Bilinear Diffie-Hellman Problem Research Articles

How to Watermark Cryptographic Functions by Bilinear Maps

We introduce a notion of watermarking for cryptographic functions and propose a concrete scheme for watermarking cryptographic functions. Informally speaking, a digital watermarking scheme for cryptographic functions embeds information, called a mark, into functions such as one-way functions and decryption functions of public-key encryption. There are two basic requirements for watermarking schemes. A mark-embedded function must be functionally equivalent to the original function. It must be difficult for adversaries to remove the embedded mark without damaging the original functionality. In spite of its importance and usefulness, there have only been a few theoretical works on watermarking for functions (or programs). Furthermore, we do not have rigorous definitions of watermarking for cryptographic functions and concrete constructions. To solve the problem above, we introduce a notion of watermarking for cryptographic functions and define its security. Furthermore, we present a lossy trapdoor function (LTF) based on the decisional bilinear Diffie-Hellman problem problem and a watermarking scheme for the LTF. Our watermarking scheme is secure under the symmetric external Diffie-Hellman assumption in the standard model. We use techniques of dual system encryption and dual pairing vector spaces (DPVS) to construct our watermarking scheme. This is a new application of DPVS.

A hierarchical group key agreement protocol using orientable attributes for cloud computing

Group key agreement is one of the key technologies for ensuring information exchange security among group members. Due to different sensitivities of the information, group members may only want to exchange certain secret information under certain circumstances, and also due to different access permissions of member, certain information exchange may aim at different access authorities. Aiming at these requirements, a hierarchical group key agreement protocol using orientable attribute (HGKA-OA) is proposed in this paper. In this protocol, different secret information is shared among a set of members who have different authority levels. Assuming different permission levels correspond to different attributes or their combinations of the terminal, when one people has some secret information he can exchange information with some people who have the appropriate level of security permissions, rather than all the members in the group. The proposed scheme eliminates a majority of the computation task of terminals by moving identity authentication computation to the registration. In addition, the group key factors are also calculated before the group key agreement, which eliminates most of computation overhead due to group key agreement. This protocol is proven secure under the Decisional Bilinear Diffie-Hellman (DBDH) problem assumption and performance analysis shows that the proposed scheme is more efficient than existing works.

An attribute-based encryption scheme with multiple authorities on hierarchical personal health record in cloud

In the personal health record (PHR) system, the patient’s health records are usually outsourced to a large database, such as the cloud service provider. In order to guarantee the confidentiality of this data , achieve access control with flexibility and fine-grained property, it usually employs ciphertext-policy attribute-based encryption (CP-ABE) scheme in cloud computing. However, the outsourced data have the characteristic of multi-level hierarchy, and the general CP-ABE is inappropriate for being applied in distributed cloud service systems directly to provide the security of hierarchy structure of outsourced data. In this paper, to overcome this challenge, a PHR hierarch CP-ABE scheme with multiple authorities is presented. This protocol integrated some different access structures into a single one, which the hierarchical PHR is encrypted based on. There are multiple authorities to generate and distribute user’s private key all together. According to this mode, it enables to avoid the problem of key escrow and conform to the distributed characteristic of cloud service systems. However, it has no trusted single or central one in these authorities. Moreover, this proposed scheme resists $$(N-1)$$ corrupted authorities out of N authorities in the collusion attack. Based on the intractability of the standard decisional bilinear Diffie–Hellman problem, the security of this protocol is proven to be semantic secure. Finally, by comparison analysis, this protocol exhibits a better performance.

A revocable certificateless encryption scheme with high performance

Featuring no key escrow and no certificate, certificateless public key cryptography (CLPKC) has received much attention. A necessary problem in CLPKC is how to revoke a compromised/misbehaving user, which still remains to be efficiently solved: all existing methods are not practical for use owing to either enormous computation (secret channels), or a costly mediator. In this paper, we present a new approach for revocation in CLPKC and give a revocable certificateless encryption (RCLE) scheme. In the new scheme, a user's private key contains three parts: an initial partial private key, a time key and a secret value. The time key is updated at every time period and is transmitted over a public channel. Our construction offers higher performance than previous solutions. Based on the bilinear Diffie-Hellman problem, our RCLE scheme is provably secure in the random oracle model.

