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Abstract: We introduce the notion of a black box field and discuss the problem of explicitly exposing field elements given in a black box form. We present several sub-exponential algorithms for this problem using a technique due to Maurer. These algorithms make use of elliptic curves over finite fields in a crucial way. We present three applications for our results: (1) We show that any algebraically homomorphic encryption scheme can be broken in expected sub-exponential time. The existence of such... (Update)
Context of citations to this paper: More
...open problem for years [15] it is still unknown whether such homomorphic encryption schemes exist. On the one hand, Boneh and Lipton [7] have shown that all such deterministic encryption schemes are insecure; on the other hand, Sander, Young, and Yung [25] propose a scheme...
...with encrypted data. In 1991, Feigenbaum and Merritt [11] directly addressed algebraic homomorphic schemes of the form stated above. In [5], Boneh and Lipton showed that deterministic algebraically homomorphic encryption schemes over ring ZN can be broken in subexponential...
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BibTeX entry: (Update)
D. Boneh and R. J. Lipton, "Searching for elements in black box fields and applications, " in Proc. CRYPTO '96, LNCS 1109, 1996. http://citeseer.ist.psu.edu/boneh96searching.html More
@misc{ boneh96searching,
author = "D. Boneh and R. Lipton",
title = "Searching for elements in black box fields and applications",
text = "D. Boneh and R. J. Lipton, Searching for elements in black box fields and
applications, in Proc. CRYPTO '96, LNCS 1109, 1996.",
year = "1996",
url = "citeseer.ist.psu.edu/boneh96searching.html" }
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