| D. Boneh and R. J. Lipton, \Searching for elements in black box elds and applications, " in Proc. CRYPTO '96, 1996. |
....to addition and multiplication on the message space, then Bob can without interaction compute E(f(x) and send it back to Alice. Although this has been a prominent open problem for years [16] it is still unknown whether such homomorphic encryption schemes exist. On the one hand, Boneh and Lipton [8] have shown that all such deterministic encryption schemes are insecure; on the other hand, Sander, Young, and Yung [27] propose a scheme that allows the necessary operations on encrypted data, but comes at the cost of a multiplicative blowup per gate, which limits the possible computations to ....
D. Boneh and R. J. Lipton, \Searching for elements in black box elds and applications, " in Proc. CRYPTO '96, 1996.
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