Cryptographic Assumptions Research Articles

Faster fog-aided private set intersectionwith integrity preserving

Private set intersection (PSI) allows two parties to compute the intersection of their private sets while revealing nothing except the intersection. With the development of fog computing, the need has arisen to delegate PSI on outsourced datasets to the fog. However, the existing PSI schemes are based on either fully homomorphic encryption (FHE) or pairing computation. To the best of our knowledge, FHE and pairing operations consume a huge amount of computational resource. It is therefore an untenable scenario for resource-limited clients to carry out these operations. Furthermore, these PSI schemes cannot be applied to fog computing due to some inherent problems such as unacceptable latency and lack of mobility support. To resolve this problem, we first propose a novel primitive called “faster fog-aided private set intersection with integrity preserving”, where the fog conducts delegated intersection operations over encrypted data without the decryption capacity. One of our technical highlights is to reduce the computation cost greatly by eliminating the FHE and pairing computation. Then we present a concrete construction and prove its security required under some cryptographic assumptions. Finally, we make a detailed theoretical analysis and simulation, and compare the results with those of the state-of-the-art schemes in two respects: communication overhead and computation overhead. The theoretical analysis and simulation show that our scheme is more efficient and practical.

Efficient public key encryption with equality test in the standard model

Public key encryption with equality test (PKEET) is a special kind of public encryption scheme (PKE) that allows a tester to perform equality tests on ciphertexts generated by different public keys as well as the same public key. This feature enables us to apply PKEET to various scenarios in practice, such as efficient data management on encrypted databases and spam filtering in encrypted email systems. From these reasons, since Yang et al. [1] first proposed the concept of PKEET, there have been proposed many PKEET schemes to improve efficiency or to enhance functionalities. However, to the best of our knowledge, almost all existing schemes were presented under assuming the existence of random oracles, except for generic construction proposed by Lee et al. On the other hand, their generic approach for PKEET employs a 2-level hierarchical identity-based encryption and a strongly unforgeable one-time signature, which suffers from low efficiency.In this paper, we propose an efficient PKEET scheme under a specific cryptographic assumption in the standard model. To this end, we first encrypt a message and its hash value in a parallel way by following the recently proposed strategy. Then, to prevent adaptive chosen ciphertext attacks (CCA2), we give a link between them by adapting the technique which was originally proposed for identity-based encryption and previously exploited to design efficient CCA2-secure PKE schemes. We show that our proposed construction satisfies formal security requirements for PKEET under the decisional bilinear Diffie–Hellman (DBDH) assumption in the standard model. As a result, we obtain a new PKEET scheme which has shorter ciphertext and trapdoor sizes, and improves computational costs for encryption, decryption, and test algorithms, by about 60%, 77%, and 66%, respectively, compared to a PKEET instantiation obtained by the prior generic framework.

Provably secure group key management scheme based on proxy re-encryption with constant public bulletin size and key derivation time

Users share a group key to decrypt encryptions for the group using a group key management scheme. In this paper, we propose a re-encryption-based group key management scheme, which uses a unidirectional proxy re-encryption scheme with special properties to enable group members share the updated group key with minimum storage and computation overhead. In particular, we propose a proxy re-encryption scheme that supports direct re-encryption key derivation using intermediate re-encryption keys. Unlike multi-hop re-encryption, the proposed proxy re-encryption scheme does not involve repeated re-encryption of the message. All the computations are done on the re-encryption key level and only one re-encryption is sufficient for making the group key available to the users. The proposed scheme is the first for group key management based on proxy re-encryption that is secure against collusion. The individual users store just one individual secret key with group key derivation requiring O\((\log N)\) computation steps for a group of N users. Size of the public bulletin maintained to facilitate access to the most recent group key for off-line members is O(N) and remains constant with respect to the number of group updates. The proposed group key management scheme confronts attacks by a non-member and even a collusion attack under standard cryptographic assumptions.

