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Cryptographic Formula Obfuscation

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Foundations and Practice of Security (FPS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11358))

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Abstract

Under intractability assumptions commonly used in cryptography, we show an efficient program obfuscator for large classes of programs, including any arbitrary monotone formula over statements expressed as equalities to a secret. Previously, only a handful set of individual functions were known to have such program obfuscators. This result has both theoretical and practical relevance. On the theoretical side, it significantly increases the class of functions that are known to have a cryptographically secure program obfuscator, and it shows that general-purpose program obfuscation results do exist with at least some level of generality, despite the likely impossibility, proved in [2], to achieve a related notion of obfuscation for any arbitrary polynomial-time program. On the practical side, there are many computational programs that can be expressed as monotone formulae over equality statements, and can now be securely obfuscated. Our most foundational contribution is a new type of obfuscation: protecting the privacy of the formula gates, and thus of much of the computation carried out by the program, in addition to the privacy of secrets used by the program. Previous program obfuscators only targeted the privacy of secrets used by the program.

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Acknowledgements

Many thanks to Brian Coan for interesting discussions on these results. I am still very grateful to Alfredo De Santis, Giuseppe Persiano, and Moti Yung, coauthors in past work cited here, for several enjoyable conversations on using formula labelings in constructions of other cryptographic primitives.

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Authors and Affiliations

  1. Perspecta Labs, Basking Ridge, NJ, USA

    Giovanni Di Crescenzo

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  1. Giovanni Di Crescenzo
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Correspondence to Giovanni Di Crescenzo .

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Editors and Affiliations

  1. Dalhousie University, Halifax, NS, Canada

    Nur Zincir-Heywood

  2. École des Mines de Nancy, Nancy, France

    Guillaume Bonfante

  3. Concordia University, Montreal, QC, Canada

    Mourad Debbabi

  4. Telecom SudParis, Evry, France

    Joaquin Garcia-Alfaro

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Supported by the Defense Advanced Research Projects Agency (DARPA) SafeWare program via U.S. Army Research Office (ARO), contract number W911NF-15-C-0233. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation hereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of DARPA, ARO or the U.S. Government.

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Di Crescenzo, G. (2019). Cryptographic Formula Obfuscation. In: Zincir-Heywood, N., Bonfante, G., Debbabi, M., Garcia-Alfaro, J. (eds) Foundations and Practice of Security. FPS 2018. Lecture Notes in Computer Science(), vol 11358. Springer, Cham. https://doi.org/10.1007/978-3-030-18419-3_14

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  • DOI: https://doi.org/10.1007/978-3-030-18419-3_14

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  • Online ISBN: 978-3-030-18419-3

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