New constructions of equality test scheme for cloud-assisted wireless sensor networks

Public key encryption with equality test enables the user to determine whether two ciphertexts contain the same information without decryption. Therefore, it may serve as promising cryptographic technique for cloud-assisted wireless sensor networks (CWSNs) to maintain data privacy. In this paper, an efficient RSA with equality test algorithm is proposed. The presented scheme also handles the attackers based on their authorization ability. Precisely, the proposed scheme is proved to be one-way against chosen-ciphertext attack security and indistinguishable against chosen ciphertext attacks. Moreover, the experimental evaluations depict that the underlying scheme is efficient in terms of encryption, decryption, and equality testing. Thus, this scheme may be used as a practical solution in context of CWSNs, where the users may compare two ciphertexts without decryption.


Response:
Thank you for your careful comments. We have rewritten the Introduction thoroughly (please see Page1 and 2).
With the development of Internet of Things (IoT) and the technology of cloud computing [1], cloud-assisted wireless sensor networks (CWSNs) are widely applied in many fields, such as agriculture, military, transportation, medical and other similar fields. Although, CWSNs have extensive applications, but there also exist challenges to be addressed such as reduction of energy consumption. Recently in 2020, Guermazi et al. proposed a method to reduce energy consumption as well as to extend the lifetime of wireless sensor network [2]. For the evaluation models, Cao et al. proposed five intelligent evaluation models and implemented their experiments on the Nearest Closer Protocol with the J-Sim simulation tool [3]. The security of data is another imperative issue. Practically, extensive amount of data is being transmitted and stored on distributed servers, where it may face several threats. Therefore, to protect the confidentiality of such data is particularly important [4]. At present, various cryptographic algorithms are introduced for CWSNs environment. However, private key is necessary to obtain information from the encrypted data, that reduces the availability of data. … … Since, the equality test algorithm is based on a ray. Therefore, comparing the proposal with the schemes based on bilinear pairing, it is simpler and easier to implement. Thank you sincerely for your comments on our work. According to your valuable suggestions, we have read some works about the schemes with equality test carefully. We have described the performance analysis form encryption and decryption algorithms in references of [23-26] to our works. Details are as follows: 2E+1I CEnc and CDec: the computation complexity of algorithms for encryption and decryption; E, P and I: the exponentiation operation, the pairing operation and the inversion operation in the group G.
In Table 11, we present the comparison with the earlier PKEwET schemes while considering the computation complexity of encryption and decryption algorithms. It shows that the presented scheme achieves lower computational complexity. Again, we sincerely appreciate the time you spent in reviewing our paper.

Reviewer #2: New Constructions of Equality Test Scheme for Cloud-Assisted Wireless
Sensor Networks is presented in this paper. It is an interesting topic and contribution is also good. However, I have following queries on this paper: 1. Explain the novelty of your work presented in this work.

Response:
Thank you sincerely for your comments on our work. We have explain the novelty of our work as follows: In our work, we introduce the idea of public key encryption with equality test into RSA scheme. The proposed scheme fills the gap of RSA algorithm in the context of equality test over ciphertext. To the best of our knowledge, this is the novel algorithm of RSA with equality test. To enhance the security of the scheme, a simple and efficient Fujisaki and Okamoto method is introduced. More precisely, To prove the efficiency of the proposed scheme, the performance analysis is presented on 512, 1024 and 2048 bits. The time of algorithm is compared in context of KenGen , encryption, decryption and test algorithms.
These comparisons validate the claim of scheme efficiency. To simplify the scheme, the equality test algorithm is based on a ray. Therefore, comparing the proposal with the schemes based on bilinear pairing, it is simpler and easier to implement.
2. Paper needs to polish and provide a detailed explanation of theoretical aspects such as conditions and theorems, and practical issues like algorithms, rules and possible applications.

