Optimal and Efficient Searchable Encryption with Single Trapdoor for Multi-Owner Data Sharing in Federated Cloud Computing

Cloud computing, an Internet based computing model, has changed the way of data owners store and manage data. In such environment, data sharing is very important with more efficient data access control. Issuing an aggregate key to users on data enables and authorizes them to search for data of select encrypted files using trapdoor or encrypted keyword. The existing schemes defined for this purpose do have certain limitations. For instance, Cui et al. scheme is elegant but lacks in flexibility in access control in presence of multiple data owners sharing data to users. Its single trapdoor approach needs transformation into individual trapdoors to access data of specific data owner. Moreover, the existing schemes including that of Cui et al. does not support federated cloud.  In this paper we proposed an efficient key aggregate searchable encryption scheme which enables multiple featuressuch as support for truly single aggregate key to access data of many data owners, federated cloud support,query privacy, controlled search process and security against cross-pairing attack. It has algorithms for setup, keygen, encrypt, extract, aggregate, trapdoor, test and federator. In multi-user setting it is designed to serve data owners and users with secure data sharing through key aggregate searchable encryption The proposed scheme supports federated cloud. Experimental results revealed that the proposed scheme is provably secure withrelatively less computational overhead and time complexity when compared with the state of the art

Contributions to Lattice–based Cryptography

Post–quantum cryptography (PQC) is a new and fast–growing part of Cryptography. It focuses on developing cryptographic algorithms and protocols that resist quantum adversaries (i.e., the adversaries who have access to quantum computers). To construct a new PQC primitive, a designer must use a mathematical problem intractable for the quantum adversary. Many intractability assumptions are being used in PQC. There seems to be a consensus in the research community that the most promising are intractable/hard problems in lattices. However, lattice–based cryptography still needs more research to make it more efficient and practical. The thesis contributes toward achieving either the novelty or the practicality of lattice– based cryptographic systems

Proxy Re-Encryption and Re-Signatures from Lattices

Proxy re-encryption (PRE) and Proxy re-signature (PRS) were introduced by Blaze, Bleumer and Strauss [Eurocrypt \u2798]. Basically, PRE allows a semi-trusted proxy to transform a ciphertext encrypted under one key into an encryption of the same plaintext under another key, without revealing the underlying plaintext. Since then, many interesting applications have been explored, and many constructions in various settings have been proposed, while PRS allows a semi-trusted proxy to transform Alice\u27s signature on a message into Bob\u27s signature on the same message, but the proxy cannot produce new valid signature on new messages for either Alice or Bob. Recently, for PRE related progress, Cannetti and Honhenberger [CCS \u2707] defined a stronger notion -- CCA-security and construct a bi-directional PRE scheme. Later on, several work considered CCA-secure PRE based on bilinear group assumptions. Very recently, Kirshanova [PKC \u2714] proposed the first single-hop CCA1-secure PRE scheme based on learning with errors (LWE) assumption. For PRS related progress, Ateniese and Hohenberger [CCS\u2705] formalized this primitive and provided efficient constructions in the random oracle model. At CCS 2008, Libert and Vergnaud presented the first multi-hop uni-directional proxy re-signature scheme in the standard model, using assumptions in bilinear groups. In this work, we first point out a subtle but serious mistake in the security proof of the work by Kirshanova. This reopens the direction of lattice-based CCA1-secure constructions, even in the single-hop setting. Then we construct a single-hop PRE scheme that is proven secure in our new tag-based CCA-PRE model. Next, we construct the first multi-hop PRE construction. Lastly, we also construct the first PRS scheme from lattices that is proved secure in our proposed unified security mode

A Lattice-Based Identity-Based Proxy Blind Signature Scheme in the Standard Model

A proxy blind signature scheme is a special form of blind signature which allowed a designated person called proxy signer to sign on behalf of original signers without knowing the content of the message. It combines the advantages of proxy signature and blind signature. Up to date, most proxy blind signature schemes rely on hard number theory problems, discrete logarithm, and bilinear pairings. Unfortunately, the above underlying number theory problems will be solvable in the postquantum era. Lattice-based cryptography is enjoying great interest these days, due to implementation simplicity and provable security reductions. Moreover, lattice-based cryptography is believed to be hard even for quantum computers. In this paper, we present a new identity-based proxy blind signature scheme from lattices without random oracles. The new scheme is proven to be strongly unforgeable under the standard hardness assumption of the short integer solution problem (SIS) and the inhomogeneous small integer solution problem (ISIS). Furthermore, the secret key size and the signature length of our scheme are invariant and much shorter than those of the previous lattice-based proxy blind signature schemes. To the best of our knowledge, our construction is the first short lattice-based identity-based proxy blind signature scheme in the standard model