Practical attribute‐based signature schemes for circuits from bilinear map

Attribute-based signatures allow us to sign anonymously, in such a way that the signature proves that the signer's attributes satisfy some predicate, but it hides any other information on the signer's attributes beyond that fact. As well as any cryptographic primitive, one of the important goals of the research on this primitive is to construct a scheme that is expressive (supports a wide class of predicates), is practically efficient, and is based on well-studied cryptographic assumptions. The authors construct attribute-based signature schemes that support any Boolean circuit of unbounded depth and number of gates, are practically efficient, from the symmetric bilinear Diffie–Hellman assumption. Toward this end, they combine the Groth–Sahai proof system, which serve as an efficient proof system for algebraic equations, and the Groth–Ostrovsky–Sahai proof system, which are still inefficient, but can prove any NP language via a Karp reduction to circuit satisfiability.

Efficient authentication scheme based on near-ring root extraction problem

An authentication protocolis the type of computer communication protocol or cryptography protocol specifically designed for transfer of authentication data between two entities. We have planned a two new entity authentication scheme on the basis of root extraction problem near-ring in this article. We suggest that this problem is suitably difficult to serve as a cryptographic assumption over the platform of near-ring N. The security issues also discussed.

Pseudorandom Generators with Optimal Seed Length for Non-Boolean Poly-Size Circuits

A sampling procedure for a distribution P over {0, 1} ℓ is a function C : {0, 1} n → {0, 1} ℓ such that the distribution C ( U n ) (obtained by applying C on the uniform distribution U n ) is the “desired distribution” P . Let n > r ≥ ℓ = n Ω(1) . An ϵ- nb-PRG (defined by Dubrov and Ishai [2006]) is a function G : {0, 1} r → {0, 1} n such that for every C : {0, 1} n → {0, 1} ℓ in some class of “interesting sampling procedures,” C ′( U r ) = C ( G ( U r )) is ϵ-close to C ( U n ) in statistical distance . We construct poly-time computable nb-PRGs with r = O (ℓ) for poly-size circuits relying on the assumption that there exists β > 0 and a problem L in E = DTIME(2 O ( n ) ) such that for every large enough n , nondeterministic circuits of size 2 β n that have NP-gates cannot solve L on inputs of length n . This assumption is a scaled nonuniform analog of (the widely believed) EXP ≠ Σ 2 P , and similar assumptions appear in various contexts in derandomization. Previous nb-PRGs of Dubrov and Ishai have r = Ω(ℓ 2 ) and are based on very strong cryptographic assumptions or, alternatively, on nonstandard assumptions regarding incompressibility of functions on random inputs. When restricting to poly-size circuits C : {0, 1} n → {0, 1} ℓ with Shannon entropy H ( C ( U n )) ⩽ k , for ℓ > k = n Ω(1) , our nb-PRGs have r = O ( k ). The nb-PRGs of Dubrov and Ishai use seed length r = Ω( k 2 ) and require that the probability distribution of C ( U n ) is efficiently computable. Our nb-PRGs follow from a notion of “conditional PRGs,” which may be of independent interest. These are PRGs where G ( U r ) remains pseudorandom even when conditioned on a “large” event { A ( G ( U r )) = 1}, for an arbitrary poly-size circuit A . A related notion was considered by Shaltiel and Umans [2005] in a different setting, and our proofs use ideas from that paper, as well as ideas of Dubrov and Ishai. We also give an unconditional construction of poly-time computable nb-PRGs for poly( n )-size, depth d circuits C : {0, 1} n → {0, 1} ℓ with r = O (ℓ · log d + O (1) n ). This improves upon the previous work of Dubrov and Ishai that has r ≥ ℓ 2 . This result follows by adapting a recent PRG construction of Trevisan and Xue [2013] to the case of nb-PRGs. We also show that this PRG can be implemented by a uniform family of constant-depth circuits with slightly increased seed length.

