We describe plausible lattice-based constructions with properties that approximate the soughtafter multilinear maps in hard-discrete-logarithm groups, and show an example application of such multi-linear maps that can be realized using our approximation. The security of our constructions relies on seemingly hard problems in ideal lattices, which can be viewed as extensions of the assumed hardness of the NTRU function.
In this work, we study indistinguishability obfuscation and functional encryption for general circuits:Indistinguishability obfuscation requires that given any two equivalent circuits C0 and C1 of similar size, the obfuscations of C0 and C1 should be computationally indistinguishable.In functional encryption, ciphertexts encrypt inputs x and keys are issued for circuits C. Using the key SKC to decrypt a ciphertext CTx = Enc(x), yields the value C(x) but does not reveal anything else about x. Furthermore, no collusion of secret key holders should be able to learn anything more than the union of what they can each learn individually.
We put forth the concept of witness encryption. A witness encryption scheme is defined for an NP language L (with corresponding witness relation R). In such a scheme, a user can encrypt a message M to a particular problem instance x to produce a ciphertext. A recipient of a ciphertext is able to decrypt the message if x is in the language and the recipient knows a witness w where R(x, w) holds. However, if x is not in the language, then no polynomial-time attacker can distinguish between encryptions of any two equal length messages. We emphasize that the encrypter himself may have no idea whether x is actually in the language.Our contributions in this paper are threefold. First, we introduce and formally define witness encryption. Second, we show how to build several cryptographic primitives from witness encryption. Finally, we give a candidate construction based on the NP-complete Exact Cover problem and Garg, Gentry, and Halevi's recent construction of "approximate" multilinear maps.Our method for witness encryption also yields the first candidate construction for an open problem posed by Rudich in 1989: constructing computational secret sharing schemes for an NP-complete access structure.
Abstract. In this work, we provide the first construction of AttributeBased Encryption (ABE) for general circuits. Our construction is based on the existence of multilinear maps. We prove selective security of our scheme in the standard model under the natural multilinear generalization of the BDDH assumption. Our scheme achieves both Key-Policy and Ciphertext-Policy variants of ABE. Our scheme and its proof of security directly translate to the recent multilinear map framework of Garg, Gentry, and Halevi.
Abstract. In [8,9] Boneh et al. presented the first fully collusion-resistant traitor tracing and trace & revoke schemes. These schemes are based on composite order bilinear groups and their security depends on the hardness of the subgroup decision assumption. In this paper we present new, efficient trace & revoke schemes which are based on prime order bilinear groups, and whose security depend on the hardness of the Decisional Linear Assumption or the External Diffie-Hellman (XDH) assumption. This allows our schemes to be flexible and thus much more efficient than existing schemes in terms a variety of parameters including ciphertext size, encryption time, and decryption time. For example, if encryption time was the major parameter of concern, then for the same level of practical security as [8] our scheme encrypts 6 times faster. Decryption is 10 times faster. The ciphertext size in our scheme is 50% less when compared to [8].We provide the first implementations of efficient fully collusion-resilient traitor tracing and trace & revoke schemes. The ideas used in this paper can be used to make other cryptographic schemes based on composite order bilinear groups efficient as well.
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