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Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2022: Advances in Cryptology – EUROCRYPT 2022 pp 645–669Cite as

Cryptanalysis of Candidate Obfuscators for Affine Determinant Programs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13275))

Abstract

At ITCS 2020, Bartusek et al. proposed a candidate indistinguishability obfuscator (\(i\mathcal {O}\)) for affine determinant programs (ADPs). The candidate is special since it directly applies specific randomization techniques to the underlying ADP, without relying on the hardness of traditional cryptographic assumptions like discrete-log or learning with errors. It is relatively efficient compared to the rest of the \(i\mathcal {O}\) candidates. However, the obfuscation scheme requires further cryptanalysis since it was not known to be based on any well-formed mathematical assumptions.

In this paper, we show cryptanalytic attacks on the \(i\mathcal {O}\) candidate provided by Bartusek et al. Our attack exploits the weakness of one of the randomization steps in the candidate. The attack applies to a fairly general class of programs. At the end of the paper we discuss plausible countermeasures to defend against our attacks.

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Notes

  1. 1.

    Here, we actually define a new class of branching programs that can be seen as a generalization of the deterministic BPs whose out degree of every vertex is not limited by 1 for all \(\mathbf {x}\). This new notion can be helpful when obfuscating ADPs.

  2. 2.

    The transformation is actually applied to an ADP. We describe it by BP because BP is a DAG and thus can be better understood. You can understand the RLS here in this way: it decodes the input ADP back to a BP first, then it does the transformation and encodes the resulting BP as the final ADP.

  3. 3.

    There are many potential ways of applying RLS. The RLS transformation here is the candidate given in [8].

  4. 4.

    For the same reason, we will ignore the sign of the minors in the rest of this paper.

  5. 5.

    Recall that when encoding a BP into an ADP, the lowermost row and the leftmost column are deleted. Thus, if the dimension of \(L(\mathbf {x})\) is \(\ell \), the number of nodes should be \(\ell +1\).

  6. 6.

    The family of ADPs here is only a subset of all ADPs our attack could apply.

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Acknowledgments

We thank anonymous reviewers for their helpful comments. Y.C. is supported by Tsinghua University start-up funding and Shanghai Qi Zhi Institute. Yu Yu was supported by the National Key Research and Development Program of China (Grant Nos. 2020YFA0309705 and 2018YFA0704701) and the National Natural Science Foundation of China (Grant Nos. 62125204 and 61872236). Yu Yu also acknowledges the support from the XPLORER PRIZE.

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Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, 200240, China

    Li Yao & Yu Yu

  2. Tsinghua University, Beijing, 100084, China

    Yilei Chen

  3. Shanghai Qi Zhi Institute, Shanghai, 200232, China

    Yilei Chen & Yu Yu

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  1. Li Yao
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Correspondence to Li Yao .

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  1. University of Haifa, Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Warsaw, Warsaw, Poland

    Stefan Dziembowski

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Yao, L., Chen, Y., Yu, Y. (2022). Cryptanalysis of Candidate Obfuscators for Affine Determinant Programs. In: Dunkelman, O., Dziembowski, S. (eds) Advances in Cryptology – EUROCRYPT 2022. EUROCRYPT 2022. Lecture Notes in Computer Science, vol 13275. Springer, Cham. https://doi.org/10.1007/978-3-031-06944-4_22

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