We present a constant-size signature scheme under the CDH assumption. It has a tighter security reduction than any other constant-size signature scheme with a security reduction to solving some intractable search problems. Hofheinz, Jager, and Knapp (PKC 2012) presented a constant-size signature scheme under the CDH assumption with a reduction loss of O(q), where q is the number of signing queries. They also proved that the reduction loss of O(q) is optimal in a black-box security proof. To the best of our knowledge, no constant-size signature scheme has been proposed with a tighter reduction (to the hardness of a search problem) than that proposed by Hofheinz et al., even if it is not re-randomizable. We remark that our scheme is not re-randomizable. We achieve the reduction loss of O(q/d), where d is the number of group elements in a public key.

Identity-based encryption (IBE) is an advanced form of public key encryption and one of the most important cryptographic primitives. Of the many constructions of IBE schemes, the one proposed by Boneh and Boyen (in Eurocrypt 2004) is quite important from both practical and theoretical points of view. The scheme was standardized as IEEE P1363.3 and is the basis for many subsequent constructions. In this paper, we investigate its multi-challenge security, which means that an adversary is allowed to query challenge ciphertexts multiple times rather than only once. Since single-challenge security implies multi-challenge security, and since Boneh and Boyen provided a security proof for the scheme in the single-challenge setting, the scheme is also secure in the multi-challenge setting. However, this reduction results in a large security loss. Instead, we give tight security reduction for the scheme in the multi-challenge setting. Our reduction is tight even if the number of challenge queries is not fixed in advance (that is, the queries are unbounded). Unfortunately, we are only able to prove the security in a selective setting and rely on a non-standard parameterized assumption. Nevertheless, we believe that our new security proof is of interest and provides new insight into the security of the Boneh-Boyen IBE scheme.

This paper proposes an inner-product encryption (IPE) scheme, which achieves selectively fully-attribute-hiding security in the standard model almost tightly reduced from the decisional linear (DLIN) assumption, and whose ciphertext is almost the shortest among the existing (weakly/fully) attribute-hiding IPE schemes, i.e., it consists of n+4 elements of G and 1 element of GT for a prime-order symmetric bilinear group (G, GT), where n is the dimension of attribute/predicate vectors. We also present a variant of the proposed IPE scheme that enjoys shorter public and secret keys with preserving the security. A hierarchical IPE (HIPE) scheme can be realized that has short ciphertexts and selectively fully-attribute-hiding security almost tightly reduced from the DLIN assumption.

Recently, Au et al. proposed a practical hierarchical identity-based encryption (HIBE) scheme and a hierarchical identity-based signature (HIBS) scheme. In this paper, we point out that there exists security weakness both for their HIBE and HIBS scheme. Furthermore, based on q-ABDHE, we present a new HIBE scheme which is proved secure in the standard model and it is also efficient. Compared with all previous HIBE schemes, ciphertext size as well as decryption cost are independent of the hierarchy depth. Ciphertexts in our HIBE scheme are always just four group elements and decryption requires only two bilinear map computations.

In this paper, we present an efficient variant of the Boneh-Franklin scheme that achieves a tight security reduction. Our scheme is basically an IBE scheme under two keys, one of which is randomly chosen and given to the user. It can be viewed as a continuation of an idea introduced by Katz and Wang; however, unlike the Katz-Wang variant, our scheme is quite efficient, as its ciphertext size is roughly comparable to that of the original full Boneh-Franklin scheme. The security of our scheme can be based on either the gap bilinear Diffie-Hellman (GBDH) or the decisional bilinear Diffie-Hellman (DBDH) assumptions.