# Biblio

In this work, we will present a new hybrid cryptography method based on two hard problems: 1- The problem of the discrete logarithm on an elliptic curve defined on a finite local ring. 2- The closest vector problem in lattice and the conjugate problem on square matrices. At first, we will make the exchange of keys to the Diffie-Hellman. The encryption of a message is done with a bad basis of a lattice.

With the rapid development of the contemporary society, wide use of smart phone and vehicle sensing devices brings a huge influence on the extensive data collection. Network coding can only provide weak security privacy protection. Aiming at weak secure feature of network coding, this paper proposes an information transfer mechanism, Weak Security Network Coding with Homomorphic Encryption (HE-WSNC), and it is integrated into routing policy. In this mechanism, a movement model is designed, which allows information transmission process under Wi-Fi and Bluetooth environment rather than consuming 4G data flow. Not only does this application reduce the cost, but also improve reliability of data transmission. Moreover, it attracts more users to participate.

Generating a secure source of publicly-verifiable randomness could be the single most fundamental technical challenge on a distributed network, especially in the blockchain context. Many current proposals face serious problems of scalability and security issues. We present a protocol which can be implemented on a blockchain that ensures unpredictable, tamper-resistant, scalable and publicly-verifiable outcomes. The main building blocks of our protocol are homomorphic encryption (HE) and verifiable random functions (VRF). The use of homomorphic encryption enables mathematical operations to be performed on encrypted data, to ensure no one knows the outcome prior to being generated. The protocol requires O(n) elliptic curve multiplications and additions as well as O(n) signature signing and verification operations, which permits great scalability. We present a comparison between recent approaches to the generation of random beacons.

Protocols for securely testing the equality of two encrypted integers are common building blocks for a number of proposals in the literature that aim for privacy preservation. Being used repeatedly in many cryptographic protocols, designing efficient equality testing protocols is important in terms of computation and communication overhead. In this work, we consider a scenario with two parties where party A has two integers encrypted using an additively homomorphic scheme and party B has the decryption key. Party A would like to obtain an encrypted bit that shows whether the integers are equal or not but nothing more. We propose three secure equality testing protocols, which are more efficient in terms of communication, computation or both compared to the existing work. To support our claims, we present experimental results, which show that our protocols achieve up to 99% computation-wise improvement compared to the state-of-the-art protocols in a fair experimental set-up.

Due to privacy threats associated with computation of outsourced data, processing data on the encrypted domain has become a viable alternative. Secure computation of encrypted data is relevant for analysing datasets in areas (such as genome processing, private data aggregation, cloud computations) that require basic arithmetic operations. Performing division operation over-all encrypted inputs has not been achieved using homomorphic schemes in non-interactive modes. In interactive protocols, the cost of obtaining an encrypted quotient (from encrypted values) is computationally expensive. To the best of our knowledge, existing homomorphic solutions on encrypted division are often relaxed to consider public or private divisor. We acknowledge that there are other techniques such as secret sharing and garbled circuits adopted to compute secure division, but we are interested in homomorphic solutions. We propose an efficient and interactive two-party protocol that computes the fixed-point quotient of two encrypted inputs, using an efficient and secure comparison protocol as a sub-protocol. Our proposal provides a computational advantage, with a linear complexity in the digit precision of the quotient. We provide proof of security in the universally composable framework and complexity analyses. We present experimental results for two cryptosystem implementations in order to compare performance. An efficient prototype of our protocol is implemented using additive homomorphic scheme (Paillier), whereas a non-efficient fully-homomorphic scheme (BGV) version is equally presented as a proof of concept and analyses of our proposal.

The huge amount of generated data offers special advantages mainly in dynamic and scalable systems. In fact, the data generator entities need to share the generated data with each other which leads to the use of cloud services. A cloud server is considered as an untrusted entity that offers many advantages such as large storing space, computation speed... etc. Hence, there is a need to cope with how to protect the stored data in the cloud server by proposing adaptive solutions. The main objective is how to provide an encryption scheme allowing the user to maintains some functions such as addition, multiplication and to preserve the order on the encrypted cloud data. Many algorithms and techniques are designed to manipulate the stored encrypted cloud data. This paper presents an adaptive and efficient fully homomorphic encryption technique to protect the user's data stored in the cloud, where the cloud server executes simple operations.

Edge detection is one of the most important topics of image processing. In the scenario of cloud computing, performing edge detection may also consider privacy protection. In this paper, we propose an edge detection and image segmentation scheme on an encrypted image with Sobel edge detector. We implement Gaussian filtering and Sobel operator on the image in the encrypted domain with homomorphic property. By implementing an adaptive threshold decision algorithm in the encrypted domain, we obtain a threshold determined by the image distribution. With the technique of garbled circuit, we perform comparison in the encrypted domain and obtain the edge of the image without decrypting the image in advanced. We then propose an image segmentation scheme on the encrypted image based on the detected edges. Our experiments demonstrate the viability and effectiveness of the proposed encrypted image edge detection and segmentation.