Abstract
In this paper, we present two non-zero inner-product encryption (NIPE) schemes that are adaptively secure under a standard assumption, the decisional linear (DLIN) assumption, in the standard model. One of the proposed NIPE schemes features constant-size ciphertexts and the other features constant-size secret-keys. Our NIPE schemes imply an identity-based revocation (IBR) system with constant-size ciphertexts or constant-size secret-keys that is adaptively secure under the DLIN assumption. Any previous IBR scheme with constant-size ciphertexts or constant-size secret-keys was not adaptively secure in the standard model. This paper also presents two zero inner-product encryption (ZIPE) schemes each of which has constant-size ciphertexts or constant-size secret-keys and is adaptively secure under the DLIN assumption in the standard model. They imply an identity-based broadcast encryption system with constant-size ciphertexts or constant-size secret-keys that is adaptively secure under the DLIN assumption. We also extend the proposed ZIPE schemes in two directions, one is a fully-attribute-hiding ZIPE scheme with constant-size secret-keys, and the other a hierarchical ZIPE scheme with constant-size ciphertexts.
Highlights
1.1 BackgroundFunctional encryption (FE) is an advanced concept of encryption or a generalization of public-key encryption (PKE) and identity-based encryption (IBE)
Identity-based broadcast encryption (IBBE) [1,8,12,16,30] and revocation (IBR) [21] schemes can be thought of as functional encryption systems where a ciphertext is encrypted for a set of identities S = {I D1, . . . , I Dn} in IBBE
Katz et al [19] introduced a functional encryption scheme for zero inner products, zero inner product encryption (ZIPE) where a ciphertext encrypted with vector x can be decrypted by any key associated with vector v such that v · x = 0, i.e., relation RZIPE(v, x) = 1 iff v · x = 0
Summary
Functional encryption (FE) is an advanced concept of encryption or a generalization of public-key encryption (PKE) and identity-based encryption (IBE). Katz et al [19] introduced a functional encryption scheme for zero inner products, zero inner product encryption (ZIPE) where a ciphertext encrypted with vector x can be decrypted by any key associated with vector v such that v · x = 0, i.e., relation RZIPE(v, x) = 1 iff v · x = 0. Their scheme is selectively secure in the standard model and the ciphertext size is linear in the dimension of vectors, n, it achieves an additional security property, attribute-hiding, in which x is hidden from the ciphertext. No ZIPE scheme with constant-size secret-keys has been presented
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