Private Key Size Research Articles

Efficient Data Sharing With Privacy Preservation Over Lattices for Secure Cloud Storage

Data sharing is a basic data processing mechanism in the cloud storage. Data confidentiality and the receiver privacy are two important requirements of data-sharing systems. Because the data owner does not wish anyone who is not authorized to access the shared data and the authenticated data receiver also does not wish anyone else to know that he/she has accessed the shared data from the data owner. Broadcast encryption gives a possible solution to these requirements of data-sharing systems. This article constructs a data-sharing system over lattice by designing an efficient identity-based broadcast encryption (IBBE) scheme which achieves the data confidentiality and the identity privacy simultaneously. Besides the data owner, no one knows the identities of the authenticated data receivers in the proposed data-sharing system. Data confidentiality is achieved by the indistinguishability under the selective identity and the chosen ciphertext attacks (IND-sID-CCA) of the proposed IBBE scheme. It is proven in the random oracle model that the IND-sID-CCA security is based on the hardness of the learning with errors problem which can resist the quantum attacks. Inherited from the proposed IBBE scheme, the proposed data-sharing system also has several other characters which are suitable to the practical application. The most important feature is that all the public parameters size, private key size, and the ciphertext length are constant for any data receivers set in the proposed system. Hence, the proposed system adapts to the situation of large receiver group. Moreover, the proposed data-sharing system supports efficient member joining. When a new user asks to access the uploaded data, the existing receiver does not need to update his/her private key. The decryption cost of the existing receiver will remain unchanged when the outsourced data have been updated. Detailed performance analysis and a simulated experiment of the designed core algorithm are given by using Java program on a personal computer Intel Core i7-8700 K (3.7 GHz), 32 G RAM which verifies the design results in this article.

Heterogeneous online/offline signcryption for secure communication in Internet of Things

Internet of things (IoT) is a promising network that combines various information sensing devices with the Internet to realize the interconnection of pervasive things. Security is a pivotal issue to ensure widespread adoption of the IoT. To ensure the security of data transmission, in this paper, we construct a heterogeneous online and offline signcryption from a wireless sensor network (WSN) to an Internet server. In our construction, the WSN is in certificateless cryptosystem (CLC) which does not involve public key certificate management problem in public key infrastructure (PKI) and key escrow problem in identity based cryptosystem (IBC), while the server is in IBC which avoids public key certificate management problem. For signcryption process, the proposed scheme is split into two steps: offline step and online step. In the former step, a lot of time-consuming calculations are completed, but do not involve the message to be transmitted. In the latter step, only some lightweight calculations are involved, but message must be available. Confidentiality, authentication, non-repudiation, and integrity can be achieved in a logical single step. Meanwhile, a formal security proof is given in the random oracle model. In addition, an elaborate performance analysis demonstrates that our proposed scheme has advantages in terms of computational cost and private key size, offline storage, as well as communication overhead. Therefore, our construction can be well applied to the IoT.

Complementary set encryption for privacy-preserving data consolidation

Privacy-preserving data consolidation is one of the prominent research topics in the big data era, mostly because of the need of consolidating data from various database communities, which are highly sensitive or competitive in nature. This leads to a new emerging problem namely how to accomplish data consolidation among different organization data sets or databases appropriately without revealing any competitive or sensitive information to non-owners. To address this issue, we first introduce a new encryption notion called “complementary set encryption” (CSE) to apply to privacy-preserving data consolidation. In this notion, to provide privacy protection, the data in one database will be encrypted under a set W prior to being sent to the other database, and a decryption key will be generated with another set Q. The data will be decrypted and consolidated into the other database, if and only if both sets W and Q are complementary. Here, the “complementary” means that the intersection of set W and set Q is empty and meanwhile the union of both is to be completed into a universal set exactly. We then describe two constructions of CSE under the public-key setting. Our first construction is designed under a weaker security notion – “payload hiding”, which only preserves the data privacy but achieves a higher performance. The second construction is a stronger security notion, which we refer to as an “attribute hiding”, which preserves both the privacy of the data and its associated set W. Finally, we provide a formal analysis to prove the security of our two constructions, followed by a theoretical performance comparison and an experimental evaluation. In particular, the first construction is of an independent interest in the context of cryptography since it was able to stand out for its efficiency as a predicate encryption scheme in the sense that it features both low communication overhead and computational costs simultaneously, and only requires a private key size of O(1), a ciphertext size of O(1), and only O(1) pairing computations.