A revocable certificateless encryption scheme with high performance

Featuring no key escrow and no certificate, certificateless public key cryptography (CLPKC) has received much attention. A necessary problem in CLPKC is how to revoke a compromised/misbehaving user, which still remains to be efficiently solved: all existing methods are not practical for use owing to either enormous computation (secret channels), or a costly mediator. In this paper, we present a new approach for revocation in CLPKC and give a revocable certificateless encryption (RCLE) scheme. In the new scheme, a user's private key contains three parts: an initial partial private key, a time key and a secret value. The time key is updated at every time period and is transmitted over a public channel. Our construction offers higher performance than previous solutions. Based on the bilinear Diffie-Hellman problem, our RCLE scheme is provably secure in the random oracle model.

Multi-message and multi-receiver heterogeneous signcryption scheme for ad-hoc networks

ABSTRACTSecurity is a significant issue for ad-hoc networks. Heterogeneous signcryption schemes proposed in recent years satisfy privacy and authentication of messages and reduce cost of computation and communication in a logical step. In this article, we present a new efficient heterogeneous signcryption scheme that shifts between the public key infrastructure (PKI) and the identity-based cryptosystem (IBC). The proposed scheme is suitable for broadcast communication conditions in which senders can signcrypt multiple messages for multiple receivers simultaneously in the ad-hoc networks. This scheme is proved to satisfy confidentiality and unforgeability on the basis of the assumptions of bilinear Diffie-Hellman problem (BDHP), q-Diffie-Hellman inversion problem (q-DHIP), q-bilinear Diffie-Hellman inversion problem (q-BDHIP), and computational Diffie-Hellman problem (CDHP) in the random oracle model. We discuss the efficiency of our scheme theoretically. In the efficiency analysis phase, we show that our scheme is practical and efficient. In the performance analysis phase, we present additional tests, data, and explanations to prove that our scheme can be applied in ad-hoc networks. Finally, we apply our scheme to a simulated ad-hoc network.

Related-key secure key encapsulation from extended computational bilinear Diffie–Hellman

As a special type of fault injection attacks, Related-Key Attacks (RKAs) allow an adversary to manipulate a cryptographic key and subsequently observe the outcomes of the cryptographic scheme under these modified keys. In the real life, related-key attacks are already practical enough to be implemented on cryptographic devices. To avoid cryptographic devices suffering from related-key attacks, it is necessary to design a cryptographic scheme that resists against such attacks. This paper proposes an efficient RKA-secure Key Encapsulation Mechanism (KEM), in which the adversary can modify the secret key sk to any value f(sk), as long as, f is a polynomial function of a bounded degree d. Especially, the polynomial-RKA security can be reduced to a hard search problem, namely d-extended computational Bilinear Diffie-Hellman (BDH) problem, in the standard model. Our construction essentially refines the security of Haralambiev et al.’s BDH-based KEM scheme from chosen-ciphertext security to related-key security. The main technique applied in our scheme is the re-computation of the public key in the decryption algorithm so that any (non-trivial) modification to the secret key can be detected.

An efficient signcryption for data access control in cloud computing

Data storage is one of main services in cloud computing. How to ensure the confidentiality and authorized access of data is the central issue of data storage. In this paper, we propose a novel data access control scheme that can simultaneously achieve confidentiality and authentication for cloud computing. In this scheme, users store encrypted data in the cloud. When a user wants to access the data, the data owner delegates the cloud to re-encrypt the data and only the authorized user can decrypt the data. The cloud can not get any plaintext information about the data. In addition, the authorized user can verify the integrity and authentication of the data. We realize the data access control scheme by proposing an identity-based signcryption (IBSC) scheme with proxy re-encryption. We prove that the IBSC scheme has the indistinguishability against adaptive chosen ciphertext attack under the decisional bilinear Diffie-Hellman problem and existential unforgeability against adaptive chosen message attack under the computational Diffie-Hellman problem in the random oracle model.

