Composite-order Groups Research Articles

ID-Based Ring Signature against Continual Side Channel Attack

The security of the signature scheme is destroyed because its secret information of the signature system is leaked due to the side channel attack. Ring signature has good application value, which can provide more flexibility and complete anonymity. It can be used in some systems such as anonymous authentication in ad hoc networks, electronic voting and crypto coin based on blockchain. Because of the side channel attack, the private key of the ring signature system may be exposed, which may cause insecurity. We present a ring signature system against continuous side channel attack. Because of the symmetry of the ring, the user’s identity has good privacy protection. The proposed scheme is completely secure without a random oracle model and the private key disclosure rate is close to 1/3. Through the dual system technique, the existential unforgeability and unconditional anonymity of the scheme are proved in the composite order group based on the subgroup decision assumption.

Identity-Based and Leakage-Resilient Broadcast Encryption Scheme for Cloud Storage Service

Cloud storage services are an important application of cloud computing. An increasing number of data owners store their data on cloud platforms. Since cloud platforms are far away from users, data security and privacy protection are very important issues that need to be addressed. Identity-based broadcast encryption (IBBE) is an important method to provide security and privacy protection for cloud storage services. Because the side channel attacks may lead to the disclosure of the key information of the cryptographic system, which will damage the security of the system, this paper provides an identity-based broadcast encryption with leakage resilience by state partition (LR-SP-IBBE). By using a binary extractor to compensate for the loss in entropy of the symmetric key caused by side-channel attacks, the proposed scheme randomizes the encapsulated symmetric key. Furthermore, using a state partition technique, we split the private key into two parts, and the corresponding decryption was divided into two stages. Through the double-system encryption skill, the security and leakage-resilience were proved in the composite order group model.

Efficient identity based ring signature scheme in prime order group

Aiming at the problem of long signature generation and verification time caused by low operation efficiency in ring signature algorithm based on composite order group, an asymmetric identity based ring signature scheme based on prime order group is proposed. The model definition and specific identity based ring signature scheme design of the proposed scheme are described, and the correctness and security of the proposed scheme are analyzed. Finally, the efficiency of the core operation part of the algorithm is explained. Compared with the correlation signature algorithm based on composite order group, the optimization has a great improvement in operation overhead and performance, and the designed scheme is unforgeable. The designed signature scheme meets the unconditional anonymity and unforgeability of ring signature.

Efficient ciphertext-policy attribute-based encryption with blackbox traceability

Traitor tracing scheme is a paradigm to classify the users who illegal use of their decryption keys in cryptosystems. In the ciphertext-policy attribute-based cryptosystem, the decryption key usually contains the users’ attributes, while the real identities are hidden. The decryption key with hidden identities enables malicious users to intentionally leak decryption keys or embed the decryption keys in the decryption device to gain illegal profits with a little risk of being discovered. To mitigate this problem, the concept of blackbox traceability in the ciphertext-policy attribute-based scheme was proposed to identify the malicious user via observing the I/O streams of the decryption device. However, current solutions with blackbox traceability are impractical since either the composite-order group or the linear complexity of system users is required. In this article, we proposed a secure ciphertext-policy attribute-based set encryption scheme with the short decryption key. The proposed scheme bases on the prime-order group to improve computational performances and aggregates multiple attributes into a constant-size attribute set to reduce the costs of communication overheads. By applying our proposed scheme with fingerprint codes, we then give an instantiation of the ciphertext-policy attribute-based scheme with blackbox traceability. Our scheme is provably secure under various q-type assumptions.