Delegation of Computation with Verification Outsourcing: Curious Verifiers

In the Cloud Computing paradigm, a user often reduces financial, personnel, and computational burdens by outsourcing computation and other IT services to a professional service provider. However, to be able to assure the correctness of the result, the user still needs to perform the verification himself. Such verification may be tedious and expensive. Consequently, users are likely to outsource (again) the verification workload to a third party. Other scenarios such as auditing and arbitrating may also require the use of third-party verification. Outsourcing verification will introduce new security challenges. One such challenge is to protect the computational task and the results from the untrusted third party verifier. In this work, we address this problem by proposing an efficient verification outsourcing scheme. To our knowledge, this is the first solution to the verification outsourcing problem. We show that, without using expensive fully-homomorphic encryption, an honest-but-curious third party can help to verify the result of an outsourced computational task without having to learn either the computational task or the result thereof. We have implemented our design by combining a novel commitment protocol and an additive-homomorphic encryption in the argument system model. The total cost of the verification in our design is less than the verifier's cost in the state-of-the-art argument systems that rely only on standard cryptographic assumptions.

An Authenticated Key Agreement Scheme Based on Cyclic Automorphism Subgroups of Random Orders

Group-based cryptography is viewed as a modern cryptographic candidate solution to blocking quantum computer attacks, and key exchange protocols on the Internet are one of the primitives to ensure the security of communication. In 2016 Habeeb et al proposed a “textbook” key exchange protocol based on the semidirect product of two groups, which is insecure for use in real-world applications. In this paper, after discarding the unnecessary disguising notion of semidirect product in the protocol, we establish a simplified yet enhanced authenticated key agreement scheme based on cyclic automorphism subgroups of random orders by making hybrid use of certificates and symmetric-key encryption as challenge-and-responses in the public-key setting. Its passive security is formally analyzed, which is relative to the cryptographic hardness assumption of a computational number-theoretic problem. Cryptanalysis of this scheme shows that it is secure against the intruder-in-the-middle attack even in the worst case of compromising the signatures, and provides explicit key confirmation to both parties.

Patient-Controlled Attribute-Based Encryption for Secure Electronic Health Records System.

In recent years, many countries have been trying to integrate electronic health data managed by each hospital to offer more efficient healthcare services. Since health data contain sensitive information of patients, there have been much research that present privacy preserving mechanisms. However, existing studies either require a patient to perform various steps to secure the data or restrict the patient to exerting control over the data. In this paper, we propose patient-controlled attribute-based encryption, which enables a patient (a data owner) to control access to the health data and reduces the operational burden for the patient, simultaneously. With our method, the patient has powerful control capability of his/her own health data in that he/she has the final say on the access with time limitation. In addition, our scheme provides emergency medical services which allow the emergency staffs to access the health data without the patient's permission only in the case of emergencies. We prove that our scheme is secure under cryptographic assumptions and analyze its efficiency from the patient's perspective.

Bilinear‐map accumulator‐based verifiable intersection operations on encrypted data in cloud

SummaryThe intersection operation on multisets has many applications in different scenarios, such as data mining and pattern matching. This motivates us to study the problem that when users outsource their private encrypted sets and delegate the set‐intersection operation on the corresponding plaintexts to the cloud, the cloud can manage to conduct the operation and make the result verifiable without the decryption capability. We formally introduced a model of Verifiable Intersection Operations on Encrypted Data in Cloud and presented the definitions of the correctness and security properties. We also proposed a concrete scheme basing on the bilinear‐map accumulator and re‐encryption. The scheme was proved secure under some cryptographic assumptions. And the experimental results of the algorithm implementation show the scheme is partly practical for real scenarios. Copyright © 2016 John Wiley & Sons, Ltd.

