Safe and efficient collection of users’ electronic consumption data is a basic function of the smart grid. Anonymous aggregate signature is a fine option to realize this feature, which can not only reduce the computing cost of the data center (DC) but also protect the user’s identity information from leaking. The security proofs of all known identity-based aggregate signature (IBAS) schemes were completed in the random oracle model (ROM). Regrettably, these schemes are not necessarily secure in real life. In this article, we first propose the system model and security demands of an identity-based designated verifier anonymous aggregate signature (IB-DVAAS) scheme for smart grids. We then come up with a concrete scheme, only the designated DC can check the validity of an aggregate signature, but it cannot recognize the real identity of the signers. Next, we display the security proofs in the standard model. Finally, we conduct an analysis on performance for six aggregate signature schemes. Only three pairing operations are required and hash-to-point operations are not used, the calculation cost of the new scheme is lower than that of other schemes.

In this paper, we find all Lucas numbers written in the form $\overline{c\cdots cd\cdots d}$, where $\overline{c\cdots cd\cdots d}$ is the concatenation of two repdigits in base 10 with $c,d\in \{0,1,\cdots ,9\}$, $c\ne d$ and $c>0$.

As we all know, the random oracle model (ROM) is a simulation of the hash function and cannot replace the actual computation of hash function and the public-key cryptography scheme, which was proved to be secure in ROM may be insecure when instantiating random oracles with concrete hash functions in practical applications. So far as we know, certificateless proxy signcryption (CLPSC) scheme’s security is only proved by applying ROM. Therefore, it is quite important to construct a CLPSC scheme in the standard model (SM). In this article, we propose the first CLPSC scheme in SM, which can achieve public verifiability and we prove that this scheme is EUF-CMA-CLPSC security and IND-CCA-CLPSC security against type I adversary $\mathcal {A}_{I}$ and Type II adversary $\mathcal {A}_{II}$ . Additionally, we compare our scheme’s performance with several previous schemes’ performance in terms of calculation, communication, and security. The results show that our CLPSC scheme has better security performance, which is suitable for a unmanned aerial vehicle network.

With the rapid development of wireless communication technologies and the popularity of mobile communication devices, people can easily access the Internet through their mobile communication devices. Compared with the traditional wired communication, this brings great convenience to people’s lives, but at the same time, it also brings greater challenges in terms of security and privacy. In order to protect the confidentiality of the transmitted message and prevent the identity information of message recipients from being leaked, some certificateless multireceiver encryption (CLMRE) schemes that could realize the anonymity of the receivers have been proposed. But most of the proposed schemes are either under the random oracle model (ROM), or based on bilinear pairings and hash-to-point (HTP) operations, which lead to expensive operation costs in encryption or decryption. In the ROM, in order to gain the value of the hash function, the adversary makes a query to the challenger, but in the standard model (SM), the adversary can compute the hash function directly. The cryptographic scheme based on the SM has higher security than the cryptographic scheme based on the ROM. Therefore, it is very meaningful and necessary to design an efficient CLMRE scheme without bilinear pairings and HTP operations under the SM, which is suitable for mobile communication devices. In this article, we propose the first CLMRE scheme without bilinear parings and HTP operations in the SM, and we prove that this scheme is indistinguishable and anonymous against Type-I adversary $\mathcal {A}_\text{I}$ and Type-II adversary $\mathcal {A}_{\text{II}}$ . Additionally, we compare our scheme’s performance in calculation and communication with several previous schemes. The analysis shows that our novel scheme based on the SM is efficient in terms of calculation, communication, and it is suitable for mobile communication devices.

In this paper, we find all Fibonacci and Lucas numbers written in the form $2^a+3^b+5^c+7^d$ , in non-negative integers $a,b,c,d$ , with $0\le \max \{a,b,c\}\le d$ .