Ultra Lightweight Multiple-Time Digital Signature for the Internet of Things Devices

Digital signatures are basic cryptographic tools to provide authentication and integrity in the emerging ubiquitous systems in which resource-constrained devices are expected to operate securely and efficiently. However, existing digital signatures might not be fully practical for such resource-constrained devices (e.g., medical implants) that have energy limitations. Some other computationally efficient alternatives (e.g., one-time/multiple-time signatures) may introduce high memory and/or communication overhead due to large private key and signature sizes. In this paper, our contributions are two-fold: First, we develop a new lightweight multiple-time digital signature scheme called Signer Efficient Multiple-time Elliptic Curve Signature ( <inline-formula><tex-math notation="LaTeX">$\mathtt {SEMECS}{}$</tex-math></inline-formula> ), which is suitable for resource-constrained embedded devices. <inline-formula><tex-math notation="LaTeX">$\mathtt {SEMECS}{}$</tex-math></inline-formula> achieves optimal signature and private key sizes for an EC-based signature <i>without</i> requiring any EC operation (e.g., EC scalar multiplication or addition) at the signer. We prove <inline-formula><tex-math notation="LaTeX">$\mathtt {SEMECS}{}$</tex-math></inline-formula> is secure (in random oracle model) with a tight security reduction. Second, we fully implemented <inline-formula><tex-math notation="LaTeX">$\mathtt {SEMECS}{}$</tex-math></inline-formula> on 8-bit AVR microprocessor with a comprehensive energy consumption analysis and comparison. Our experiments confirm up to 19× less battery-consumption for <inline-formula><tex-math notation="LaTeX">$\mathtt {SEMECS}{}$</tex-math></inline-formula> as compared to its fastest (full-time) counterpart, SchnorrQ, while offering significant performance advantages over its multiple-time counterparts in various fronts. We open-source our implementation for public testing and adoption.

BESTIE: Broadcast Encryption Scheme for Tiny IoT Equipment

In public key broadcast encryption, anyone can securely transmit a message to a group of receivers such that privileged users can decrypt it. The three important parameters of the broadcast encryption scheme are the length of the ciphertext, the size of private/public key, and the performance of encryption/decryption. It is suggested to decrease them as much as possible; however, it turns out that decreasing one increases the other in most schemes. This paper proposes a new broadcast encryption scheme for tiny Internet of Things (IoT) equipment (BESTIE), minimizing the private key size in each user. In the proposed scheme, the private key size is O(logn), the public key size is O(logn), the encryption time per subset is O(logn), the decryption time is O(logn), and the ciphertext text size is O(r), where n denotes the maximum number of users, and r indicates the number of revoked users. The proposed scheme is the first subset difference-based broadcast encryption scheme to reduce the private key size O(logn) without sacrificing the other parameters. We prove that our proposed scheme is secure under q-Simplified Multi-Exponent Bilinear Diffie-Hellman (q-SMEBDH) in the standard model.

A post-quantum hybrid encryption based on QC-LDPC codes in the multi-user setting

The encryption schemes based on coding theory are one of the most accredited choices in post-quantum scenario, where QC-LDPC codes are usually employed to construct concrete schemes due to the well security and good efficiency. In this work, we introduce a new IND-CCA secure multi-instance framework for code-based hybrid encryption primitive in the random oracle model, which is derived from our new multi-instance KEM and DEM building modules.We note that previous multi-instance KEM and DEM are usually derived from single-instance KEM and DEM, and hence suffers from large parameter sizes and security loss. Nevertheless, our multi-instance KEM is a direct construction based on a key generation function and a one-way trapdoor function, and our multi-instance DEM is constructed from a standard DEM and MAC with a tag in the input to achieve a tighter security loss. Finally, we present a IND-CCA secure multi-instance hybrid encryption scheme based on QC-LDPC codes in the random oracle model, where the scheme achieves small private key size and only consumes addition and multiplication operations over F2[x].

Revocable Broadcast Encryption with Constant Ciphertext and Private Key Size

In a revocable broadcast encryption scheme, the group manager can flexibly set revoked users who cannot decrypt the ciphertext. Many applications of the revocable broadcast encryption have been found in the secure cloud data sharing. An adaptively secure revocable broadcast encryption system with constant ciphertext and private key size under standard assumptions is more suitable for use in the cloud environment. Few existing revocable broadcast encryption schemes meet such a requirement. We propose a revocable broadcast encryption scheme with constant size ciphertext and private key by combining the RSA cryptographic accumulator with an efficient identity based encryption system. We prove it to be adaptively secure under standard assumptions using dual system encryption techniques.

