The tight security bound of the KAC (Key-Alternating Cipher) construction whose round permutations are independent from each other has been well studied. Then a natural question is how the security bound will change when we use fewer permutations in a KAC construction. In CRYPTO 2014, Chen et al. proved that 2-round KAC with a single permutation (2KACSP) has the same security level as the classic one (i.e., 2-round KAC). But we still know little about the security bound of incompletely-independent KAC constructions with more than 2 rounds. In this paper,we will show that a similar result also holds for 3-round case. More concretely, we prove that 3-round KAC with a single permutation (3KACSP) is secure up to $\varTheta(2^{\frac{3n}{4}})$ queries, which also caps the security of 3-round KAC. To avoid the cumbersome graphical illustration used in Chen et al.'s work, a new representation is introduced to characterize the underlying combinatorial problem. Benefited from it, we can handle the knotty dependence in a modular way, and also show a plausible way to study the security of $r$KACSP. Technically, we abstract a type of problems capturing the intrinsic randomness of $r$KACSP construction, and then propose a high-level framework to handle such problems. Furthermore, our proof techniques show some evidence that for any $r$, $r$KACSP has the same security level as the classic $r$-round KAC in random permutation model.

We introduce a new cryptographic primitive which is the signature analogue of fuzzy identity based encryption(IBE). We call it fuzzy identity based signature(IBS). It possesses similar error-tolerance property as fuzzy IBE that allows a user with the private key for identity $\omega$ to decrypt a ciphertext encrypted for identity $\omega'$ if and only if $\omega$ and $\omega'$ are within a certain distance judged by some metric. A fuzzy IBS is useful whenever we need to allow the user to issue signature on behalf of the group that has certain attributes. Fuzzy IBS can also be applied to biometric identity based signature. To our best knowledge, this primitive was never considered in the identity based signature before. We give the definition and security model of the new primitive and present the first practical implementation based on Sahai-Waters construction\cite{6} and the two level hierarchical signature of Boyen and Waters\cite{9}. We prove that our scheme is existentially unforgeable against adaptively chosen message attack without random oracles.

In this paper, we propose a new method for designing public key cryptosystems based on general non-commutative rings. The key idea of our proposal is that for a given non-commutative ring, we can define polynomials and take them as the underlying work structure. By doing so, it is easy to implement Diffie-Helman-like key exchange protocol. And consequently, ElGamal-like cryptosystems can be derived immediately. Moreover, we show how to extend our method to non-commutative groups (or semi-groups).

Two variants of CA-based public key authentication framework are proposed in this paper. The one is termed as public key cryptosystem without certificate management center (PKCwCMC) and the other is termed as proxy signature based authentication framework (PS-based AF). Moreover, we give an implementation of the former based on quadratic residue theory and an implementation of the latter from RSA. Both of the two variants can be looked as lite-CA based authentication frameworks since the workload and deployment of CAs in these systems are much lighter and easier than those of in the traditional CA-based PKC.