Efficient Public Key Encryption Scheme Research Articles

Polar coding for Ring-LWE-based public key encryption

The ring learning with errors (RLWE) problem can be used to construct efficient post-quantum public key encryption schemes. An error distribution, normally a Gaussian-like distribution, is involved in the RLWE problem. In this work we focus on using polar codes to alleviate a natural trade-off present in RLWE public key encryption schemes; namely, we would like a wider error distribution to increase security, but a wider error distribution comes at the cost of an increased probability of decryption error. The motivation of this work is to improve the bit-security level by using wider error distribution while keeping the target decryption failure rate achievable. The approach we proposed in this work is twofold. Firstly, we formulate RLWE public key encryption as a channel model with some noise terms known by the decoder. This makes our approach distinguished from existing research of this kind in the literature which ignores these known terms. Secondly, we design polar codes for the derived channel model. Theoretically and numerically, we show the proposed modeling and polar coding scheme contributes to a considerable bit-security level improvement compared with NewHope, a submission to National Institute of Standards and Technology (NIST), with almost the same parameters. Moreover, polar encoding and decoding support isochronous implementations in the sense that the timings of associated operations are irrelevant to the sensitive information.

Pairing-Free for Public Key Encryption With Equality Test Scheme

The modular exponentiation has been proved better in terms of computational efficiency as compared to bilinear pairing. Therefore, discrete logarithm, a concept of modular exponentiation may be incorporated to present improved security schemes. With this aim, an efficient public key encryption scheme with equality test (PKEwET) is proposed in this paper. Unlike the most of existing bilinear pairing based PKEwET schemes, the presented scheme employs discrete logarithm to improve the computational efficiency. Moreover, we introduce the verification process during the test phase to validate the ciphertext and to improve the security comparative to the prevalent schemes. The performance analysis depicts that the proposed scheme is quite efficient and more practical than the existing PKEwET schemes. More precisely, compared to Lin et al.'s scheme, the time cost has been reduced by at least 39% for the decryption process. Furthermore, for the type-3 test phase, the time cost has been reduced by at least 68%.

An efficient certificateless public key encryption scheme with authorized equality test in healthcare environments

The challenges confronting the privacy of outsourcing medical data have become a significant concern for patients and healthcare providers. The encryption of this sensitive data before outsourcing to the healthcare server present an effective solution for protection. However, searching on different ciphertexts while protecting the privacy of data remains a research challenge. Indeed, most of the existing schemes are inefficient, particularly for deployment on mobile devices due to limited resources (e.g. computing power, battery lifetime, and storage capacity). In this paper, we propose a CertificateLess Public-Key Encryption with Authorized Equality Test (CLPKE-AET) scheme. With the CLPKE-AET scheme, an authorized cloud server is permitted to check the equivalence of two different ciphertexts consisting of the same messages. Moreover, We provide four types of authorizations, base on which an authorized user can directly search on different user’s ciphertext using different methods while enhancing the privacy of the user’s data. We present our construction from bilinear pairing and demonstrate its security under modified Bilinear Diffie-Hellman (mBDHI) assumption in the Random Oracle Model (ROM). Finally, compared with other’s similar schemes, the performance analysis shows that our CLPKE-AET scheme is practical and more suitable for healthcare environments.

Secure and efficient public key multi-channel broadcast encryption schemes

In the modern era of digital technology, sending different messages to different group of users are essential in many real-life applications, like TV broadcast, radio broadcast etc. Multi-channel broadcast encryption (MCBE) is a mechanism which sends different messages to different group of users efficiently. We have proposed two multi-channel broadcast encryption schemes in the public key setting. Our first construction is selectively secure against chosen-plaintext attack, whereas the second one achieves adaptive security which is the strongest security model in the broadcast setting. Besides, our second construction is dynamic, whereas none of the existing MCBE constructions supports the dynamic property. Moreover, our second MCBE construction is the first inclusive-exclusive MCBE construction, where the broadcaster can reduce the encryption and decryption cost by choosing the smallest set between the set of subscribes and revoked users in the encryption and decryption phase respectively.