Response:
Thanks for your friendly comments. We have introduced security algorithm of the Table 1 and  Table 2 into our work as follows: As described in Table 1, the KeyGen algorithm takes 1 k and sp as inputs, then, outputs the public key pk and private key sk. A1 asks for key queries, decryption queries and authorization queries. Then S initiate the challenge phase. S chooses a message m and outputs ciphertext ct * by performing encryption algorithm Enc(pk,m). Then, A1 inquires more queries in phase 2, including key queries, decryption queries and authorization queries. But it must satisfy the requirements of O4 and O5. Afterwards, A1 outputs a message of m, a guessing of ct * . As mentioned in Table 2, the KeyGen algorithm takes 1 k and sp as inputs, then, outputs the public key pk and private key sk. A2 asks for key queries and decryption queries. A2 chooses two message m0 and m1 for S. Then, S performs challenge phase. S chooses a message mb (b {0,1}) and outputs ciphertext ct * by performing encryption algorithm (Enc(pk,mb)). Then, A2 inquires more queries in phase 2, such as key queries and decryption queries. But it must satisfy the requirements of O4 and O5. Then, A2 outputs the guess of b. 3. The Introduction section needs to be re-written to improve its quality and readability.
Improve the quality of illustrations in this paper and explain those properly. Following are some of relevant and recent references which need to be discussed in the revised manuscript: Sensored Semantic Annotation for Traffic Control Based on Knowledge Inference in Video A Multi-Conditional Proxy Broadcast Re-Encryption Scheme for Sensor Networks Modeling deep learning neural networks with denotational mathematics in UbiHealth environment Evaluation models for the nearest closer routing protocol in wireless sensor networks A novel energy consumption approach to extend the lifetime for wireless sensor network IoT-based Big Data secure management in the Fog over a 6G Wireless Network IoT transaction processing through cooperative concurrency control on fog-cloud computing environment

Response:
We agree with you. Again, we sincerely appreciate the time you spent in reviewing our paper. We have rewrited the Introduction and redrawned the picture (see Page 1-3). Moreover we have added some typical studies in Background Knowledge (see Page1 and 4).
With the development of Internet of Things (IoT) and the technology of cloud computing [1], cloud-assisted wireless sensor networks (CWSNs) are widely applied in many fields, such as agriculture, military, transportation, medical and other similar fields. Although, CWSNs have extensive applications, but there also exist challenges to be addressed such as reduction of energy consumption. Recently in 2020, Guermazi et al. proposed a method to reduce energy consumption as well as to extend the lifetime of wireless sensor network [2]. Thank you sincerely for your comments on our work. We have rewrited the contribution of our work as follows: The idea of public key encryption with equality test is introduced into RSA scheme. The proposed scheme fills the gap of RSA algorithm in the context of equality test over ciphertext. The major target of this paper is to make the RSA algorithm enjoying the equality test of ciphertexts. To the best of our knowledge, this is the novel algorithm of RSA with equality test.
A simple and efficient Fujisaki and Okamoto method is introduced to enhance the security of the proposed scheme. More precisely, a semantically secure public-key encryption scheme against passive adversaries is improved to a non-malleable public-key encryption scheme against adaptive chosen ciphertext attacks in the random oracle model.
To prove the efficiency of the proposed scheme, the performance analysis is presented on 512, 1024 and 2048 bits. The time of algorithm is compared in context of KenGen , encryption, decryption and test algorithms. These comparisons validate the claim of scheme efficiency.
Since, the equality test algorithm is based on a ray. Therefore, comparing the proposal with the schemes based on bilinear pairing, it is simpler and easier to implement.
6. There are many English and grammatical issues in the paper which need to be rectified.
We agree with you. We have checked the manuscript carefully again both in English and in depth to improve the quality of our manuscript. Here we list some corrections ( for an incomplete list) as follows: (1) " Although the application of CWSNs is very extensive, it still faces many challenges, especially the energy consumed. " has been changed to " Although, CWSNs have extensive applications, but there also exist challenges to be addressed such as reduction of energy consupmtion. "