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Implementing Indistinguishability Obfuscation Using GGH15

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Information Security and Cryptology (Inscrypt 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10726))

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Abstract

Obfuscation is an extraordinarily powerful object that has been shown to enable a whole set of new cryptographic possibilities. Because of the impossibility of the general-purpose virtual black-box (VBB) obfuscation, Barak et al. suggested to implement a weak variant which is called the indistinguishability obfuscation (iO). The iO is the substrate of various cryptographic primitives such as the universal function encryption, the self-bilinear map and so on. However, current obfuscation is too cumbersome to implement in practice.

In this paper, we implement an obfuscation for NC1 circuits by using the GGH15 multilinear map. Several techniques are proposed to improve the efficiency and adaptability of the implementation. We reduce the matrix dimension and the depth of encoding graph to increase the speed of confusion. Splitting the matrix into block matrix and encoding each block instead of using the entire matrix will reduce the size of matrix effectively. The plaintext matrix will be one block of the matrix. Besides, we put matrices into groups and encode one group on path \(u\,\rightsquigarrow \,v\). Then the depth of the graph depends on the number of groups rather than the number of matrices. Those methods have led to a significant reduction in the rate of obfuscation.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 61672550, No. 61379154) and the Fundamental Research Funds for the Central Universities (No. 17lgjc45).

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Authors and Affiliations

  1. School of Data and Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Zheng Zhang, Fangguo Zhang & Huang Zhang

  2. Guangdong Key Laboratory of Information Security, Guangzhou, 510006, China

    Zheng Zhang, Fangguo Zhang & Huang Zhang

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  1. Zheng Zhang
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  2. Fangguo Zhang
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  3. Huang Zhang
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Correspondence to Fangguo Zhang .

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Editors and Affiliations

  1. Xidian University, Xi’an, China

    Xiaofeng Chen

  2. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  3. Columbia University, New York, New York, USA

    Moti Yung

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Zhang, Z., Zhang, F., Zhang, H. (2018). Implementing Indistinguishability Obfuscation Using GGH15. In: Chen, X., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2017. Lecture Notes in Computer Science(), vol 10726. Springer, Cham. https://doi.org/10.1007/978-3-319-75160-3_4

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  • DOI: https://doi.org/10.1007/978-3-319-75160-3_4

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  • Online ISBN: 978-3-319-75160-3

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