Adaptively secure efficient broadcast encryption with constant-size secret key and ciphertext

In those broadcast application scenarios with a great quantity of receivers, e.g., the data access control system in cloud storage service, the single sender is apt to become the efficiency bottleneck of the system, because the computation and storage overhead of the sender will grow rapidly with the amount of qualified receivers. In order to overcome this problem, we first introduce the novel conception of complete binary identity tree which is adopted to manage the qualified receivers. Then we design the prune-merge algorithm to further optimize the structure of the tree and cut down the amount of receivers. The algorithm effectively reduces the computation and storage cost of the trusted authority in the system. Subsequently, in virtue of composite-order bilinear groups, we bring forward an efficient public key broadcast encryption scheme combined its application to the system of data access control in cloud storage service. Compared with the existing schemes, the lengths of system public parameters, secret key and ciphertext in our scheme are all constant. In addition, the number of secret keys in our scheme increases logarithmically with the maximum amount of receivers, while the numbers of secret keys in the existing schemes increase linearly with the maximum amount of receivers. Furthermore, the proposed scheme is proved to guarantee adaptive security under general subgroup decision assumption in the standard model. The performance analysis manifests that our scheme is feasible for those broadcast applications with fixed senders.

An ElGamal-like Secure Channel Free Public Key Encryption with Keyword Search Scheme

The idea of public key encryption with keyword search (PEKS), proposed by Boneh et al., enables one to send a trapdoor containing a encrypted keyword to query data without revealing the keyword. In Boneh et al.’s design, the trapdoor has to be transferred through a secure channel, which is both costly and inefficient. Baek et al. then proposed an efficient secure channel free public key encryption scheme with keyword search (SCF-PEKS). After that, vast amounts of research have focused on the protection against the off-line keyword guessing attack (OKGA) by enhancing the model. However, most of the PEKS/SCF-PEKS schemes developed so far are constructed by applying bilinear pairing and are susceptible to off-line keyword guessing attacks. In this paper, we propose a new SCF-PEKS scheme based on the ElGamal cryptosystem. The proposed scheme is not only secure against off-line keyword guessing attacks but also improves the efficiency.

An efficient and secure searchable public key encryption scheme with privacy protection for cloud storage

In the area of searchable encryption, the searchable public key encryption (SPE) is an attractive technique in secure cloud storage. SPE assures the data confidentiality without affecting the usage of the data stored in the cloud. Furthermore, compared with the symmetric searchable encryption, SPE does not require key distribution and management. We investigate the security of the searchable public key encryption based on the traditional Boneh’s framework. Although existing SPE schemes can enable users to search over encrypted data, most of these schemes are vulnerable to the file-injection attack and the insider keyword guessing attack. To mitigate these attacks, we propose an efficient and secure searchable public key encryption with privacy protection (SPE-PP). We then provide a concrete construction of SPE-PP that uses the Diffie–Hellman shared secret key, and we prove it can resist these attacks. Both the theoretical analysis and the experimental results show that our scheme achieves strong security along with high efficiency.

Conjunctive and Disjunctive Keyword Search over Encrypted Mobile Cloud Data in Public Key System

The searchable encryption scheme can perform keywords search operation directly over encrypted data without decryption, which is crucial to cloud storage, and has attracted a lot of attention in these years. However, it is still an open problem to develop an efficient public key encryption scheme supporting conjunctive and a disjunctive keyword search simultaneously. To achieve this goal, we introduce a keyword conversion method that can transform the query and index keywords into a vector space model. Through applying a vector space model to a predicate encryption scheme supporting inner product, we propose a novel public key encryption scheme with conjunctive and disjunctive keyword search. The experiment result demonstrates that our scheme is more efficient in both time and space as well as more suitable for the mobile cloud compared with the state-of-art schemes.

New variant for Learning with Errors Problem

The Learning with Errors (LWE) problem is a special average-case lattice problem, which has proved to be as hard as worst-case lattice problems. By this property, it has become the cornerstones for a series of cryptographic applications under the security assumption of worst-case lattice problems. However, the efficiency of these applications are not high. Therefore, how to improve the efficiency of cryptographic applications based on LWE is an urgent problem to be solved.In this paper, a new variant of LWE is proposed. By using trapdoor composed by lattice-based matrix and its dual orthogonal matrix, we construct a more efficient public key encryption (PKE) scheme based on the variant. Furthermore, by the hardness of the variant problem, we prove the new PKE scheme is chosen plaintext attack (CPA) secure. At last, we analyze the homomorphism property of the new PKE scheme.

Error-correcting pairs for a public-key cryptosystem

Code-based Cryptography (CBC) is a powerful and promising alternative for quantum resistant cryptography. Indeed, together with lattice-based cryptography, multivariate cryptography and hash-based cryptography are the principal available techniques for post-quantum cryptography. CBC was first introduced by McEliece where he designed one of the most efficient Public-Key encryption schemes with exceptionally strong security guarantees and other desirable properties that still resist to attacks based on Quantum Fourier Transform and Amplitude Amplification.The original proposal, which remains unbroken, was based on binary Goppa codes. Later, several families of codes have been proposed in order to reduce the key size. Some of these alternatives have already been broken.One of the main requirements of a code-based cryptosystem is having high performance t-bounded decoding algorithms which is achieved in the case the code has a t-error-correcting pair (ECP). Indeed, those McEliece schemes that use GRS codes, BCH, Goppa and algebraic geometry codes are in fact using an error-correcting pair as a secret key. That is, the security of these Public-Key Cryptosystems is not only based on the inherent intractability of bounded distance decoding but also on the assumption that it is difficult to retrieve efficiently an error-correcting pair.In this paper, the class of codes with a t-ECP is proposed for the McEliece cryptosystem. Moreover, we study the hardness of distinguishing arbitrary codes from those having a t-error correcting pair.