OGPADSM<SUP align="right">2</SUP>: oriented-group public auditing for data sharing with multi-user modification

In most data sharing protocols for cloud storage, to update the outsourced data, the data updating operation is only executed by data owner. Obviously, it is far from practical owing to the tremendous computational cost on data owner. Until now, there are a few protocols in which multiple cloud users are allowed to update the outsourced data with integrity assurance. And these protocols do not consider collusion attack between misbehaving cloud servers and the revoked users, which is an important challenge in data sharing protocol. To support multi-user modification and resist collusion attack, we propose a novel public auditing for data sharing with multi-user modification in this paper. Our scheme does not support public checking and efficient user revocation, but provides backward security. At the same time, our scheme is provably secure under the bilinear Diffie-Hellman problem. To increase efficiency of the auditor's verification, an improved protocol is given. In the improved protocol, only one pairing operation is required in the auditor's verification phase. By comparison with the other protocols, our scheme has lower computation cost on the auditor and stronger security.

Key-Policy Attribute-Based Encryption With Equality Test in Cloud Computing

The privacy of users must be considered as the utmost priority in distributed networks. To protect the identities of users, attribute-based encryption (ABE) was presented by Sahai et al. ABE has been widely used in many scenarios, particularly in cloud computing. In this paper, public key encryption with equality test is concatenated with key-policy ABE (KP-ABE) to present KP-ABE with equality test (KP-ABEwET). The proposed scheme not only offers fine-grained authorization of ciphertexts but also protects the identities of users. In contrast to ABE with keyword search, KP-ABEwET can test whether the ciphertexts encrypted by different public keys contain the same information. Moreover, the authorization process of the presented scheme is more flexible than that of Ma et al. ’s scheme. Furthermore, the proposed scheme achieves one-way against chosen-ciphertext attack based on the bilinear Diffie-Hellman (BDH) assumption. In addition, a new computational problem called the twin-decision BDH problem (tDBDH) is proposed in this paper. tDBDH is proved to be as hard as the decisional BDH problem. Finally, for the first time, the security model of authorization is provided, and the security of authorization based on the tDBDH assumption is proven in the random oracle model.

A novel approach for privacy homomorphism using attribute‐based encryption

AbstractIn CRYPTO'13, Gentry et al. proposed the first homomorphic encryption (HE) scheme for the attribute‐based encryption (ABE). However, Gentry's scheme requires the same index for encryption of each ciphertext and supports only the key‐policy ABE. Indeed, in SECRYPT'13, Clear et al. left an open problem in the Gentry et al. scheme viz. a scheme that requires different sets of index in HE using ABE and supports the ciphertext‐policy ABE (CP‐ABE), where the sender is assumed to be intelligent. In addition, in INDOCRYPT'12, Vaikuntanathan discussed an open problem viz. to work out the HE using cryptographic techniques other than lattice‐based cryptography. With an aim to propose the CP‐ABE scheme using HE, in this research attempt, we propose an approach that integrates the benefits of HE in CP‐ABE and yet uses pairing‐based cryptography. In our approach viz. attribute‐based HE (AB‐HE), a user is able to successfully decrypt the ciphertext only if the attributes in the policy match those in the secret key. However, in addition, our approach also allows multiple invocations of multiplication operation on the ciphertext as in a typical partially HE, coupling the advantages of the partial HE in the CP‐ABE. Further, we also propose an extension of the proposed scheme that serves as a pseudo‐fully HE, but requires the help of a key authority. The security of the proposed scheme is based on the decisional bilinear Diffie–Hellman problem. To the best of our knowledge, ours is a unique attempt in integrating HE into the attribute‐based cryptography with different indexes/policies. In addition, our AB‐HE scheme is pairing‐based, and by adding more ciphertexts, it does not blow the final ciphertext size because we use the constant length ciphertext approach for the encryption. Copyright © 2016 John Wiley & Sons, Ltd.

