We propose attribute-based encryption schemes where encryptor-specified access structures (also called ciphertext policies) are hidden. By using our schemes, an encryptor can encrypt data with a hidden access structure. A decryptor obtains her secret key associated with her attributes from a trusted authority in advance and if the attributes associated with the decryptor's secret key do not satisfy the access structure associated with the encrypted data, the decryptor cannot decrypt the data or guess even what access structure was specified by the encryptor. We prove security of our construction based on the Decisional Bilinear Diffie-Hellman assumption and the Decision Linear assumption. In our security notion, even the legitimate decryptor cannot obtain the information about the access structure associated with the encrypted data more than the fact that she can decrypt the data.
Abstract. Damgård et al. [11] showed a novel technique to convert a polynomial sharing of secret a into the sharings of the bits of a in constant rounds, which is called the bit-decomposition protocol. The bit-decomposition protocol is a very powerful tool because it enables bitoriented operations even if shared secrets are given as elements in the field. However, the bit-decomposition protocol is relatively expensive.In this paper, we present a simplified bit-decomposition protocol by analyzing the original protocol. Moreover, we construct more efficient protocols for a comparison, interval test and equality test of shared secrets without relying on the bit-decomposition protocol though it seems essential to such bit-oriented operations. The key idea is that we do computation on secret a with c and r where c = a + r, c is a revealed value, and r is a random bitwise-shared secret. The outputs of these protocols are also shared without being revealed.The realized protocols as well as the original protocol are constantround and run with less communication rounds and less data communication than those of [11]. For example, the round complexities are reduced by a factor of approximately 3 to 10.
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