Adaptively Secure Non-interactive CCA-Secure Threshold Cryptosystems: Generic Framework and Constructions

In threshold cryptography, private keys are divided into n shares, each one of which is given to a different server in order to avoid single points of failure. In the case of threshold public-key encryption, at least t out of n servers need to contribute to the decryption process. A threshold primitive is said robust if no coalition of t malicious servers can prevent remaining honest servers from successfully completing private key operations. Non-interactive schemes, considered the most practical ones, allow servers to contribute to decryption without interactions. So far, most non-interactive threshold cryptosystems were only proved secure against static corruptions. In the adaptive corruption scenario (where the adversary can corrupt servers at any time, based on its complete view), all existing robust threshold encryption schemes that also resist chosen-ciphertext attacks (CCA) till recently require interaction in the decryption phase. A very specific method (in composite order groups) for getting rid of interaction was recently suggested, leaving the question of more generic frameworks and constructions with better security and, in particular, better exibility (i.e., compatibility with distributed key generation). This paper advances the state of the art and describes a general construction of adaptively secure robust non-interactive threshold cryptosystems with chosen-ciphertext security. We define the novel notion of all-but-one perfectly sound threshold hash proof systems that can be seen as (threshold) hash proof systems with publicly verifiable and simulation-sound proofs. We show that this notion generically implies threshold cryptosystems combining the aforementioned properties. Then, we provide efficient instantiations under well-studied assumptions in bilinear groups (e.g., in such groups of prime order). These instantiations have a tighter security proof in the single-challenge setting and are indeed compatible with distributed key generation protocols.

Construction of strongly regular graphs having an automorphism group of composite order

In this paper we outline a method for constructing strongly regular graphs from orbit matrices admitting an automorphism group of composite order. In 2011, C. Lam and M. Behbahani introduced the concept of orbit matrices of strongly regular graphs and developed an algorithm for the construction of orbit matrices of strongly regular graphs with a presumed automorphism group of prime order, and construction of corresponding strongly regular graphs. The method of constructing strongly regular graphs developed and employed in this paper is a generalization of that developed by C. Lam and M. Behbahani. Using this method we classify SRGs with parameters (49,18,7,6) having an automorphism group of order six. Eleven of the SRGs with parameters (49,18,7,6) constructed in that way are new. We obtain an additional 385 new SRGs(49,18,7,6) by switching. Comparing the constructed graphs with previously known SRGs with these parameters, we conclude that up to isomorphism there are at least 727 SRGs with parameters (49,18,7,6). Further, we show that there are no SRGs with parameters (99,14,1,2) having an automorphism group of order six or nine, i.e. we rule out automorphism groups isomorphic to $Z_6$, $S_3$, $Z_9$, or $E_9$.

EFFICIENT AND EXPRESSIVE KEYWORD SEARCH OVER ENCRYPTED DATA IN CLOUD

Searchable encryption allows a cloud server to conduct keyword search over encrypted data on behalf of the data users without learning the underlying plaintexts. However, most existing searchable encryption schemes only support single or conjunctive keyword search, while a few other schemes that can perform expressive keyword search are computationally inefficient since they are built from bilinear pairings over the composite-order groups. In this paper, we propose an expressive public-key searchable encryption scheme in the prime-order groups, which allows keyword search policies i.e., predicates, access structures to be expressed in conjunctive, disjunctive or any monotonic Boolean formulas and achieves significant performance improvement over existing schemes. We formally define its security and prove that it is selectively secure in the standard model. Also, we implement the proposed scheme using a rapid prototyping tool called Charm and conduct several experiments to evaluate it performance. The results demonstrate that our scheme is much more efficient than the ones built over the composite-order groups. INDEX TERMS - Searchable encryption, cloud computing, expressiveness, attribute-based encryption

Improving the Leakage Rate of Ciphertext-Policy Attribute-Based Encryption for Cloud Computing

A Leakage-Resilient Ciphertext-Policy Attribute-based Encryption (LR-CP-ABE) not only supports the fine-grained access control to encrypted data but also guarantees the security of the data under the side-channel attacks. However, the leakage rate in the existing schemes is low or related to the number of attributes. It will make these schemes suffer from continual attacks. In addition, all of them almost not consider the leakage of the users' privacy and rely on the composite order groups which will threaten the privacy security of the users and depress the users in practice. In this paper, we aim at solving the above problems and propose a scheme with the improving leakage rate in the prime order group. In the proposed scheme, an extension of the lattice-based trapdoor is used to make it achieve the maximum leakage rate $1-o(1)$ . Moreover, it achieves the anonymity which can protect the privacy of the receivers. The proposed scheme can be reduced to the standard assumption-Decision Linear (DLIN) assumption in the selective security model and resist the Chosen Plaintext Attacks (CPA security). At last, the performance comparisons are given to confirm the efficiency and security of the proposed scheme.

