Verifiable Outsourcing Algorithms for Modular Exponentiations with Improved Checkability

Ren, Yanli; Ding, Ning; Zhang, Xinpeng; Lü, Haining; Gu, Dawu

doi:10.1145/2897845.2897881

Cited by 20 publications

(30 citation statements)

References 31 publications

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“…Subsequent works for verifiable computation of the general function include other works, 6,12,22,23 and the previous works [24][25][26][27][28] concentrate on schemes to improve the efficiency for computing the specific function. Subsequent works for verifiable computation of the general function include other works, 6,12,22,23 and the previous works [24][25][26][27][28] concentrate on schemes to improve the efficiency for computing the specific function.…”

Section: Related Workmentioning

confidence: 99%

“…Gennaro et al 2 first introduced and formalized the non-interactive verifiable outsourced computation. Subsequent works for verifiable computation of the general function include other works, 6,12,22,23 and the previous works [24][25][26][27][28] concentrate on schemes to improve the efficiency for computing the specific function. Several previous schemes only allow one specific client to privately verify the result during each round of computational process, which has some inherent limitations as introduced above.…”

Section: Related Workmentioning

confidence: 99%

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An improved scheme for outsourced computation with attribute‐based encryption

Yang

Sun

Qin

et al. 2018

Concurrency and Computation

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With the wide deployment of cloud computing, outsourcing complicated computational tasks to cloud service providers has attracted much attention. An increasing number of clients with computationally constrained devices choose to outsource their heavy tasks to cloud servers to reduce the computational overhead in local. However, how to preserve the integrity of computational results becomes a challenge since commercial cloud servers are not trusted. Public verifiability is an effective mechanism to allow clients to verify the integrity of the results returned by the servers. Because the results are sensitive in many applications, it raises the problem of privacy leakage in the public verification process. In this paper, we propose an efficient verifiable computation scheme while keeping output privacy. The proposed scheme achieves blind verifiability such that the verifiers who have not the additional information (retrieve key) can verify the integrity of the result without learning the result. Furthermore, by combining with (k, n)-threshold sharing, our scheme allows the clients jointly learn the results. KEYWORDSblind verifiability, cloud computing, KP-ABE, verifiable computation INTRODUCTIONWith the rapid development of cloud technology, outsourced computation has been an important field. The technology provides not only the storage service but also the computing service, which can benefit the clients with limited resources a great deal. Meanwhile, the computationally constrained devices such as smartphones, laptops, and wearable equipments 1 have become popular. These scenarios contribute to the research of outsourced computation where the computationally weak clients (devices) outsource the expensive and complicated computation to the large and powerful servers. 2 In addition, outsourced computation is sometimes used to perform the complicated task in some cryptographic primitives 3-5 as well, which can make the primitives more efficient and practical. However, the servers are generally operated by the third-party outside the control domain of clients, and there may exist an incentive for servers to deceive clients into accepting an incorrect result. For instance, to save the computational resources, the cloud servers may not perform the advertised computation but instead return a computationally indistinguishable result to the client.In this case, the key problem is that the clients may not have enough computational resources to detect the incorrect result, which would bring trouble to clients in their subsequent works. For example, if the computational result is the statistics analysis for stock market, the incorrect result will cause the investment corporation property loss. Hence, clients need some efficient methodologies to guarantee that the returned result from servers is correct, which is a necessity in the outsourced computation paradigm.The design of verifiable outsourced computation has drawn widespread attentions. 2,6-9 In the verifiable computation scheme, the verifiability property allows the cl...

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Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

An improved scheme for outsourced computation with attribute‐based encryption

Yang

Sun

Qin

et al. 2018

Concurrency and Computation

View full text Add to dashboard Cite

show abstract

“…However, it is still possible for the outsourcer to be cheated by the server. Ren et al then constructed a verifiable outsourcing scheme of MExps, where the outsourcer can detect the error with a probability of 1 if the server misbehaves [6]. Lai et al [7] proposed an attribute-based encryption (ABE) scheme with verifiable outsourcing decryption, which guaranteed that an outsourcer can efficiently detect the wrong results.…”

Section: Related Workmentioning

confidence: 99%

“…Assume that 1 is an honest server and 2 is a malicious server. At the end of the algorithm, the outsourcer verifies the results by formulas (4)- (6). It is obvious that 2 must generate the correct value of 21 ; otherwise, formula (4) cannot pass the verification with a probability of 1.…”

Section: Theoremmentioning

confidence: 99%

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Noninteractive Verifiable Outsourcing Algorithm for Bilinear Pairing with Improved Checkability

Ren

Dong

Niu

et al. 2017

Security and Communication Networks

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It is well known that the computation of bilinear pairing is the most expensive operation in pairing-based cryptography. In this paper, we propose a noninteractive verifiable outsourcing algorithm of bilinear pairing based on two servers in the one-malicious model. The outsourcer need not execute any expensive operation, such as scalar multiplication and modular exponentiation. Moreover, the outsourcer could detect any failure with a probability close to 1 if one of the servers misbehaves. Therefore, the proposed algorithm improves checkability and decreases communication cost compared with the previous ones. Finally, we utilize the proposed algorithm as a subroutine to achieve an anonymous identity-based encryption (AIBE) scheme with outsourced decryption and an identity-based signature (IBS) scheme with outsourced verification.

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Secure delegation of group exponentiations: Efficient and fully verifiable schemes with two servers†

Moritz

Uzunkol

2019

Security and Privacy

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Recent interactions between cloud service providers and mobile resource‐constrained devices have increased the interest on the delegation of expensive computations to powerful external server providers. At the same time, security and verifiability of the delegated computation are challenging though highly demanded requirements for various application scenarios. Many security solutions using advanced cryptographic technologies require a large number of highly expensive group exponentiations (GEs). In this paper, we address the problems regarding secure and verifiable delegation of GEs. We first analyze two delegation schemes for GEs both introduced recently in Cluster Computing by Fu et al with the claim that they both provide full verifiability. Particularly, we show that the first scheme is only verifiable with a probability at most 2/3, and the second scheme is totally unverifiable. Then, we propose a secure, efficient and fully verifiable delegation scheme InvDel for a GE using two servers, where one of which is malicious. With InvDel the delegator does not require computations of any group inversions (GIs) while providing full verifiability. Then, we extend InvDel to SimInvDel which is the first, efficient and secure delegation scheme for n‐simultaneous GEs achieving full verifiability for n > 1. Secondly, we give implementation results of InvDel and SimInvDel using an Android application together with a comprehensive efficiency analysis of computation and communication with the previous schemes. For instance, when the required CPU costs for a single GE are compared with a 4092‐bit modulus, InvDel is more than 220‐times (resp. more than two times) more efficient than the local computation (resp. using a previous fully verifiable scheme proposed in the literature). Finally, we also utilize InvDel and SimInvDel to speed‐up the verification of Schnorr's signature and Cramer‐Shoup encryption schemes.

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Verifiable Outsourcing Algorithms for Modular Exponentiations with Improved Checkability

Cited by 20 publications

References 31 publications

An improved scheme for outsourced computation with attribute‐based encryption

An improved scheme for outsourced computation with attribute‐based encryption

Noninteractive Verifiable Outsourcing Algorithm for Bilinear Pairing with Improved Checkability

Secure delegation of group exponentiations: Efficient and fully verifiable schemes with two servers†

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