An efficient public-key searchable encryption scheme secure against inside keyword guessing attacks

How to efficiently search over encrypted data is an important and interesting problem in the cloud era. To solve it, Boneh et al. introduced the notion of public key encryption with keyword search (PEKS), in 2004. However, in almost all the PEKS schemes an inside adversary may recover the keyword from a given trapdoor by exhaustively guessing the keywords offline. How to resist the inside keyword guessing attack in PEKS remains a hard problem.In this paper we propose introduce the notion of Public-key Authenticated Encryption with Keyword Search (PAEKS) to solve the problem, in which the data sender not only encrypts a keyword, but also authenticates it, so that a verifier would be convinced that the encrypted keyword can only be generated by the sender. We propose a concrete and efficient construction of PAEKS, and prove its security based on simple and static assumptions in the random oracle model under the given security models. Experimental results show that our scheme enjoys a comparable efficiency with Boneh et al.’s scheme.

An efficient RSA-based certificateless public key encryption scheme

In order to resolve the key escrow in identity-based scheme and the significant cost of using a PKI system in traditional public key scheme, the notion of certificateless public key cryptography (CL-PKC) was introduced. The first certificateless public key encryption scheme (CL-PKE) was proposed by Al-Riyami and Paterson, and then further schemes were developed. However, most of them are constructed from the bilinear pairing which is a time costing operation. In this paper, we construct an efficient CL-PKE scheme from RSA since RSA is the de facto Internet standard and is widely used in many applications. The security is based on Kilian–Petrank’s RSA assumption which is a variant of RSA.

Efficient Chosen-Ciphertext Secure Encryption from R-LWE

In order to construct efficient public-key encryption scheme that is secure against adaptive chosen-ciphertext attacks (CCA), an efficient signature scheme and an identity-based encryption (IBE) scheme from the learning with errors over rings are presented firstly in this paper, whose security are reducible to the hardness of the shortest vector problem in the worst case on ideal lattices. Secondly, a CCA-secure public key cryptosystem is constructed on the basis of the IBE and signature proposed above. The efficiency analysis indicates the proposed signature and encryption schemes are much more efficient than correlative cryptosystems. The security analysis shows that the IBE scheme is secure against chosen-plaintext attacks, and the public-key encryption scheme is CCA-secure in the random oracle model.

An Efficient Public Key Encryption Scheme Based on QC-MDPC Lattices

In this paper, we introduce a new family of lattices, namely QC-MDPC lattices, which are a special case of LDPC lattices, and an improved bit flipping algorithm for decoding of these lattices. Encoding and decoding implementations of QC-MDPC lattices are practical in high dimensions. Indeed, to take advantage of practical decoding, we use “Construction-A” lattices which makes a tight connection between the structure of lattices and codes. Using these features, we design a lattice-based public key encryption scheme enjoying linear encryption and decryption complexities. The proposed scheme has a reasonable key size due to the sparseness of the parity-check matrix, and the quasi-cyclic structure of the parity-check and generator matrices. Besides, the message expansion of the proposed scheme is smaller than other lattice-based and code-based cryptosystems with comparative parameters. All these features provide a lattice-based public key encryption scheme with reasonable key size, linear encryption, and decryption algorithms and small message expansion. On the other hand, we show that the cryptosystem is resistant against all known attacks both on lattice-based and code-based cryptosystems for different levels of security.

