. Journal of the ACM\u00a033(4), 792\u2013807 (1986)","journal-title":"Journal of the ACM"},{"issue":"2","key":"22_CR20","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1007\/s00145-002-0038-7","volume":"16","author":"O. Goldreich","year":"2003","unstructured":"Goldreich, O., Rosen, V.: On the Security of Modular Exponentiation with Application to the Construction of Pseudorandom Generators. J. Cryptology\u00a016(2), 71\u201393 (2003)","journal-title":"J. Cryptology"},{"issue":"4","key":"22_CR21","doi-asserted-by":"publisher","first-page":"1364","DOI":"10.1137\/S0097539793244708","volume":"28","author":"J. Hastad","year":"1999","unstructured":"Hastad, J., Impagliazzo, R., Levin, L.A., Luby, M.: A Pseudorandom Generator from any One-way Function. SIAM J. Comput.\u00a028(4), 1364\u20131396 (1999) (Early version is in STOC 1989)","journal-title":"SIAM J. Comput."},{"key":"22_CR22","first-page":"376","volume":"47","author":"J. Hastad","year":"1993","unstructured":"Hastad, J., Schrift, A., Shamir, A.: The Discrete Logarithm Modulo a Composite Hides O(n) Bits. JCSS\u00a047, 376\u2013404 (1993)","journal-title":"JCSS"},{"key":"22_CR23","volume-title":"Introduction to Number Theory","author":"L. Hua","year":"1982","unstructured":"Hua, L.: Introduction to Number Theory. Springer, Berlin (1982)"},{"key":"22_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"475","DOI":"10.1007\/3-540-44987-6_29","volume-title":"Advances in Cryptology - EUROCRYPT 2001","author":"J. Katz","year":"2001","unstructured":"Katz, J., Ostrovsky, R., Yung, M.: Efficient password-authenticated key exchange using human-memorable passwords. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol.\u00a02045, pp. 475\u2013494. Springer, Heidelberg (2001)"},{"key":"22_CR25","series-title":"LNM","volume-title":"The Developement of the Number Field Sieve","year":"1993","unstructured":"Lenstra, A.K., Lenstra Jr., H.W. (eds.): The Developement of the Number Field Sieve. LNM, vol.\u00a01554. Springer, Heidelberg (1993)"},{"key":"22_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/3-540-48658-5_11","volume-title":"Advances in Cryptology - CRYPTO \u201994","author":"C. Lim","year":"1994","unstructured":"Lim, C., Lee, P.: More Flexible Exponentiation with Precomputation. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol.\u00a0839, pp. 95\u2013107. Springer, Heidelberg (1994)"},{"key":"22_CR27","doi-asserted-by":"crossref","unstructured":"Long, D.L., Wigderson, A.: How Discreet is the Discrete Log. In: STOC 1983, pp. 413\u2013420 (1983)","DOI":"10.1145\/800061.808772"},{"issue":"2\/3","key":"22_CR28","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1023\/A:1008350005447","volume":"19","author":"A.M. Odlyzko","year":"2000","unstructured":"Odlyzko, A.M.: Discrete Logarithms: The Past and the Future. Des. Codes Cryptography\u00a019(2\/3), 129\u2013145 (2000)","journal-title":"Des. Codes Cryptography"},{"key":"22_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1007\/BFb0055737","volume-title":"Advances in Cryptology - CRYPTO \u201998","author":"S. Patel","year":"1998","unstructured":"Patel, S., Sundaram, G.S.: An Efficient Discrete Log Pseudo Random Generator. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol.\u00a01462, pp. 304\u2013317. Springer, Heidelberg (1998)"},{"key":"22_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/11681878_8","volume-title":"Theory of Cryptography","author":"C. Peikert","year":"2006","unstructured":"Peikert, C., Rosen, A.: Efficient Collision-Resistant Hashing from Worst-Case Assumptions on Cyclic Lattices. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol.\u00a03876, pp. 145\u2013166. Springer, Heidelberg (2006)"},{"key":"22_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/978-3-540-46588-1_9","volume-title":"Public Key Cryptography","author":"D. Pointcheval","year":"2000","unstructured":"Pointcheval, D.: The Composite Discrete Logarithm and Secure Authentication. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol.\u00a01751, pp. 113\u2013128. Springer, Heidelberg (2000)"},{"key":"22_CR32","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1145\/359340.359342","volume":"2","author":"R. Rivest","year":"1978","unstructured":"Rivest, R., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public-key Cryptosystems. Communications of ACM\u00a02, 120\u2013126 (1978)","journal-title":"Communications of ACM"},{"key":"22_CR33","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/3-540-44647-8_21","volume-title":"Advances in Cryptology - CRYPTO 2001","author":"A. Shamir","year":"2001","unstructured":"Shamir, A., Tauman, Y.: Improved Online\/Offline Signature Schemes. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol.\u00a02139, pp. 355\u2013367. Springer, Heidelberg (2001)"},{"issue":"1676","key":"22_CR34","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1098\/rsta.1993.0139","volume":"345","author":"O. Schirokauer","year":"1993","unstructured":"Schirokauer, O.: Discrete Logarithm and Local Units. Philosophical Transactions: Physical Science and Engineering\u00a0345(1676), 409\u2013423 (1993)","journal-title":"Philosophical Transactions: Physical Science and Engineering"},{"key":"22_CR35","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","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":"22_CR36","doi-asserted-by":"crossref","unstructured":"Vazirani, U., Vazirani, V.: Efficient and Secure Pseudo-random number generation. In: FOCS 1984, pp. 458\u2013463 (1984)","DOI":"10.1109\/SFCS.1984.715948"},{"key":"22_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/11426639_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2005","author":"X. Wang","year":"2005","unstructured":"Wang, X., Lai, X., Feng, D., Chen, H., Yu, X.: Cryptanalysis of the Hash Functions MD4 and RIPEMD. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol.\u00a03494, pp. 1\u201318. Springer, Heidelberg (2005)"},{"key":"22_CR38","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/11426639_2","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2005","author":"X. Wang","year":"2005","unstructured":"Wang, X., Yu, H.: How to Break MD5 and Other Hash Functions. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol.\u00a03494, pp. 19\u201335. Springer, Heidelberg (2005)"},{"key":"22_CR39","series-title":"Lecture Notes in Computer Science","first-page":"17","volume-title":"Advances in Cryptology \u2013 CRYPTO 2005","author":"X. Wang","year":"2005","unstructured":"Wang, X., Yin, Y.L., Yu, H.: Finding Collisions in the Full SHA-1. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol.\u00a03621, pp. 17\u201336. Springer, Heidelberg (2005)"},{"key":"22_CR40","doi-asserted-by":"crossref","unstructured":"Yao, A.: Theory and Applications of Trapdoor Functions (Extended Abstract). In: FOCS 1982, pp. 80\u201391 (1982)","DOI":"10.1109\/SFCS.1982.45"}],"container-title":["Lecture Notes in Computer Science","Information Security and Privacy"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11780656_22.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T03:16:57Z","timestamp":1619493417000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11780656_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540354581","9783540354598"],"references-count":40,"URL":"https:\/\/doi.org\/10.1007\/11780656_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006]]}}}