On the Design and Improvement of Lattice-based Cryptosystems

Digital signatures and encryption schemes constitute arguably an integral part of cryptographic schemes with the goal to meet the security needs of present and future private and business applications. However, almost all public key cryptosystems applied in practice are put at risk due to its vulnerability to quantum attacks as a result of Shor's quantum algorithm. The magnitude of economic and social impact is tremendous inherently asking for alternatives replacing classical schemes in case large-scale quantum computers are built. Lattice-based cryptography emerged as a powerful candidate attracting lots of attention not only due to its conjectured resistance against quantum attacks, but also because of its unique security guarantee to provide worst-case hardness of average-case instances. Hence, the requirement of imposing further assumptions on the hardness of randomly chosen instances disappears, resulting in more efficient instantiations of cryptographic schemes. The best known lattice attack algorithms run in exponential time. In this thesis we contribute to a smooth transition into a world with practically efficient lattice-based cryptographic schemes. This is indeed accomplished by designing new algorithms and cryptographic schemes as well as improving existing ones. Our contributions are threefold. First, we construct new encryption schemes that fully exploit the error term in LWE instances. To this end, we introduce a novel computational problem that we call Augmented LWE (A-LWE), differing from the original LWE problem only in the way the error term is produced. In fact, we embed arbitrary data into the error term without changing the target distributions. Following this, we prove that A-LWE instances are indistinguishable from LWE samples. This allows to build powerful encryption schemes on top of the A-LWE problem that are simple in its representations and efficient in practice while encrypting huge amounts of data realizing message expansion factors close to 1. This improves, to our knowledge, upon all existing encryption schemes. Due to the versatility of the error term, we further add various security features such as CCA and RCCA security or even plug lattice-based signatures into parts of the error term, thus providing an additional mechanism to authenticate encrypted data. Based on the methodology to embed arbitrary data into the error term while keeping the target distributions, we realize a novel CDT-like discrete Gaussian sampler that beats the best known samplers such as Knuth-Yao or the standard CDT sampler in terms of running time. At run time the table size amounting to 44 elements is constant for every discrete Gaussian parameter and the total space requirements are exactly as large as for the standard CDT sampler. Further results include a very efficient inversion algorithm for ring elements in special classes of cyclotomic rings. In fact, by use of the NTT it is possible to efficiently check for invertibility and deduce a representation of the corresponding unit group. Moreover, we generalize the LWE inversion algorithm for the trapdoor candidate of Micciancio and Peikert from power of two moduli to arbitrary composed integers using a different approach. In the second part of this thesis, we present an efficient trapdoor construction for ideal lattices and an associated description of the GPV signature scheme. Furthermore, we improve the signing step using a different representation of the involved perturbation matrix leading to enhanced memory usage and running times. Subsequently, we introduce an advanced compression algorithm for GPV signatures, which previously suffered from huge signature sizes as a result of the construction or due to the requirement of the security proof. We circumvent this problem by introducing the notion of public and secret randomness for signatures. In particular, we generate the public portion of a signature from a short uniform random seed without violating the previous conditions. This concept is subsequently transferred to the multi-signer setting which increases the efficiency of the compression scheme in presence of multiple signers. Finally in this part, we propose the first lattice-based sequential aggregate signature scheme that enables a group of signers to sequentially generate an aggregate signature of reduced storage size such that the verifier is still able to check that each signer indeed signed a message. This approach is realized based on lattice-based trapdoor functions and has many application areas such as wireless sensor networks. In the final part of this thesis, we extend the theoretical foundations of lattices and propose new representations of lattice problems by use of Cauchy integrals. Considering lattice points as simple poles of some complex functions allows to operate on lattice points via Cauchy integrals and its generalizations. For instance, we can deduce for the one-dimensional and two-dimensional case simple expressions for the number of lattice points inside a domain using trigonometric or elliptic functions

Research Philosophy of Modern Cryptography

Proposing novel cryptography schemes (e.g., encryption, signatures, and protocols) is one of the main research goals in modern cryptography. In this paper, based on more than 800 research papers since 1976 that we have surveyed, we introduce the research philosophy of cryptography behind these papers. We use ``benefits and ``novelty as the keywords to introduce the research philosophy of proposing new schemes, assuming that there is already one scheme proposed for a cryptography notion. Next, we introduce how benefits were explored in the literature and we have categorized the methodology into 3 ways for benefits, 6 types of benefits, and 17 benefit areas. As examples, we introduce 40 research strategies within these benefit areas that were invented in the literature. The introduced research strategies have covered most cryptography schemes published in top-tier cryptography conferences

Public Key Encryption with Keyword Search from Lattices in Multiuser Environments

A public key encryption scheme with keyword search capabilities is proposed using lattices for applications in multiuser environments. The proposed scheme enables a cloud server to check if any given encrypted data contains certain keywords specified by multiple users, but the server would not have knowledge of the keywords specified by the users or the contents of the encrypted data, which provides data privacy as well as privacy for user queries in multiuser environments. It can be proven secure under the standard learning with errors assumption in the random oracle model