Energy big data: A survey <s> 1) HOMOMORPHIC ENCRYPTION SCHEME <s> An encryption method is presented with the novel property that publicly revealing an encryption key does not thereby reveal the corresponding decryption key. This has two important consequences: (1) Couriers or other secure means are not needed to transmit keys, since a message can be enciphered using an encryption key publicly revealed by the intented recipient. Only he can decipher the message, since only he knows the corresponding decryption key. (2) A message can be “signed” using a privately held decryption key. Anyone can verify this signature using the corresponding publicly revealed encryption key. Signatures cannot be forged, and a signer cannot later deny the validity of his signature. This has obvious applications in “electronic mail” and “electronic funds transfer” systems. A message is encrypted by representing it as a number M, raising M to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n , of two large secret primer numbers p and q. Decryption is similar; only a different, secret, power d is used, where e * d ≡ 1(mod (p - 1) * (q - 1)). The security of the system rests in part on the difficulty of factoring the published divisor, n . <s> BIB001 </s> Energy big data: A survey <s> 1) HOMOMORPHIC ENCRYPTION SCHEME <s> This paper investigates a novel computational problem, namely the Composite Residuosity Class Problem, and its applications to public-key cryptography. We propose a new trapdoor mechanism and derive from this technique three encryption schemes : a trapdoor permutation and two homomorphic probabilistic encryption schemes computationally comparable to RSA. Our cryptosystems, based on usual modular arithmetics, are provably secure under appropriate assumptions in the standard model. <s> BIB002 </s> Energy big data: A survey <s> 1) HOMOMORPHIC ENCRYPTION SCHEME <s> Let ψ be a 2-DNF formula on boolean variables x1,...,xn ∈ {0,1}. We present a homomorphic public key encryption scheme that allows the public evaluation of ψ given an encryption of the variables x1,...,xn. In other words, given the encryption of the bits x1,...,xn, anyone can create the encryption of ψ(x1,...,xn). More generally, we can evaluate quadratic multi-variate polynomials on ciphertexts provided the resulting value falls within a small set. We present a number of applications of the system: ::: ::: In a database of size n, the total communication in the basic step of the Kushilevitz-Ostrovsky PIR protocol is reduced from $\sqrt{n}$ to $\sqrt[3]{n}$. ::: ::: An efficient election system based on homomorphic encryption where voters do not need to include non-interactive zero knowledge proofs that their ballots are valid. The election system is proved secure without random oracles but still efficient. ::: ::: A protocol for universally verifiable computation. <s> BIB003 </s> Energy big data: A survey <s> 1) HOMOMORPHIC ENCRYPTION SCHEME <s> We propose a fully homomorphic encryption scheme -- i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in three steps. First, we provide a general result -- that, to construct an encryption scheme that permits evaluation of arbitrary circuits, it suffices to construct an encryption scheme that can evaluate (slightly augmented versions of) its own decryption circuit; we call a scheme that can evaluate its (augmented) decryption circuit bootstrappable. Next, we describe a public key encryption scheme using ideal lattices that is almost bootstrappable. Lattice-based cryptosystems typically have decryption algorithms with low circuit complexity, often dominated by an inner product computation that is in NC1. Also, ideal lattices provide both additive and multiplicative homomorphisms (modulo a public-key ideal in a polynomial ring that is represented as a lattice), as needed to evaluate general circuits. Unfortunately, our initial scheme is not quite bootstrappable -- i.e., the depth that the scheme can correctly evaluate can be logarithmic in the lattice dimension, just like the depth of the decryption circuit, but the latter is greater than the former. In the final step, we show how to modify the scheme to reduce the depth of the decryption circuit, and thereby obtain a bootstrappable encryption scheme, without reducing the depth that the scheme can evaluate. Abstractly, we accomplish this by enabling the encrypter to start the decryption process, leaving less work for the decrypter, much like the server leaves less work for the decrypter in a server-aided cryptosystem. <s> BIB004 </s> Energy big data: A survey <s> 1) HOMOMORPHIC ENCRYPTION SCHEME <s> Due to the