Cryptology ePrint Archive: Report 2015/1096

Watermarking Cryptographic Capabilities

Aloni Cohen and Justin Holmgren and Ryo Nishimaki and Vinod Vaikuntanathan and Daniel Wichs

Abstract: A watermarking scheme for programs embeds some information called a mark into a program while preserving its functionality. No adversary can remove the mark without damaging the functionality of the program. In this work, we study the problem of watermarking various cryptographic programs such as pseudorandom function (PRF) evaluation, decryption, and signing. For example, given a PRF F, we create a marked program C~ that evaluates F(). An adversary that gets C~ cannot come up with any program C* in which the mark is removed but which still evaluates the PRF correctly on even a small fraction of the inputs.

The work of Barak, Goldreich, Impagliazzo, Rudich, Sahai, Vadhan, and Yang (CRYPTO'01 and Journal of ACM 59(2)) shows that, assuming indistinguishability obfuscation (iO), such watermarking is impossible if the marked program C~ evaluates the original program with perfect correctness. In this work we show that, assuming iO, such watermarking is possible if the marked program C~ is allowed to err with even a negligible probability, which would be undetectable to the user.

Our watermarking schemes are public key, meaning that we use a secret marking key to embed marks in programs, and a public detection key that allows anyone to detect marks in programs. Our schemes are secure against chosen program attacks where the adversary is given oracle access to the marking functionality. We emphasize that our security notion of watermark non-removability considers arbitrary adversarial strategies to modify the marked program, in contrast to the prior works (Nishimaki, EUROCRYPT '13).

Category / Keywords: public-key cryptography / watermarking, indistingushability obfuscation, puncturable PRFs

Original Publication (with major differences): STOC 2016

Date: received 10 Nov 2015, last revised 8 Feb 2016

Contact author: nishimaki ryo at lab ntt co jp

Available format(s): PDF | BibTeX Citation

Note: Added acknowledgements

Version: 20160208:114745 (All versions of this report)

Short URL: ia.cr/2015/1096

Discussion forum: Show discussion | Start new discussion


[ Cryptology ePrint archive ]