Strong Designated Verifier Signature Scheme with Undeniability and Strong Unforgeability in the Standard Model

Strong designated verifier signature can provide an efficient way to protect the identity privacy of the signer and the integrity of the data transmitted over the public channel. These characteristics make it very useful in outsourcing computing, electronic voting, electronic bidding, electronic auction and other fields. However, most strong designated verifier signature schemes are unable to identify the real signature generator when the signer and the designated verifier dispute a signature. In addition, the existing strong designated verifier signature schemes in the standard model rarely satisfy strong unforgeability, and thus cannot prevent the attacker from forging a valid signature on any previously signed message. Therefore, designing a strong designated verifier signature scheme without random oracles that satisfies strong unforgeability and undeniability is very attractive in both practice and theory. Motivated by these concerns, we design the first undeniable strong designated verifier signature scheme without random oracles, in which the arbiter can independently perform the judgment procedure to prove whether a controversial signature is generated by the signer or the designated verifier. Under standard assumptions, the scheme is proved to be strongly unforgeable in standard model. Furthermore, it not only achieves non-transferability and privacy of the signer’s identity but also satisfies the undeniable property of traditional digital signature schemes. Performance analysis results show that the length of the signer’s private key, the designated verifier’s private key and signature length are 40 bits, 40 bits and 384 bits, respectively. Compared with he related schemes, the proposed scheme has higher performance in signature length, private key size and computational overhead. Finally, we show how to apply it to implement outsourcing computation in cloud computing.

Efficient Construction for Full Black-Box Accountable Authority Identity-Based Encryption

Accountable authority identity-based encryption (A-IBE), as an attractive way to guarantee the user privacy security, enables a malicious private key generator (PKG) to be traced if it generates and re-distributes a user private key. Particularly, an A-IBE scheme achieves full black-box security if it can further trace a decoder box and is secure against a malicious PKG who can access the user decryption results. In PKC’11, Sahai and Seyalioglu presented a generic construction for full black-box A-IBE from a primitive called dummy identity-based encryption, which is a hybrid between IBE and attribute-based encryption (ABE). However, as the complexity of ABE, their construction is inefficient and the size of private keys and ciphertexts in their instantiation is linear in the length of user identity. In this paper, we present a new efficient generic construction for full black-box A-IBE from a new primitive called token-based identity-based encryption (TB-IBE), without using ABE. We first formalize the definition and security model for TB-IBE. Subsequently, we show that a TB-IBE scheme satisfying some properties can be converted to a full black-box A-IBE scheme, which is as efficient as the underlying TB-IBE scheme in terms of computational complexity and parameter sizes. Finally, we give an instantiation with the computational complexity as $O(1)$ and the constant size master key pair, private keys, and ciphertexts.

Efficient Certificate-Based Signature with Short Key and Signature Sizes from Lattices

Certificate-based cryptography (CB-PKC) is an attractive public key setting, which reduces the complexity of public key infrastructure in traditional public key settings and resolves the key escrow problem in ID-based public key settings. In the past, a large number of certificate-based signature and encryption schemes were proposed. Nevertheless, the security assumptions of these schemes are mainly relied on the difficulties of the discrete logarithm and factorization problems. Unfortunately, both problems will be resolved when quantum computers come true in the future. Public key cryptography from lattices is one of the important candidates for post-quantum cryptography. However, there is little work on certificate-based cryptography from lattices. In the paper, we propose a new and efficient certificate-based signature (CBS) scheme from lattices. Under the short integer solution (SIS) assumption from lattices, the proposed CBS scheme is shown to be existential unforgeability against adaptive chosen message attacks. Performance comparisons are made to demonstrate that the proposed CBS scheme from lattices is better than the previous lattice-based CBS scheme in terms of private key size and signature size.

Cryptanalysis of a Compact Anonymous HIBE with Constant Size Private Keys

AbstractRecently, Zhang et al. proposed a new anonymous hierarchical identity-based encryption (anonymous HIBE) over prime order groups to achieve both constant size private key and constant size ciphertext. Moreover, a double exponent technique was used to provide anonymity. They proved that their scheme is secure and anonymous against chosen plaintext attacks in the standard model. In this paper, we point out that their scheme is insecure.

