Abstract
A watermarking scheme consists of a marking algorithm allowing one to embed some information into a program while preserving its functionality and an extraction algorithm enabling one to extract embedded information from a marked program. The main security properties of watermarking schemes include unremovability and unforgeability. However, all current watermarking schemes achieving both properties simultaneously require the extraction algorithm to access either the marking secret key or the latest state maintained by the marking algorithm. As a result, to extract information embedded in a marked program, one must communicate with a third party. This greatly limits the applicability of current watermarking schemes. In this paper, we solve this problem by presenting the first (stateless) publicly extractable watermarking scheme with unremovability and unforgeability.
R. Yang—This work was mainly done when the first author was an intern at the Department of Computing, the Hong Kong Polytechnic University.
The second to the fifth authors are sorted in the alphabetical order.
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Notes
- 1.
We will give a more detailed discussion on this in Sect. 1.2.
- 2.
One may hope to additionally use a signature scheme to provide unforgeability. That is, Alice could attach her signature on the marked program to the message embedded into it; and a program is regarded as unmarked if no valid signature in the message extracted from it is found. However, this trivial solution will damage the unremovability. More precisely, an attacker could make Alice’s signature invalid and thus remove the mark from a program via generating a functionally equivalent but differently described program.
- 3.
- 4.
- 5.
The circuit \(\mathtt {E}\), as well as all circuits \(\mathtt {E^{(\cdot )}}\) appeared in the proof of Theorem 3.1, will be padded to the same size.
- 6.
The circuit \(\mathtt {M}\), as well as all circuits \(\mathtt {M^{(\cdot )}}\) appeared in the proof of Theorem 3.1, will be padded to the same size.
- 7.
f is computed via lazy sampling, i.e., if \(\alpha _{\iota }\) is fresh, then \(\beta _{\iota }\) is sampled uniformly from \(\mathcal {K}\), and if there exists \(\iota ' < \iota \) that \(\alpha _{\iota } = \alpha _{\iota '}\), then \(\beta _{\iota }\) is set to be \(\beta _{\iota '}\).
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Acknowledgement
We appreciate the anonymous reviewers for their valuable suggestions. Part of this work was supported by the National Natural Science Foundation of China (Grant No. 61602396, U1636205, 61572294, 61632020, 61602275), the MonashU-PolyU-Collinstar Capital Joint Lab on Blockchain and Cryptocurrency Technologies, and from the Research Grants Council of Hong Kong (Grant No. 25206317). The work of Junzuo Lai was supported by the National Natural Science Foundation of China (Grant No. 61572235), and Guangdong Natural Science Funds for Distinguished Young Scholar (No. 2015A030306045).
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Yang, R., Au, M.H., Lai, J., Xu, Q., Yu, Z. (2018). Unforgeable Watermarking Schemes with Public Extraction. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_4
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