Efficient and Verifiable Algorithms for Secure Outsourcing of Cryptographic Computations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Reducing computational cost of cryptographic computations for resource-constrained devices is an active research area. One of the practical solutions is to securely outsource the computations to an external and more powerful cloud server. Modular exponentiations are the most expensive computation from the cryptographic point of view. Therefore, outsourcing modular exponentiations to a single, external and potentially untrusted cloud server while ensuring the security and privacy provide an efficient solution. In this paper, we propose new efficient outsourcing algorithms for modular exponentiations using only one untrusted cloud server. These algorithms cover public-base & private-exponent, private-base & public-exponent, private-base & privateexponent, and more generally private-base & private-exponents simultaneous modular exponentiations. Our algorithms are the most efficient solutions utilizing only one single untrusted server with best checkability probabilities. Furthermore, unlike existing schemes, which have fixed checkability probability, our algorithms provide adjustable predetermined checkability parameters. Finally, we apply our algorithms to outsource Oblivious Transfer Protocols and Blind Signatures which are expensive primitives in modern cryptography

A Review on: Association Rule Mining Using Privacy for Partitioned Database

Data Analysis techniques that are Association manage mining and Frequent thing set mining are two prominent and broadly utilized for different applications. The conventional framework concentrated independently on vertically parceled database and on a level plane apportioned databases on the premise of this presenting a framework which concentrate on both on a level plane and vertically divided databases cooperatively with protection safeguarding component. Information proprietors need to know the continuous thing sets or affiliation rules from an aggregate information set and unveil or uncover as few data about their crude information as could reasonably be expected to other information proprietors and outsiders. To guarantee information protection a Symmetric Encryption Technique is utilized to show signs of improvement result. Cloud supported successive thing set mining arrangement used to exhibit an affiliation govern mining arrangement. The subsequent arrangements are intended for outsourced databases that permit various information proprietors to proficiently share their information safely without trading off on information protection. Information security is one of the key procedures in outsourcing information to different outside clients. Customarily Fast Distribution Mining calculation was proposed for securing conveyed information. These business locales an issue by secure affiliation governs over parceled information in both even and vertical. A Frequent thing sets calculation and Distributed affiliation administer digging calculation is used for doing above method adequately in divided information, which incorporates administrations of the information in outsourcing process for disseminated databases. This work keeps up or keeps up proficient security over vertical and flat perspective of representation in secure mining applications

Revisiting Single-server Algorithms for Outsourcing Modular Exponentiation

We investigate the problem of securely outsourcing modular exponentiations to a single, malicious computational resource. We revisit recently proposed schemes using single server and analyse them against two fundamental security properties, namely privacy of inputs and verifiability of outputs. Interestingly, we observe that the chosen schemes do not appear to meet both the security properties. In fact we present a simple polynomial-time attack on each algorithm, allowing the malicious server either to recover a secret input or to convincingly fool the client with wrong outputs. Then we provide a fix to the identified problem in the ExpSOS scheme. With our fix and without pre-processing, the improved scheme becomes the best to-date outsourcing scheme for single-server case. Finally we present the first precomputation-free single-server algorithm, \pi ExpSOS for simultaneous exponentiations

Practical and Secure Outsourcing of Discrete Log Group Exponentiation to a Single Malicious Server

Group exponentiation is an important operation used in many public-key cryptosystems and, more generally, cryptographic protocols. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that this operation is outsourced from a computationally weaker client to a computationally stronger server, possibly implemented in a cloud-based architecture. While preliminary solutions to this problem considered mostly honest servers, or multiple separated servers, some of which honest, solving this problem in the case of a single (logical), possibly malicious, server, has remained open since a formal cryptographic model was introduced. Several later attempts either failed to achieve privacy or only bounded by a constant the (security) probability that a cheating server convinces a client of an incorrect result. In this paper we solve this problem for a large class of cyclic groups, thus making our solutions applicable to many cryptosystems in the literature that are based on the hardness of the discrete logarithm problem or on related assumptions. Our main protocol satisfies natural correctness, security, privacy and efficiency requirements, where the security probability is exponentially small. In our main protocol, with very limited offline computation and server computation, the client can delegate an exponentiation to an exponent of the same length as a group element by performing an exponentiation to an exponent of short length (i.e., the length of a statistical parameter). We also show an extension protocol that further reduces client computation by a constant factor, while increasing offline computation and server computation by about the same factor

