{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T21:40:09Z","timestamp":1776807609742,"version":"3.51.2"},"publisher-location":"Berlin, Heidelberg","reference-count":28,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540851738","type":"print"},{"value":"9783540851745","type":"electronic"}],"license":[{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008]]},"DOI":"10.1007\/978-3-540-85174-5_21","type":"book-chapter","created":{"date-parts":[[2008,8,20]],"date-time":"2008-08-20T12:32:02Z","timestamp":1219235522000},"page":"379-396","source":"Crossref","is-referenced-by-count":8,"title":["Communication Complexity in Algebraic Two-Party Protocols"],"prefix":"10.1007","author":[{"given":"Rafail","family":"Ostrovsky","sequence":"first","affiliation":[]},{"suffix":"III","given":"William E.","family":"Skeith","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"21_CR1","doi-asserted-by":"crossref","unstructured":"Barrington, D.: Bounded-Width Polynomial-Size Branching Programs Recognize Exactly Those Languages in NC. In: STOC 1986, pp.1\u20135 (1986)","DOI":"10.1145\/12130.12131"},{"key":"21_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1007\/978-3-540-24676-3_30","volume-title":"Advances in Cryptology - EUROCRYPT 2004","author":"D. Boneh","year":"2004","unstructured":"Boneh, D., Crescenzo, G., Ostrovsky, R., Persiano, G.: Public Key Encryption with Keyword Search. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol.\u00a03027, pp. 506\u2013522. Springer, Heidelberg (2004)"},{"key":"21_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/978-3-540-30576-7_18","volume-title":"Theory of Cryptography","author":"D. Boneh","year":"2005","unstructured":"Boneh, D., Goh, E., Nissim, K.: Evaluating 2-DNF Formulas on Ciphertexts. In: Kilian, J. (ed.) TCC 2005. LNCS, vol.\u00a03378, pp. 325\u2013341. Springer, Heidelberg (2005)"},{"key":"21_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/3-540-68697-5_22","volume-title":"Advances in Cryptology - CRYPTO \u201996","author":"D. Boneh","year":"1996","unstructured":"Boneh, D., Lipton, R.: Searching for Elements in Black Box Fields and Applications. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol.\u00a01109, pp. 283\u2013297. Springer, Heidelberg (1996)"},{"key":"21_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74143-5_4","volume-title":"Advances in Cryptology - CRYPTO 2007","author":"D. Boneh","year":"2007","unstructured":"Boneh, D., Kushilevitz, E., Ostrovsky, R., Skeith, W.: Public Key Encryption that Allows PIR Queries. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol.\u00a04622. Springer, Heidelberg (2007)"},{"key":"21_CR6","series-title":"Lecture Notes in Computer Science","volume-title":"Information Security and Privacy","author":"Y.C. Chang","year":"2004","unstructured":"Chang, Y.C.: Single Database Private Information Retrieval with Logarithmic Communication. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol.\u00a03108. Springer, Heidelberg (2004)"},{"key":"21_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","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":"21_CR8","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1145\/293347.293350","volume":"45","author":"B. Chor","year":"1998","unstructured":"Chor, B., Goldreich, O., Kushilevitz, E., Sudan, M.: Private information retrieval. J. of the ACM\u00a045, 965\u2013981 (1998)","journal-title":"J. of the ACM"},{"issue":"4","key":"21_CR9","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1109\/TIT.1985.1057074","volume":"IT-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\u00a0IT-31(4), 469\u2013472 (1985)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"1","key":"21_CR10","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. J. Comp. Sys. Sci.\u00a028(1), 270\u2013299 (1984)","journal-title":"J. Comp. Sys. Sci."},{"key":"21_CR11","first-page":"305","volume":"13","author":"D. Grigoriev","year":"2004","unstructured":"Grigoriev, D., Ponomarenko, I.: Homomorphic public-key cryptosystems over groups and rings. Quaderni di Mathematica\u00a013, 305\u2013325 (2004)","journal-title":"Quaderni di Mathematica"},{"key":"21_CR12","unstructured":"Herstein, I.N.: Abstract Algebra. Prentice-Hall, Englewood Cliffs (1986, 1990, 1996)"},{"key":"21_CR13","volume-title":"Algebra","author":"T.W. Hungerford","year":"1984","unstructured":"Hungerford, T.W.: Algebra. Springer, Berlin (1984)"},{"key":"21_CR14","series-title":"Lecture Notes in Computer Science","volume-title":"Theory of Cryptography","author":"Y. Ishai","year":"2005","unstructured":"Ishai, Y., Kushilevitz, E., Ostrovsky, R.: Sufficient Conditions for Collision-Resistant Hashing. In: Kilian, J. (ed.) TCC 2005. LNCS, vol.