Permutation groups containing a regular abelian subgroup: the tangled history of two mistakes of Burnside

AbstractA groupKis said to be a B-group if every permutation group containingKas a regular subgroup is either imprimitive or 2-transitive. In the second edition of his influential textbook on finite groups, Burnside published a proof that cyclic groups of composite prime-power degree are B-groups. Ten years later, in 1921, he published a proof that every abelian group of composite degree is a B-group. Both proofs are character-theoretic and both have serious flaws. Indeed, the second result is false. In this paper we explain these flaws and prove that every cyclic group of composite order is a B-group, using only Burnside’s character-theoretic methods. We also survey the related literature, prove some new results on B-groups of prime-power order, state two related open problems and present some new computational data.

An efficient and expressive ciphertext-policy attribute-based encryption scheme with partially hidden access structures, revisited

Ciphertext-policy attribute-based encryption (CP-ABE) has been regarded as one of the promising solutions to protect data security and privacy in cloud storage services. In a CP-ABE scheme, an access structure is included in the ciphertext, which, however, may leak sensitive information about the underlying plaintext and the privileged recipients in that anyone who sees the ciphertext is able to learn the attributes of the privileged recipients from the associated access structure. In order to address this issue, CP-ABE with partially hidden access structures was introduced where each attribute is divided into an attribute name and an attribute value and the attribute values of the attributes in an access structure are not given in the ciphertext. Though a number of CP-ABE schemes with partially hidden access structures have been proposed, most of them only enable restricted access structures, whereas several other schemes supporting expressive access structures are computationally inefficient due to the fact that they are built in the composite-order groups. To our knowledge, there has been little attention paid to the design of expressive CP-ABE schemes with partially hidden access structures in the prime-order groups. In this paper, we revisit this problem, and present an expressive CP-ABE scheme supporting partially hidden access structures in the prime-order groups with improved efficiency.

Efficient and Privacy-Preserving Polygons Spatial Query Framework for Location-Based Services

With the pervasiveness of mobile devices and the development of wireless communication technique, location-based services (LBSs) have made our life more convenient, and the polygons spatial query, which can provide more flexible LBS, has attracted considerable interest recently. However, the flourish of polygons spatial query still faces many challenges including the query information privacy. In this paper, we present an efficient and privacy-preserving polygons spatial query framework for location-based services, called Polaris. With Polaris, the LBS provider (LP) outsources the encrypted LBS data to cloud server (CS), and the registered user can query any polygon range to get accurate LBS results without divulging his/her query information to the LP and CS. Specifically, an efficient special polygons spatial query (SPSQ) algorithm over ciphertext is constructed, based on an improved homomorphic encryption technology over composite order group. With SPSQ, Polaris can search outsourced encrypted LBS data in CS by the encrypted request, and respond the encrypted polygons spatial query results accurately. Detailed security analysis shows that the proposed Polaris can resist various known security threats. In addition, performance evaluations via implementing Polaris on smartphone and workstation with real LBS dataset demonstrate Polaris' effectiveness in term of real environment.

Functional encryption for computational hiding in prime order groups via pair encodings

Lewko and Waters introduced the computational hiding technique in Crypto'12. In their technique, two computational assumptions that achieve selective and co-selective security proofs lead to adaptive security of an encryption scheme. Later, pair encoding framework was introduced by Attrapadung in Eurocrypt'14. The pair encoding framework generalises the computational hiding technique for functional encryption (FE). It has been used to achieve a number of new FE schemes such as FE for regular languages and unbounded attribute based encryption allowing multi-use of attributes. Nevertheless, the generalised construction of Attrapadung's pair encoding for those schemes is adaptively secure only in composite order groups, which leads to efficiency loss. It remains a challenging task to explore constructions in prime order groups for gaining efficiency improvement, which leaves the research gap in the existing literature. In this work, we aim to address this drawback by proposing a new generalised construction for pair encodings in prime order groups. Our construction will lead to a number of new FE schemes in prime order groups, which have been previously introduced only in composite order groups by Attrapadung.