Effective and Secure Access Control for Multi-Authority Cloud Storage Systems

Ciphertext-Policy Attribute-Based Encryption (CP-ABE) is a promising cryptographic tool to implement access control for secure cloud storage systems. However, most existing access control schemes based on CP-ABE for the multi-authority cloud storage systems rely on a fully trusted global certificate authority. It is just an ideal assumption while there never exists a fully trusted global certificate authority in reality. In this paper, we construct a system with multiple certificate authorities (CA). The parameters of those CAs could be verified when an authority suspects the messages received from the correlative certificate authority. Besides, we construct a verifiable secret sharing (VSS) scheme to realize the decentralization of the certificate authority in our scheme. The scheme adopts the Pedersen commitment in combination with the properties of bilinear-pairs on elliptic curve and bilinear Diffie-Hellman problem. The analysis shows that our scheme is highly efficient, authentic and provably secure under the security model. Our scheme simultaneously supports efficient attribute revocation.

New chosen-ciphertext secure identity-based encryption with tight security reduction to the bilinear Diffie–Hellman problem

We propose a new identity-based encryption (IBE) system that achieves a tight security reduction to the bilinear Diffie–Hellman (BDH) problem in the random oracle model. Tightness indicates that some level of IBE system security can be straightforwardly based on the hardness of the BDH problem at the same security level. Achieving such tightness requires two strategies: (1) a key generation technique for all identities, and (2) a searching method for the solution to the BDH problem. To implement the first strategy, our system relies on a key generation paradigm recently introduced with the Park–Lee IBE system. To implement the second strategy, we base our system on the strong twin BDH problem that includes access to a decision oracle. We compare the efficiency of our system with that of the previous Nishioka IBE system (based on the Katz–Wang key generation paradigm) combined with another tight variant of the Fujisaki–Okamoto transform.

Strong Designated Verifier Signature Scheme Resisting Replay Attack

Strong designated verifier signature shows that only designated user can verify the validity of the signature, others who have not signer’s secret key or verifier’s secret key cannot judge the signature’s originator. Lee et al. presented a designated verifier signature scheme to realize signature’s verification in the limited time. We demonstrate that Lee et al.’s scheme was insecure, and other legal user can forge valid signatures which convince designated verifier. In this paper, we show a concrete forgery attack to Lee et al.’s scheme and propose a new strong designated verifier signature scheme with time limit. In our new scheme, the message and time stamp need not transmit publicly, which were embedded in signature via the method of message recovery, only singer and designated verifier can recover these secrete values. Based on the Bilinear Diffie-Hellman problem and Pre-Image Resistance assumption, it is proved that our new strong designated verifier signature scheme can resist the ordinary forgery attack and replay attack, and enforce signature verification with time limit. DOI: http://dx.doi.org/10.5755/j01.itc.44.2.7625

Secure medical information sharing in cloud computing.

Medical information sharing is one of the most attractive applications of cloud computing, where searchable encryption is a fascinating solution for securely and conveniently sharing medical data among different medical organizers. However, almost all previous works are designed in symmetric key encryption environment. The only works in public key encryption do not support keyword trapdoor security, have long ciphertext related to the number of receivers, do not support receiver revocation without re-encrypting, and do not preserve the membership of receivers. In this paper, we propose a searchable encryption supporting multiple receivers for medical information sharing based on bilinear maps in public key encryption environment. In the proposed protocol, data owner stores only one copy of his encrypted file and its corresponding encrypted keywords on cloud for multiple designated receivers. The keyword ciphertext is significantly shorter and its length is constant without relation to the number of designated receivers, i.e., for n receivers the ciphertext length is only twice the element length in the group. Only the owner knows that with whom his data is shared, and the access to his data is still under control after having been put on the cloud. We formally prove the security of keyword ciphertext based on the intractability of Bilinear Diffie-Hellman problem and the keyword trapdoor based on Decisional Diffie-Hellman problem.

