Secure outsourcing algorithms of modular exponentiations with optimal checkability based on a single untrusted cloud server

Fu, Anmin; Zhu, Yiming; Yang, Guomin; Yu, Shui; Yu, Yan

doi:10.1007/s10586-018-2830-7

Cited by 16 publications

(11 citation statements)

References 41 publications

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“…In this section, we show verifiability issues for very recently proposed delegation schemes MExp and M2Exp proposed by Fu et al in cluster computing 11 under the OUP-assumption. We recall the original schemes MExp and M2Exp briefly before introducing the attacks to make the issues understandable for the readers.…”

Section: Verifiability Issues In Two Recent Delegation Schemesmentioning

confidence: 86%

“…This, however, annihilates the contribution regarding the full verifiability of M2Exp, actually M2Exp is totally unverifiable, that is, only 0-verifiable. Hence, for n > 1 and the claim regarding full verifiability [11] (Thm. 8, pp.…”

Section: And Outputs the Valuementioning

confidence: 88%

“…However, none of these schemes provide full verifiability property; even worse it is shown in Reference 13 that the scheme in Reference 10 offers considerably less verifiability probability (ie, only ≈1/2 probability if n goes to infinity) than the original verifiability claim (ie, ≈1 if n goes to infinity). Very recently Fu et al 11 introduced both for single delegation and for simultaneous delegation efficient schemes, where it is claimed that the schemes provide full verifiability. In an earlier version of the current paper, presented at the International Conference on Intelligent, Secure and Dependable Systems in Distributed and Cloud Environments [1], we proposed a delegation scheme for n‐simultaneous multiplications of GEs, provided its security analysis and implementation results in an Android application, and gave efficiency comparisons with the previous schemes 1 .…”

Section: Related Workmentioning

confidence: 99%

“…Our contribution in this paper is that we address the problem of secure, efficient, and verifiable delegation of GEs. Our main contributions are the followings: We first analyze the two delegation schemes MExp and M2Exp recently proposed in Reference 11 show that these schemes do not provide the claimed verifiability guarantees. In particular, we show that the scheme MExp is only verifiable with a probability at most two‐third, and the scheme M2Exp is totally unverifiable, that is, a malicious server can always manipulate the outputs and cheat the client. We introduce a secure, efficient, and fully verifiable delegation scheme InvDel for a single GE, which is the most efficient secure delegation scheme when compared with the previous schemes requiring no computation of GIs by the delegator.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Verifiability Issues In Two Recent Delegation Schemesmentioning

confidence: 86%

Section: And Outputs the Valuementioning

confidence: 88%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…In 2018, Fu et al presented two schemes [33,34] and claimed that their verifiability are equal to one, but similar to Rangasamy's attack on Li's scheme, it can be shown that these scheme has a verifiability of zero. In 2018, Rangasamy [31] presented a scheme that, like Zhou's scheme, requires a covert computation modulus.…”

Section: Single-server Schemesmentioning

confidence: 99%

Fully Verifiable Outsourcing of Single and Composite Modular Exponentiation with Single Untrusted Cloud Server

Torki

Mala

Ashouri-Talouki

et al. 2022

Preprint

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Modular exponentiation is considered one of the most widely used, yet costly operations in public-key cryptography, especially for resource-constrained devices in a peer-to-peer networks such as net of IoT or sensor devices. However, it can be computed at a relatively low cost with the help of outsourcing. The first contribution of this paper is investigating the security of the Su et al.’s scheme which, our first attack confirms that the verifiability of this scheme is less than the authors’ claim and our second attack reveals that a malicious server is able to forge user signature. The second contribution of this paper is investigating the verifiability of Ding’s scheme, a scheme previously claimed to provide high verifiability, and we shows that this scheme is not verifiable. The third contribution is centered around proposing two practical and secure outsourcing schemes for outsourc-ing computations of single and composite modular exponentiation, in the single-server model. It is worth noting that both of our proposed schemes offer higher efficiency and security than the previous schemes as their verifiability are equal to one, while the recorded verifiability of the previous schemes decreases by the number of exponentiations utilized.

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On Single-Server Delegation of RSA

Crescenzo¹,

Khodjaeva

Ta³

et al. 2023

Lecture Notes in Computer Science

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Secure outsourcing algorithms of modular exponentiations with optimal checkability based on a single untrusted cloud server

Cited by 16 publications

References 41 publications

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

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

Fully Verifiable Outsourcing of Single and Composite Modular Exponentiation with Single Untrusted Cloud Server

On Single-Server Delegation of RSA

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