Efficient and Expressive Keyword Search Over Encrypted Data in Cloud

Searchable encryption allows a cloud server to conduct keyword search over encrypted data on behalf of the data users without learning the underlying plaintexts. However, most existing searchable encryption schemes only support single or conjunctive keyword search, while a few other schemes that are able to perform expressive keyword search are computationally inefficient since they are built from bilinear pairings over the composite-order groups. In this paper, we propose an expressive public-key searchable encryption scheme in the prime-order groups, which allows keyword search policies (i.e., predicates, access structures) to be expressed in conjunctive, disjunctive or any monotonic Boolean formulas and achieves significant performance improvement over existing schemes. We formally define its security, and prove that it is selectively secure in the standard model. Also, we implement the proposed scheme using a rapid prototyping tool called Charm [37], and conduct several experiments to evaluate it performance. The results demonstrate that our scheme is much more efficient than the ones built over the composite-order groups.

An Efficient Privacy-Preserving Outsourced Computation over Public Data

In this paper, we propose a new efficient privacy-preserving outsourced computation framework over public data, called EPOC. EPOC allows a user to outsource the computation of a function over multi-dimensional public data to the cloud while protecting the privacy of the function and its output. Specifically, we introduce three types of EPOC in order to tradeoff different levels of privacy protection and performance. We present a new cryptosystem called Switchable Homomorphic Encryption with Partially Decryption (SHED) as the core cryptographic primitive for EPOC. We introduce two coding techniques, called message pre-coding technique and message extending and coding technique respectively, for messages encrypted under a composite order group. Furthermore, we propose a Secure Exponent Calculation Protocol with Public Base (SEPB), which serves as the core sub-protocol in EPOC. Detailed security analysis shows that the proposed EPOC achieves the goal of outsourcing computation of a private function over public data without privacy leakage to unauthorized parties. In addition, performance evaluations via extensive simulations demonstrate that EPOC is efficient in both computation and communications.

Adaptive Security of Broadcast Encryption, Revisited

We provide a strong security notion for broadcast encryption, called adaptive security in the multichallenge setting (MA-security), where the adversary can adaptively have access to the key generation oracle and the encryption oracle many times (multichallenge). The adversary specially can query for the challenge ciphertexts on different target user sets adaptively, which generalizes the attacks against broadcast encryptions in the real world setting. Our general result shows that the reduction of the adaptive secure broadcast encryption will lose a factor of q in the MA setting, where q is the maximum number of encryption queries. In order to construct tighter MA-secure broadcast encryptions, we investigate Gentry and Water’s transformation and show that their transformation can preserve MA-security at the price of reduction loss on the advantage of the underlying symmetric key encryption. Furthermore, we remove the q-type assumption in Gentry and Water’s semistatically secure broadcast encryption by using Hofheinz-Koch-Striecks techniques. The resulting scheme instantiated in a composite order group is MA-secure with constant-size ciphertext header.

New directly revocable attribute-based encryption scheme and its application in cloud storage environment

Attribute-based encryption (ABE) is a special type of cryptosystem, which provide encryption and decryption functions based on users attributes. Due to the functionality and flexibility of ABE, it is considered to be suitable for providing data security and privacy preserving security in the cloud storage environment. However, lack of user revocation mechanism is considered to be a disadvantage of traditional ABE. In this paper, we study the direct revocation mechanism of ciphertext-policy ABE (CP-ABE), construct a new directly revocable CP-ABE in the composite order group, and prove it to achieve adaptive security using dual system encryption in the standard model. On this basis, we introduce user revocation centre (URC) in this system, and outsource the revocation tasks to URC. Users need not to master the latest revocation list for encrypting, and need not to pay any additional computing for revocation. In addition, when revocation list changes, URC can update the ciphertexts for users. Finally, we introduce how to deploy our schemes in cloud storage environment.