Pinocchio

To instill greater confidence in computations outsourced to the cloud, clients should be able to verify the correctness of the results returned. To this end, we introduce Pinocchio, a built system for efficiently verifying general computations while relying only on cryptographic assumptions. With Pinocchio, the client creates a public evaluation key to describe her computation; this setup is proportional to evaluating the computation once. The worker then evaluates the computation on a particular input and uses the evaluation key to produce a proof of correctness. The proof is only 288 bytes, regardless of the computation performed or the size of the IO. Anyone can check the proof using a public verification key. Crucially, our evaluation on seven applications demonstrates that Pinocchio is efficient in practice too. Pinocchio's verification time is a fixed 10 ms plus 0.4--15 μs per IO element: 5--7 orders of magnitude less than previous work; indeed Pinocchio is the first general-purpose system to demonstrate verification cheaper than native execution (for some apps). The worker's proof effort is still expensive, but Pinocchio reduces it by 19×--60× relative to prior work. As an additional feature, Pinocchio allows the worker to include private inputs in the computation and prove that she performed the computation correctly without revealing any information about the private inputs to the client. Finally, to aid development, Pinocchio provides an end-to-end toolchain that compiles a subset of C into programs that implement the verifiable computation protocol.<!-- END_PAGE_1 -->

A new publicly verifiable data possession on remote storage

In this paper, a new verifiable data possession construction supporting both private and public verifiability simultaneously is proposed from a linearly homomorphic cryptography method, which allows a server to integrate l selected block-tag pairs into a single block-tag pair as a response to user’s query. In our scheme, the data owner who uses the private verification and anyone else who runs the public verification algorithm simultaneously on the same set of meta-data and based on the same setup procedure can securely authenticate the integrity of client’s data file stored at cloud server without retrieving the whole original data file. Besides, in fact our simultaneous privately and publicly verifiable scheme can also be adjusted to elliptic curve group. The scheme proposed is efficient on both client and server sides, especially in computation on cloud server side, which is almost optimal among those existing publicly verifiable schemes. Here the server needs not to perform any exponent operations at all, which greatly reduces client’s waiting time. Finally, we make the security analysis of our scheme under several cryptographic assumptions, such as difficulty of Factorization Assumption and Discrete Logarithm Problem (DLP).

The current state of art in program obfuscations: definitions of obfuscation security

Program obfuscation is a semantic-preserving transformation aimed at bringing a program into a form that impedes understanding of its algorithm and data structures or prevents extracting certain valuable information from the text of the program. Since obfuscation may find wide use in computer security, information hiding and cryptography, security requirements to program obfuscators have become a major focus of interest in the theory of software obfuscation starting from the pioneering works in this field. In this paper we give a survey of various definitions of obfuscation security and basic results that establish possibility or impossibility of secure program obfuscation under certain cryptographic assumptions.

A new public key encryption scheme based on two cryptographic assumptions

In this paper we present a new cryptosystem which is a combination of RSA variant namely rebalanced RSA-CRT and general formulation of DGDLP. Its security is depend upon integer factorization problem and general formulation of DGDLP.

Fully secure anonymous spatial encryption under affine space delegation functionality revisited

Recently, in Information Sciences, Zhang et al. (2014) claimed that they proposed the first anonymous spatial encryption under affine space delegation functionality with full security, which solves the open problems of full security proposed in Boneh and Hamburg (2008) and anonymity left in Boneh and Hamburg (2008) and Moriyama and Doi (2011). In this paper, we show their construction cannot achieve recipient anonymity as the ciphertext terms leak information about the encryption vector. Hence realizing anonymous spatial encryption with full security is still an open problem. We propose a new fully secure anonymous spatial encryption under an affine space delegation mechanism that addresses the open problem positively. Our construction utilizes composite order bilinear groups where the group order is a product of four primes and achieves the same efficiency as that of the Zhang et al. (2014) construction. Under some well-established cryptographic assumptions, the proposed construction is proven to be fully semantically secure with anonymity in the standard model within the dual encryption system framework.

Digital signature with message recovery based on factoring and discrete logarithm

ABSTRACTThere are two applications in digital signature schemes with message recovery based on a discrete logarithm problem. One is an authenticated encryption scheme, and the other is a key agreement scheme. Considering that the cryptographic assumptions will be broken in the future, the digital signature scheme with message recovery should also be designed based on two assumptions. Besides the digital signature scheme with message recovery, the authenticated encryption scheme with message linkages should also be redesigned to deal with the problem when any one of the factoring and discrete logarithm assumptions is broken. In this paper, we propose a digital signature with message recovery based on factoring and discrete logarithm and show that the scheme is secure. In comparison with Zhang ET AL.'s scheme, our proposed scheme is the most efficient one in terms of communication cost and computation complexity.

