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Abstract: Motivated by questions about secure multi-party computation, we introduce and study a new natural representation of functions by polynomials, which we term randomizing polynomials. "Standard" low-degree polynomials over a finite field are easy to compute with a small number of communication rounds in virtually any setting for secure computation. However, most Boolean functions cannot be evaluated by a polynomial whose degree is smaller than their input size. We get around this barrier by... (Update)
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BibTeX entry: (Update)
Y. Ishai and E. Kushilevitz. Randomizing polynomials: A new representation with applications to round-ecient secure computation. In Proc. 41st IEEE Symposium on the Foundations of Computer Science (FOCS), Oct. 2000. http://citeseer.ist.psu.edu/ishai00randomizing.html More
@inproceedings{ ishai00randomizing,
author = "Yuval Ishai and Eyal Kushilevitz",
title = "Randomizing Polynomials: A New Representation with Applications to Round-Efficient Secure Computation",
booktitle = "{IEEE} Symposium on Foundations of Computer Science",
pages = "294-304",
year = "2000",
url = "citeseer.ist.psu.edu/ishai00randomizing.html" }
Citations (may not include all citations):645 How to share a secret (context) - Shamir - 1979
287 Multiparty unconditionally secure protocols (context) - Chaum, Crepeau et al. - 1988
250 How to play any mental game (context) - Goldreich, Micali et al. - 1987
219 Completeness theorems for non-cryptographic fault-tolerant d.. (context) - Ben-Or, Goldwasser et al. - 1988
189 Algebraic methods in the theory of lower bounds for Boolean .. (context) - Smolensky - 1987
185 How to generate and exchange secrets (context) - Yao - 1986
179 Security and composition of multi-party cryptographic protoc.. - Canetti - 2000
167 Protocols for secure computations (context) - Yao - 1982
154 Secure multi-party computation - Goldreich - 2000
127 Verifiable secret sharing and multiparty protocols with hone.. (context) - Rabin, Ben-Or - 1989
120 Secure computation (context) - Micali, Rogaway
100 Founding cryptography on oblivious transfer (context) - Kilian - 1988
86 New directions in testing (context) - Lipton - 1989
59 Security with low communication overhead (context) - Beaver, Feigenbaum et al.
57 the degree of Boolean functions as real polynomials - Nisan, Szegedy - 1994
53 A minimal model for secure computation - Feige, Kilian et al. - 1994
51 Lower bounds for the size of circuits of bounded depth with .. (context) - Razborov - 1987
49 Non-cryptographic fault-tolerant computing in a constant num.. (context) - Bar-Ilan, Beaver - 1989
47 The round complexity of secure protocols - Beaver, Micali et al. - 1990
45 General secure multiparty computation from any linear secret.. - Cramer, Damgard et al. - 2000
35 Non-interactive cryptocomputing for NC - Sandler, Young et al. - 1999
31 The polynomial method in circuit complexity - Beigel - 1993
28 The complexity of matrix rank and feasible systems of linear.. - Allender, Beals et al. - 1996
27 Representing Boolean functions as polynomials modulo composi.. - Barrington, Beigel et al. - 1992
21 Private simultaneous messages protocols with applications - Ishai, Kushilevitz - 1997
20 One-round secure computationand secure autonomousmobile agen.. - Cachin, Camenisch et al. - 2000
16 Lower bounds on representing Boolean functions as polynomial.. - Tsai - 1993
14 Secure distributed linear algebra in a constant number of ro.. - Cramer, Damgard - 2000
12 and the polynomial hierarchy (context) - Tarui, threshold - 1991
11 Efficient multiparty computations secure against an adaptive.. - Cramer, Damgard et al.
9 Minimal-latency secure function evaluation (context) - Beaver - 2000
5 The bit extraction problem of t-resilient functions (context) - Chor, Goldreich et al. - 1985
4 On arithmetic branching programs - Beimel, Gal - 1998
2 Probabilstic Methods and Pseudo-Randomness (context) - Goldreich - 1999
1 Fact-track multiparty computations with applications to thre.. (context) - Gennaro, Rabin et al. - 1998
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