\u00a03378. Springer, Heidelberg (2005)"},{"key":"21_CR15","doi-asserted-by":"crossref","unstructured":"Kushilevitz, E., Ostrovsky, R.: Replication is not needed: Single database, computationally-private information retrieval. In: FOCS 1997, pp. 364\u2013373 (1997)","DOI":"10.1109\/SFCS.1997.646125"},{"key":"21_CR16","doi-asserted-by":"crossref","unstructured":"Lipmaa, H.: An Oblivious Transfer Protocol with Log-Squared Communication. IACR ePrint Cryptology Archive 2004\/063","DOI":"10.1007\/11556992_23"},{"key":"21_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1007\/BFb0054118","volume-title":"Advances in Cryptology - EUROCRYPT \u201998","author":"U. Maurer","year":"1998","unstructured":"Maurer, U., Wolf, S.: Lower bounds on generic algorithms in groups. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol.\u00a01403, pp. 72\u201384. Springer, Heidelberg (1998)"},{"key":"21_CR18","doi-asserted-by":"publisher","first-page":"522","DOI":"10.2307\/2034697","volume":"16","author":"W. Maurer","year":"1965","unstructured":"Maurer, W., Rhodes, J.: A property of finite non-Abelian simple groups. Proc. Am. Math. Soc.\u00a016, 522\u2013554 (1965)","journal-title":"Proc. Am. Math. Soc."},{"key":"21_CR19","series-title":"Lecture Notes in Computer Science","first-page":"397","volume-title":"Advances in Cryptology \u2013 CRYPTO 2005","author":"R. Ostrovsky","year":"2005","unstructured":"Ostrovsky, R., Skeith, W.: Private Searching on Streaming Data. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol.\u00a03621, pp. 397\u2013430. Springer, Heidelberg (2005); Journal of Cryptology 20(4), 397\u2013430 (October 2007)"},{"key":"21_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71677-8_26","volume-title":"Public Key Cryptography \u2013 PKC 2007","author":"R. Ostrovsky","year":"2007","unstructured":"Ostrovsky, R., Skeith, W.: A Survey of Single Database PIR: Techniques and Applications. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol.\u00a04450. Springer, Heidelberg (2007)"},{"key":"21_CR21","unstructured":"Ostrovsky, R., Skeith, W.: Algebraic Lower Bounds for Computing on Encrypted Data. Electronic Colloquium on Computational Complexity report TR07-22"},{"key":"21_CR22","series-title":"Lecture Notes in Computer Science","first-page":"223","volume-title":"Advances in Cryptology - EUROCRYPT \u201999","author":"P. Paillier","year":"1999","unstructured":"Paillier, P.: Public Key Cryptosystems based on CompositeDegree Residue Classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol.\u00a01592, pp. 223\u2013238. Springer, Heidelberg (1999)"},{"key":"21_CR23","unstructured":"Rappe, D.K.: Homomorphic Cryptosystems and their Applications Ph.D. Thesis, under E. Becker and J. Patarin (2004)"},{"key":"21_CR24","first-page":"169","volume-title":"Foundations of Secure Computation","author":"R.L. Rivest","year":"1978","unstructured":"Rivest, R.L., Adleman, L., Dertouzos, M.L.: On data banks and privacy homomorphisms. In: DeMillo, R.A., et al. (eds.) Foundations of Secure Computation, pp. 169\u2013179. Academic Press, London (1978)"},{"key":"21_CR25","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R.L. Rivest","year":"1978","unstructured":"Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. Commun. ACM\u00a021, 120\u2013126 (1978)","journal-title":"Commun. ACM"},{"key":"21_CR26","doi-asserted-by":"crossref","unstructured":"Sander, T., Young, A., Yung, M.: Non-Interactive CryptoComputing For NC1. In: FOCS 1999, pp. 554\u2013567 (1999)","DOI":"10.1109\/SFFCS.1999.814630"},{"key":"21_CR27","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":"21_CR28","first-page":"400","volume":"43","author":"H. Werner","year":"1974","unstructured":"Werner, H.: Finite simple non-Abelian groups are functionally complete. Bull. Soc. Roy. Sci. Li\u00e8ge\u00a043, 400 (1974)","journal-title":"Bull. Soc. Roy. Sci. Li\u00e8ge"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2013 CRYPTO 2008"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-85174-5_21","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,31]],"date-time":"2025-01-31T15:57:56Z","timestamp":1738339076000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-85174-5_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008]]},"ISBN":["9783540851738","9783540851745"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-85174-5_21","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008]]}}}