Algebraic immunity is an important cryptographic property of Boolean functions. The notion of algebraic immunity of Boolean functions has been generalized in several ways to vector-valued functions over arbitrary finite fields. In this paper, the results of Ref. [25] are generalized to arbitrary finite fields. We obtain vector-valued functions over arbitrary finite fields such that their algebraic immunities can reach the upper bounds. Furthermore, all the component functions, together with their some nonzero linear combinations, of vector-valued Boolean functions achieved by this construction have optimal algebraic immunities simultaneously.
Multi-proxy signature is a scheme that an original signer delegates his or her signing capability to a proxy group.In the scheme,only the cooperation of all proxy signers in the proxy group can create a signature on behalf of the original signer.Jin and Wen firstly defined the formal security model of certificateless multi-proxy signature(CLMPS) and proposed a concrete CLMPS scheme.However,their construction has three problems:the definition of the strengthened security model is inaccurate,the concrete signature scheme has a security flaw,and the proof of the security is imperfect.With further consideration,a remedial strengthened security model is redefined,and an improved scheme is also proposed,which is existentially unforgeable against adaptively chosen-warrant,chosen-message and chosen-identity attacks in the random oracles.In this condition,the computational Diffie-Hellman(CDH) assumption is used to prove full security for our CLMPS scheme.
The discrimination of quantum operations plays a key role in quantum information and computation. Unlike discriminating quantum states, it has some special properties which can be carried out in practice. In this paper, we provide a general description of discriminating quantum operations. Concretely speaking, we describe the distinguisha- bility between quantum operations using a measure called operator fidelity. It is shown that, employing the theory of operator fidelity, we can not only verify some previous results to discriminate unitary operations, but also exhibit a more general discrimination condition. We further apply our results to analysing the security of some quantum cryptographic protocols and discuss the realization of our method using well-developed quantum algorithms.
We propose a new scheme for controlled quantum teleportation with Bell states in which classical keys for controllers' portion are used. We also discuss the security of the proposed scheme and show that it can satisfy the requirements for controlled quantum teleportation. The comparison between this scheme and the previous ones shows that it is more economical and efficient.
We present two novel quantum secure direct communication(QSDC) protocols over different collective-noise channels.Different from the previous QSDC schemes over collective-noise channels,which are all source-encrypting protocols,our two protocols are based on channel-encryption.In both schemes,two authorized users first share a sequence of EPR pairs as their reusable quantum key.Then they use their quantum key to encrypt and decrypt the secret message carried by the decoherence-free states over the collective-noise channel.In theory,the intrinsic efficiencies of both protocols are high since there is no need to consume any entangled states including both the quantum key and the information carriers except the ones used for eavesdropping checks.For checking eavesdropping,the two parties only need to perform two-particle measurements on the decoy states during each round.Finally,we make a security analysis of our two protocols and demonstrate that they are secure.