Secure k-Nearest Neighbor Query over Encrypted Data in Outsourced Environments

For the past decade, query processing on relational data has been studied extensively, and many theoretical and practical solutions to query processing have been proposed under various scenarios. With the recent popularity of cloud computing, users now have the opportunity to outsource their data as well as the data management tasks to the cloud. However, due to the rise of various privacy issues, sensitive data (e.g., medical records) need to be encrypted before outsourcing to the cloud. In addition, query processing tasks should be handled by the cloud; otherwise, there would be no point to outsource the data at the first place. To process queries over encrypted data without the cloud ever decrypting the data is a very challenging task. In this paper, we focus on solving the k-nearest neighbor (kNN) query problem over encrypted database outsourced to a cloud: a user issues an encrypted query record to the cloud, and the cloud returns the k closest records to the user. We first present a basic scheme and demonstrate that such a naive solution is not secure. To provide better security, we propose a secure kNN protocol that protects the confidentiality of the data, user's input query, and data access patterns. Also, we empirically analyze the efficiency of our protocols through various experiments. These results indicate that our secure protocol is very efficient on the user end, and this lightweight scheme allows a user to use any mobile device to perform the kNN query.Comment: 23 pages, 8 figures, and 4 table

Delegating a Product of Group Exponentiations with Application to Signature Schemes

Many public-key cryptosystems and, more generally, cryptographic protocols, use group exponentiations as important primitive operations. To expand the applicability of these solutions to computationally weaker devices, it has been advocated that a computationally weaker client (i.e., capable of performing a relatively small number of modular multiplications) delegates such primitive operations to a computationally stronger server. Important requirements for such delegation protocols include privacy of the client's input exponent and security of the client's output, in the sense of detecting, except for very small probability, any malicious server's attempt to convince the client of an incorrect exponentiation result. Only recently, ecient protocols for the delegation of a xed-based exponentiation, over cyclic and RSA-type groups with certain properties, have been presented and proved to satisfy both requirements. In this paper we show that a product of many xed-base exponentiations, over a cyclic groups with certain properties, can be privately and securely delegated by keeping the client's online number of modular multiplications only slightly larger than in the delegation of a single exponentiation. We use this result to show the rst delegations of entire cryptographic schemes: the well-known digital signature schemes by El-Gamal, Schnorr and Okamoto, over the q-order subgroup in Zp, for p; q primes, as well as their variants based on elliptic curves. Previous ecient delegation results seem limited to the delegation of single algorithms within cryptographic schemes

Hide The Modulus: A Secure Non-Interactive Fully Verifiable Delegation Scheme for Modular Exponentiations via CRT

Security protocols using public-key cryptography often requires large number of costly modular exponentiations (MEs). With the proliferation of resource-constrained (mobile) devices and advancements in cloud computing, delegation of such expensive computations to powerful server providers has gained lots of attention. In this paper, we address the problem of verifiably secure delegation of MEs using two servers, where at most one of which is assumed to be malicious (the OMTUP-model). We first show verifiability issues of two recent schemes: We show that a scheme from IndoCrypt 2016 does not offer full verifiability, and that a scheme for $n$ simultaneous MEs from AsiaCCS 2016 is verifiable only with a probability $0.5909$ instead of the author\u27s claim with a probability $0.9955$ for $n=10$. Then, we propose the first non-interactive fully verifiable secure delegation scheme by hiding the modulus via Chinese Remainder Theorem (CRT). Our scheme improves also the computational efficiency of the previous schemes considerably. Hence, we provide a lightweight delegation enabling weak clients to securely and verifiably delegate MEs without any expensive local computation (neither online nor offline). The proposed scheme is highly useful for devices having (a) only ultra-lightweight memory, and (b) limited computational power (e.g. sensor nodes, RFID tags)

Efficient Delegated Private Set Intersection on Outsourced Private Datasets

Private set intersection (PSI) is an essential cryptographic protocol that has many real world applications. As cloud computing power and popularity have been swiftly growing, it is now desirable to leverage the cloud to store private datasets and delegate PSI computation to it. Although a set of efficient PSI protocols have been designed, none support outsourcing of the datasets and the computation. In this paper, we propose two protocols for delegated PSI computation on outsourced private datasets. Our protocols have a unique combination of properties that make them particularly appealing for a cloud computing setting. Our first protocol, O-PSI, satisfies these properties by using additive homomorphic encryption and point-value polynomial representation of a set. Our second protocol, EO-PSI, is mainly based on a hash table and point-value polynomial representation and it does not require public key encryption; meanwhile, it retains all the desirable properties and is much more efficient than the first one. We also provide a formal security analysis of the two protocols in the semi-honest model and we analyze their performance utilizing prototype implementations we have developed. Our performance analysis shows that EO-PSI scales well and is also more efficient than similar state-of-the-art protocols for large set sizes