Abstract
The Internet of things (IoT) market is booming with emerging applications in the automation process, transportation, customer transactions, industries, and healthcare by utilizing various IoT devices and sensors. IoT adoption helps organizations and companies to avoid high labour costs and improve their services. Also, people are gaining full control over their lives by using IoT devices like smart wearables, smart vehicles, laptops, tablets, and iPhones. However, devices cannot fully protect the secret data of the users. Localization of confidential information may be leaked due to a single server failure. Distributed cryptography plays a significant role to avoid a single point of failure by distributing a cryptographic operation among several servers instead of depending on a single server. In particular, threshold cryptography has the power to perform any cryptographic operation securely despite the compromise of a certain subset of servers. The Threshold trapdoor function (TTDF) is a thresholdized version of the Trapdoor function (TDF), an important base primitive in cryptography. TTDF facilitates sharing of the master trapdoor key among multiple servers so that at least a threshold number of servers jointly can invert the evaluated value of a randomly chosen function from the collection of TTDF. There are constructions of TTDF from the decisional Diffie-Hellman (DDH) and the learning with errors (LWE) assumptions which are strong as compared to the computational Diffie-Hellman (CDH) assumption. It is crucial to realize TTDF from a weaker hardness assumption. In this work, we provide the first TTDF construction under the hardness of the CDH problem by integrating Shamir’s threshold secret sharing with the CDH-based recyclable one-way function with encryption (OWFE) of Garg and Hajiabadi (8). Motivated by the concept of Garg et al. for building TDF using recyclableOWFE, we share the master trapdoor key by Shamir’s threshold secret sharing and provide a shared trapdoor key to each server so that each server can compute an inversion share of the image of a domain element. At least a threshold number of servers jointly can invert the image to recover the preimage. But, fewer than a threshold number of servers jointly are not able to invert the image. Our proposed TTDF achieves one-wayness despite the compromise of a certain subset of servers. Our security proof is in the standard model against the selective adversary. Our proposal yields a shorter image size as compared to the existing DDH-based TTDF scheme of Tu et al. (IET Inf Secur 14(2):220–231, 2019). Moreover, in comparison to the previous TTDF, our scheme performs better regarding communication bandwidth.
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The work is supported by the Department of Science and Technology, Ministry of Science and Technology (DST/INSPIRE Fellowship/2018/IF180048). The authors declare no competing interests.
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Belel, A., Dutta, R. & Mukhopadhyay, S. Communication-friendly threshold trapdoor function from weaker assumption for distributed cryptography. Ann. Telecommun. 78, 221–233 (2023). https://doi.org/10.1007/s12243-022-00937-4
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DOI: https://doi.org/10.1007/s12243-022-00937-4