increasing popularity of cloud computing, more and more data owners are motivated to outsource their data to cloud servers for great convenience and reduced cost in data management. However, sensitive data should be encrypted before outsourcing for privacy requirements, which obsoletes data utilization like keyword-based document retrieval. In this paper, we present a secure multi-keyword ranked search scheme over encrypted cloud data, which simultaneously supports dynamic update operations like deletion and insertion of documents. Specifically, the vector space model and the widely-used TF _ IDF model are combined in the index construction and query generation. We construct a special tree-based index structure and propose a “Greedy Depth-first Search” algorithm to provide efficient multi-keyword ranked search. The secure kNN algorithm is utilized to encrypt the index and query vectors, and meanwhile ensure accurate relevance score calculation between encrypted index and query vectors. In order to resist statistical attacks, phantom terms are added to the index vector for blinding search results. Due to the use of our special tree-based index structure, the proposed scheme can achieve sub-linear search time and deal with the deletion and insertion of documents flexibly. Extensive experiments are conducted to demonstrate the efficiency of the proposed scheme. <s> BIB005 </s> Energy big data: A survey <s> 1) HOMOMORPHIC ENCRYPTION SCHEME <s> In cloud computing, searchable encryption scheme over outsourced data is a hot research field. However, most existing works on encrypted search over outsourced cloud data follow the model of “one size fits all” and ignore personalized search intention. Moreover, most of them support only exact keyword search, which greatly affects data usability and user experience. So how to design a searchable encryption scheme that supports personalized search and improves user search experience remains a very challenging task. In this paper, for the first time, we study and solve the problem of personalized multi-keyword ranked search over encrypted data (PRSE) while preserving privacy in cloud computing. With the help of semantic ontology WordNet, we build a user interest model for individual user by analyzing the user’s search history, and adopt a scoring mechanism to express user interest smartly. To address the limitations of the model of “one size fit all” and keyword exact search, we propose two PRSE schemes for different search intentions. Extensive experiments on real-world dataset validate our analysis and show that our proposed solution is very efficient and effective. <s> BIB006
The transmitted information are always private, so encryption technology is necessary to prevent unpredictable attacks BIB005 , BIB006 . Paillier BIB002 used an homomorphic probabilistic encryption scheme to deal with the composite residuosity class problem. Boneh et al. BIB003 proposed another homomorphic encryption scheme which can encrypt the information and ensure the confidentiality. The encryption protocol has three following components: • Key generation: When given a security coefficient, this algorithm generates public keys and global parameters. Set n = q 1 · q 2 , where q 1 , q 2 are primes. Select N ∈ Z * n 2 such that N has an order which is a multiple of n and , where Z * represents the adjoint matrix of Z. Set λ(n) = lcm(q 1 − 1, q 2 − 1), where lcm means the least common multiple. Let i represents the i-th intended receiver that a message is sent for. Then the public key of i-th receiver can be expressed as: PK [i] = (n, N ), the secret key can be expressed as: • Encryption method: Select m ∈ Z n which represents a message. Choose a random number r ∈ Z * n . Then the ciphertext c can be given by: c = E(m) = N m r n mod n 2 where r n is an enhancing factor to make the homomorphic computation indeterministic. • Decryption method: Decryption from c to m is according to: where the L-function takes input from the data set U = {u|u = 1 mod nandu < n 2 } and the output can be calculated in: L(u) = (u − 1)/n. Supposing c 1 = E(m 1 ) and c 2 = E(m 2 ) are two ciphertexts for m 1 , m 2 ∈ Z n respectively, then the sum of the plaintexts S can be obtained from the ciphertexts: Except for the additive homomorphism model above, the same information can be encrypted into different ciphertexts by various homomorphism encryption techniques. Rivest et al. BIB001 used a multiplicative homomorphism encryption method to keep privacy and authority in an electronic mail system. Gentry BIB004 proposed fully homomorphic scheme which can support complicated functions.