An Efficient Privacy-Preserving Location-Based Services Query Scheme in Outsourced Cloud

With the pervasiveness of location-aware mobile electronic devices and the advances of wireless communications, location-based services (LBS), which can help people enjoy a convenient life, has attracted considerable interest recently. However, the privacy issues of LBS are still challenging today. Aiming at the challenges, in this paper, we present a new efficient and privacy-preserving LBS query scheme in outsourced cloud, i.e., EPQ, for pervasive smartphones. In the EPQ scheme, the LBS provider's data are first outsourced to the cloud server in an encrypted manner, and then, a registered user can get accurate LBS query results without divulging his/her location information to the LBS provider and the cloud server. Specifically, based on an improved homomorphic encryption technique over a composite order group, a special spatial range query algorithm SRQC over ciphertext is proposed, with which EPQ achieves privacy preservation of user's query and confidentiality of LBS data in the outsourced cloud server. Through detailed security analysis, we show that EPQ can resist various known security threats. In addition, we also implement EPQ over a smartphone and three workstations with a real LBS data set, and extensive simulation results further demonstrate that the proposed EPQ scheme is highly efficient at the smartphone side and can be implemented effectively in the cloud server.

Secure and Privacy-Preserving Body Sensor Data Collection and Query Scheme.

With the development of body sensor networks and the pervasiveness of smart phones, different types of personal data can be collected in real time by body sensors, and the potential value of massive personal data has attracted considerable interest recently. However, the privacy issues of sensitive personal data are still challenging today. Aiming at these challenges, in this paper, we focus on the threats from telemetry interface and present a secure and privacy-preserving body sensor data collection and query scheme, named SPCQ, for outsourced computing. In the proposed SPCQ scheme, users’ personal information is collected by body sensors in different types and converted into multi-dimension data, and each dimension is converted into the form of a number and uploaded to the cloud server, which provides a secure, efficient and accurate data query service, while the privacy of sensitive personal information and users’ query data is guaranteed. Specifically, based on an improved homomorphic encryption technology over composite order group, we propose a special weighted Euclidean distance contrast algorithm (WEDC) for multi-dimension vectors over encrypted data. With the SPCQ scheme, the confidentiality of sensitive personal data, the privacy of data users’ queries and accurate query service can be achieved in the cloud server. Detailed analysis shows that SPCQ can resist various security threats from telemetry interface. In addition, we also implement SPCQ on an embedded device, smart phone and laptop with a real medical database, and extensive simulation results demonstrate that our proposed SPCQ scheme is highly efficient in terms of computation and communication costs.

On the group properties of substitutions defined on the subgroup cosets of finite Abelian group of composite order

Найдены необходимые и достаточные условия транзитивности и примитивности групп подстановок, образующими элементами которых являются подстановки на смежных классах абелевой группы $G$. Описано строение этих групп в случаях, когда они примитивны или когда абелева группа $G$ является прямым произведением своих подгрупп. Получены также необходимые и достаточные условия примитивности группы, порожденной правым регулярным представлением группы $G$ и одной из подстановок, определенных на смежных классах группы $G$.

Provably secure identity-based encryption resilient to post-challenge continuous auxiliary input leakage

The situation for post-challenge continuous auxiliary input leakage has not been considered in the cryptography schemes for previous literature. We present a semantic-security model with post-challenge continuous auxiliary inputs for identity-based encryption. In this model, the adversary is permitted to obtain some information of the private keys constantly and to query more information after seeing the challenge ciphertext through the side-channel attacks. Furthermore, we present an identity-based encryption scheme resilient to leakage under composite order groups. Our scheme is secure against post-challenge continuous auxiliary input, adaptive chosen-identity, and adaptive chosen plaintext attacks under three static assumptions in the standard model. Compared with existing identity-based encryption schemes under security properties and performance, our scheme is practical. Copyright © 2015 John Wiley & Sons, Ltd.