Identity-based key-exposure resilient cloud storage public auditing scheme from lattices

With the rapid development of cloud auditing services, key exposure has been highlighted as a serious security issue. Using the exposed private key of a client, cloud servers can forge previous auditing proofs to cheat auditors. To date, a few pairing-based cloud storage auditing schemes addressing key exposure have been proposed. However, they are not secure from quantum attacks, and they rely on public key infrastructure (PKI), which involves complex certificate management. In this paper, we propose an efficient identity-based key-exposure resilient public auditing scheme from lattice assumptions in cloud storage. Our scheme is not only quantum-resistant, but eliminates the need to establish a PKI. We employ lattice basis delegation technique to update a client’s private key flexibly, keeping the private key size constant. Based on the hardness of lattice assumptions, we prove the forward security of storage correctness guarantee against malicious cloud servers in detail, and that the proposed scheme preserves privacy against curious auditors. Furthermore, we conduct a performance comparison to demonstrate that our scheme is much more efficient and practical for post-quantum secure cloud storage.

Revocable hierarchical identity-based encryption with shorter private keys and update keys

Revocable hierarchical identity-based encryption (RHIBE) is an extension of HIBE that supports the revocation of user’s private keys to manage the dynamic credentials of users in a system. Many different RHIBE schemes were proposed previously, but they are not efficient in terms of the private key size and the update key size since the depth of a hierarchical identity is included as a multiplicative factor. In this paper, we propose efficient RHIBE schemes with shorter private keys and update keys and small public parameters by removing this multiplicative factor. To achieve our goals, we first present a new HIBE scheme with the different generation of private keys such that a private key can be simply derived from a short intermediate private key. Next, we show that two efficient RHIBE schemes can be built by combining our HIBE scheme, an IBE scheme, and a tree based broadcast encryption scheme in a modular way.

Security Control Redundancy Allocation Technology and Security Keys Based on Internet of Things

The Internet of Things (IoT) is widely valued by governments, academia, and industry for its huge application prospects. The core concepts of IoT are perception, control, transmission, and intelligence. It uses technology to achieve the synergy between objects and objects, people and things, and people and people so that the sensor network, the Internet and mobile communication network are based on the formation of a larger complex network system. First, a high order voting algorithm for object-networked control is proposed. In this paper, the algorithm redundancy design method for an industrial control network is studied, and the importance of the algorithmic level heterogeneous redundancy is discussed. The most popular voting algorithms are improved, and an improved majority voting algorithm is proposed. Then, it is compared with the standard majority voting algorithm and the median voting algorithm, which proves that the improved algorithm has higher accuracy and output efficiency. Then, a new security key pre-distribution scheme based on the elliptic curve is proposed, which uses different base points of the elliptic curve as the seed key group, and the probability of two neighboring nodes sharing the same private key is large by selecting the appropriate private key ring size. Other neighboring nodes that do not share the private key can secure communications through the intermediate nodes using the path key, thus guaranteeing the security of the entire sensor network’s private communications. The simulation results show that the proposed scheme has good network connectivity and defensive.

Multimodal biometric Identity Based Encryption

In this paper, we describe the first generic construction for multimodal biometric Identity Based Encryption considering two distance measures at the same time. Current protocols for fuzzy/biometric IBE are designed either for set overlap or Euclidean distance within unimodal biometrics. However, the similarity measures for biometric templates can be quite different from those considered in theoretical works. For instance, a fingerprint template usually consists of a set of minutiae, and two templates are considered as similar if more than a certain number of minutiae in one template are near distinct minutiae in the other. In this case, the similarity measure has to consider both Euclidean distance and set difference at the same time. Similarly, multimodal systems that are designed to address the limitations of unimodal systems may involve two different traits requiring different distance measures for each modality.In order to have high recognition rate and thus increased possibility of decryption even in case of white noise (slight perturbation of biometric features), our generic construction is based on two different biometric IBE systems encoding the same message. This way, employment of both distance measures is possible using multiple matchers within multimodal setting and a failure on the decryption of a message encrypted using the first biometric representation, can be compensated with an attempt on the second part of the ciphertext encrypting the same message but using a different representation of the same receiver. Specifically, we combine a fuzzy IBE-type scheme and the recently introduced Distance Based Encryption (DBE) scheme with minimum overhead in terms of public parameters, ciphertext and private key size. For this purpose, we describe an efficient biometric IBE scheme denoted as ordFIBE, which is restricted for biometrics that can be represented as an ordered/grouped set of features. We study the security of ordFIBE both in random oracle model (ROM) and for small universe of attributes in standard model. In ROM, its efficiency is further improved by employing online/offline encryption technique. Next, we instantiate the new construction by combining ordFIBE and the DBE scheme of Guo et al. (2014), which shares the same setup phase, in particular, common public parameters. Finally, we describe a new scheme for set difference metric that partially solves an open problem introduced in Katz et al. (2008).