Provably Secure and Efficient ID-based Strong Designated Verifier Signature Scheme with Message Recovery

Many ID-based strong designated verifier signature schemes have been proposed in recent years. However, most of them did not give the rigorous security proofs and did not satisfy the strongness property that anyone except the designated verifier can not check the validity of a designated verifier signature, In addition, considering some special applications, these schemes have larger data size of communication. To overcome those problems, exploiting message recovery techniques which are regarded as a useful method to shorten ID-based signatures' size, we put forward an efficient ID-based strong designated verifier signature schemes with message recovery and give its rigorous security proof in the random oracle model based on the hardness assumptions of the computational Bilinear Diffie-Hellman problem in this paper. To the best of our knowledge, it is the first ID-based strong designated verifier signature schemes with message recovery and rigorous security proofs. Due to its merits, it can be used in some special environments where the bandwidth is one of the main concerns, such as PDAs, cell phones, RFID etc.

A new efficient signcryption scheme in the standard model

We introduce an efficient signcryption scheme for hybrid authenticated encryption that is provably secure in the standard model under a strong multiuser insider setting. Our new signcryption scheme is built on the basis of a variant of Boneh-Boyen short signature, which works under bilinear groups. The new construction idea is to reuse the signature value to derive the encryption key. This could dramatically save not only the computational cost but also the communication bandwidth. The session key security of the proposed scheme is reduced to a hard problem that is a variant of bilinear decisional Diffie-Hellman problem. Copyright ©2014 John Wiley & Sons, Ltd.

Convertible Authenticated Encryption Scheme with Hierarchical Access Control

Convertible authenticated encryption (CAE) scheme with hierarchical access control has crucial benefits to the transmission of digital evidence. Such a scheme allows a judicial policeman to generate an authenticated ciphertext and only a designated investigator of Investigation of Bureau, Ministry of Justice (MJIB) has the ability to decr ypt the ciphertext and verify the corresponding signature. The designated investigator can further convert the ciphertext into an or dinary signature and give it to a judge or a prosecutor for the litigation process. A senior manager of MJIB also has the right to take over either one or all ciphertext, i.e., digital evidence, intended for his subordinate. The underlying security assumption of our proposed scheme is based on the bilinear Diffie-Hellman problem (BDHP). We prove that the proposed scheme achieves the security requirement of confidentiality against indistinguishability under adaptive chosen-ciphertext attacks (IND-CCA2) and that of unforgeability against existential forgery under adaptive chosen-message attacks (EF-CMA) in the random oracle model. Compared with related works, the proposed scheme not only provides better functionalities, but also has provable security.

Hierarchical Certificate-Based Encryption: Definition and an Efficient Construction

Certificate-based encryption is a new paradigm which was introduced by Gentry to address the complex public key revocation problem in traditional public key cryptosystems. It represents an interesting and potentially useful balance between traditional public-key encryption and identity-based encryption. In this paper, we introduce the notion of hierarchical certificate-based encryption that preserves the advantages of certificate-based encryption such as implicit certificate and key-escrow free while inheriting the properties of hierarchical identity-based encryption. We formalize the definition of hierarchical certificate-based encryption and also propose a concrete hierarchical certificate-based encryption scheme that is chosen-ciphertext secure under the hardness of bilinear Diffie-Hellman problem in the random oracle model.

Certificateless Public Key Encryption Scheme with Hybrid Problems and Its Application to Internet of Things

Certificateless cryptography aims at combining the advantages of public key cryptography and identity based cryptography to avoid the certificate management and the key escrow problem. In this paper, we present a novel certificateless public key encryption scheme on the elliptic curve over the ring, whose security is based on the hardness assumption of Bilinear Diffie-Hellman problem and factoring the large number as in an RSA protocol. Moreover, since our scheme requires only one pairing operation in decryption, it is significantly more efficient than other related schemes. In addition, based on our encryption system, we also propose a protocol to protect the confidentiality and integrity of information in the scenario of Internet of Things with constrained resource nodes.