Exponential Lower Bounds for AC 0 -Frege Imply Superpolynomial Frege Lower Bounds

We give a general transformation that turns polynomial-size Frege proofs into subexponential-size AC 0 -Frege proofs. This indicates that proving truly exponential lower bounds for AC 0 -Frege is hard, as it is a long-standing open problem to prove superpolynomial lower bounds for Frege. Our construction is optimal for proofs of formulas of unbounded depth. As a consequence of our main result, we are able to shed some light on the question of automatizability for bounded-depth Frege systems. First, we present a simpler proof of the results of Bonet et al. showing that under cryptographic assumptions, bounded-depth Frege proofs are not automatizable. Second, we show that because our proof is more general, under the right cryptographic assumptions, it could resolve the automatizability question for lower-depth Frege systems.

Secure outsourced computation of the characteristic polynomial and eigenvalues of matrix

Linear algebra plays an important role in computer science, especially in cryptography. Numerous cryptographic protocols and scientific computations are based on linear algebra, which can be reduced to some core problems, such as matrix multiplication, determinant and the characteristic polynomial of a matrix. However, it is difficult to carry out these expensive computations independently for resource-limited cloud users. Outsourced computation, a service provided by cloud computing, enables a resources-constrained client to outsource his mass computing tasks to the cloud. In this paper, we use data hiding technique to design a secure and verifiable outsourcing protocol for computing the characteristic polynomial and eigenvalues of a matrix. Our protocols achieve several desired features, such as data privacy, verifiability and efficiency. Moreover, no cryptographic assumption is needed in our protocols.

Garbling XOR Gates “For Free” in the Standard Model

Yao's garbled circuit (GC) technique is a powerful cryptographic tool which allows to encrypt a circuit $$C$$C by another circuit $${\hat{C}}$$C^ in a way that hides all information except the final output. Yao's original construction incurs a constant overhead in both computation and communication per gate of the circuit $$C$$C (proportional to the complexity of symmetric encryption). Kolesnikov and Schneider (ICALP 2008) introduced an optimized variant that garbles XOR gates for free in a way that involves no cryptographic operations and no communication. This variant has become very popular and has lead to notable performance improvements. The security of the free-XOR optimization was originally proved in the random oracle model. Despite some partial progress (Choi et al., TCC 2012), the question of replacing the random oracle with a standard cryptographic assumption has remained open. We resolve this question by showing that the free-XOR approach can be realized in the standard model under the learning parity with noise (LPN) assumption. Our result is obtained in two steps:1.We show that the random oracle can be replaced with a symmetric encryption, which remains secure under a combined form of related-key (RK) and key-dependent message (KDM) attacks.2.We show that such a symmetric encryption can be constructed based on the LPN assumption. As an additional contribution, we prove that the combination of RK and KDM security is nontrivial in the following sense: There exists an encryption scheme which achieves RK security and KDM security separately, but breaks completely at the presence of combined RK-KDM attacks.

Efficient outsourcing schemes of modular exponentiations with checkability for untrusted cloud server

Modular exponentiation is one of basic operations among most of current cryptosystems. In previous work, in order to detect the dishonest behavior of cloud servers, modular exponentiations can only be securely outsourced by using two untrusted cloud servers. However, these results cannot resist the collusion attack by the untrusted cloud servers. In this paper, we present two secure outsourcing schemes for modular exponentiations, which enable users to securely outsource modular exponentiations to a single untrusted cloud server and detect the dishonest behavior of untrusted cloud server. The first one is a secure outsourcing scheme for variable base-variable exponent modular exponentiation, while the second is for simultaneous modular exponentiations. Compared with other proposed schemes, our outsourcing schemes are superior in both efficiency and checkability. Moreover, our schemes are secure without any cryptographic assumptions. In addition, we give two applications for our outsourcing schemes, one is to construct an outsourcing scheme for Cramer–Shoup encryptions, and the other is to design an outsourcing scheme for Schnorr signatures.