Lattice-Based Revocable Certificateless Signature

Certificateless signatures (CLS) are noticeable because they may resolve the key escrow problem in ID-based signatures and break away the management problem regarding certificate in conventional signatures. However, the security of the mostly previous CLS schemes relies on the difficulty of solving discrete logarithm or large integer factorization problems. These two problems would be solved by quantum computers in the future so that the signature schemes based on them will also become insecure. For post-quantum cryptography, lattice-based cryptography is significant due to its efficiency and security. However, no study on addressing the revocation problem in the existing lattice-based CLS schemes is presented. In this paper, we focus on the revocation issue and present the first revocable CLS (RCLS) scheme over lattices. Based on the short integer solution (SIS) assumption over lattices, the proposed lattice-based RCLS scheme is shown to be existential unforgeability against adaptive chosen message attacks. By performance analysis and comparisons, the proposed lattice-based RCLS scheme is better than the previously proposed lattice-based CLS scheme, in terms of private key size, signature length and the revocation mechanism.

Provably secure identity-based identification and signature schemes from code assumptions.

Code-based cryptography is one of few alternatives supposed to be secure in a post-quantum world. Meanwhile, identity-based identification and signature (IBI/IBS) schemes are two of the most fundamental cryptographic primitives, so several code-based IBI/IBS schemes have been proposed. However, with increasingly profound researches on coding theory, the security reduction and efficiency of such schemes have been invalidated and challenged. In this paper, we construct provably secure IBI/IBS schemes from code assumptions against impersonation under active and concurrent attacks through a provably secure code-based signature technique proposed by Preetha, Vasant and Rangan (PVR signature), and a security enhancement Or-proof technique. We also present the parallel-PVR technique to decrease parameter values while maintaining the standard security level. Compared to other code-based IBI/IBS schemes, our schemes achieve not only preferable public parameter size, private key size, communication cost and signature length due to better parameter choices, but also provably secure.

Adaptive-ID Secure Identity-Based Signature Scheme from Lattices in the Standard Model

Identity-based signature (IBS) which is a paradigm built on public key cryptography has played a significant role in light-weight authentication. With the advent of the post quantum era, the lattice has become a main mathematical tool to construct quantum-immune cryptographic schemes. By utilizing an admissible hash function with compatible algorithms and lattice trapdoors as basic building blocks, we propose a new IBS scheme over lattices. The scheme is proved existentially unforgeable against adaptive identity attacks and chosen message attacks in the standard model under inhomogeneous short integer solution assumption via the generalized partitioning proof technique. Moreover, the scheme needs only logarithmic basic matrices as master public key while keeping the same private key size and signature size as those of other standard model lattice-based IBS schemes. This construction is the first adaptive-ID secure standard model IBS scheme over lattice with such space efficiency.

Circulant Rainbow: A New Rainbow Variant With Shorter Private Key and Faster Signature Generation

Rainbow is one of the most important signature schemes in multivariate public key cryptography. It enjoys a strong security guarantee and is a promising signature scheme in Post-Quantum Cryptography. However, it suffers from large key size. In this paper, we propose Circulant Rainbow with shorter private key and higher signing efficiency. In Circulant Rainbow, we introduce rotating relations into parts of Rainbow private key to speed up the signing procedure and reduce the private key size. We carefully choose security parameters so that our Circulant Rainbow is secure against all known attacks. In our experiment, Circulant Rainbow is about three times faster than original Rainbow and it can reduce the private key size by about 45%. We also make a comparison of Circulant Rainbow with some traditional signature schemes, the results show that Circulant Rainbow is a promising candidate in Post-Quantum Cryptography.

Adaptively Secure Broadcast Encryption With Constant Ciphertexts

In this paper, we present a new public key broadcast encryption (BE) for achieving adaptive security against arbitrary number of colluders. Specifically, our scheme is built from composite order multilinear maps and enjoys ciphertext overhead of a constant number of group elements which are ${O}$ (1) bits. Furthermore, the private key size and public key size are all poly-logarithmic in the total number of users. Herein, we generalize the methodology of Lewko and Waters for realizing dual system encryption to the composite order multilinear groups, and then prove the adaptive security of our scheme under static assumptions in the standard model. Compared with the state-of-the-art, our scheme achieves the adaptive security in simple and non-interactive falsifiable assumptions with the optimized parameter size for BE.