Multikey Fully Homomorphic Encryption and Applications

We propose a new notion of secure multiparty computation aided by a computationally powerful but untrusted “cloud” server. In this notion, on-the-fly multiparty computation (MPC), the cloud can noninteractively perform arbitrary dynamically chosen computations on data belonging to arbitrary dynamically chosen sets of users chosen. All users' input data and intermediate results are protected from snooping by the cloud as well as other users. This extends the standard notion of fully homomorphic encryption (FHE), where users can only enlist the cloud's help in evaluating functions on their own encrypted data. In on-the-fly MPC, each user is involved only when initially uploading his (encrypted) data to the cloud and in a final output decryption phase when outputs are revealed; the complexity of both is independent of the function being computed and the total number of users in the system. When users upload their data, they need not decide in advance which function will be computed, nor who they will compute with; they need only retroactively approve the eventually chosen functions and on whose data the functions were evaluated. This notion is qualitatively the best possible in minimizing interaction, since the users' interaction in the decryption stage is inevitable: we show that removing it would imply generic program obfuscation and is thus impossible. Our contributions are two-fold: (1) We define the new notion of multikey FHE, an enhanced FHE system which is capable of operating on inputs encrypted under multiple, unrelated keys. A ciphertext resulting from a multikey homomorphic evaluation can be jointly decrypted using the secret keys of all the users involved in the computation. We show how on-the-fly MPC can be achieved using any multikey FHE scheme. (2) We construct a multikey FHE scheme based on NTRU, a very efficient public-key encryption scheme proposed in the 1990s. It was previously not known how to make NTRU fully homomorphic even for a single party.

A New Efficient Certificateless Multi-Receiver Public Key Encryption Scheme

A New Efficient Certificateless Multi-Receiver Public Key Encryption Scheme

Adaptively secure broadcast encryption under standard assumptions with better efficiency

In this study, the authors present an efficient public-key broadcast encryption (PKBE) scheme with sub-linear size of public keys, private keys and ciphertexts and prove its adaptive security under standard assumptions. Compared with the currently best scheme of Garg et al. (CCS 2010) that provides adaptive security under standard assumptions and sub-linear size of various parameters, the ciphertext size of the author's scheme is 94% shorter and the encryption algorithm of their scheme is also 2.8 times faster than the scheme of Garg et al. To achieve their scheme, they adapt the dual system encryption technique of Waters. However, there is a challenging problem to use this technique for the construction of PKBE with sub-linear size of ciphertexts such as a tag compression problem. To overcome this problem, they first devise a novel tag update technique for broadcast encryption. Using this technique, they build an efficient PKBE scheme in symmetric bilinear groups, and prove its adaptive security under standard assumptions.

A Survey on Elliptic Curve Cryptography

Elliptic curve cryptography (ECC) is the most efficient public key encryption scheme based onelliptic curve concepts that can be used to create faster, smaller, and efficient cryptographic keys. ECCgenerates keys through the properties of the elliptic curve equation instead of the conventional method ofkey generation. This scheme can be used with public key encryption methods, such as RSA, Diffie-Hellman keyexchange and Digital Signature. Review of the four protocols which applies ECC namely Bitcoin, secureshell (SSH), transport layer security (TLS), and the Austrian e-ID Card describes the high security by usingelliptic curve cryptography.

Lattice-based identity-based resplittable threshold public key encryption scheme

Threshold public key encryption is a cryptographic primitive where a secret key of an organization is distributed among special members called decryption servers (insiders) and a certain threshold number of insiders must cooperate to decrypt any ciphertext. Threshold public key encryption with an additional randomized algorithm Tsplit is called resplittable threshold public key encryption (RTPKE). Cryptographic primitive RTPKE was introduced by Hanaoka et al. [Generic construction of chosen ciphertext secure proxy re-encryption, in CT-RSA, San Francisco, CA, USA, LNCS, O. Dunkelman, ed., Springer-Verlag, Heidelberg, 2012, pp. 349–364] in a generic construction of chosen ciphertext attack secure proxy re-encryption scheme. In MIST 2013 conference Singh et al. [Lattice based efficient threshold public key encryption scheme, J. Wirel. Mob. Netw. Ubiquitous Comput. Dependable Appl. (JoWUA) 4(4) (2013), pp. 93–107] presented lattice-based RTPKE scheme based on Regev's LWE [On lattices, learning with errors, random linear codes, and cryptography, in STOC, Baltimore, MD, USA, H.N. Gabow and R. Fagin, eds., ACM, University of Wales, Cardiff, 2005, pp. 84–93] assumption. In this paper, we propose lattice-based RTPKE scheme in the identity-based setting.

Improved Public Key Encryption Scheme Secure Against Adaptive Chosen-Ciphertext Attacks

It is an important research topic in public key cryptography to design public key encryption schemes secure against adaptive chosen-ciphertext attacks in the standard model.Kang et al.proposed an efficient public key encryption scheme,and claimed that their scheme satisfies the security of indistinguishability against adaptive chosen-ciphertext attacks(IND-CCA2).However,by giving an adaptive chosen-ciphertext attack,we indicate that their scheme is not IND-CCA2 secure.We further improved Kang et al.' s scheme to obtain a new public key encryption scheme,and prove its IND-CCA2 security in the standard model.