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On White-Box Cryptography and Obfuscation

Authors:
Amitabh Saxena
Brecht Wyseur
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URL: http://eprint.iacr.org/2008/273
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Abstract: We study the relationship between obfuscation and white-box cryptography. We capture the requirements of any white-box primitive using a \emph{White-Box Property (WBP)} and give some negative/positive results. Loosely speaking, the WBP is defined for some scheme and a security notion (we call the pair a \emph{specification}), and implies that w.r.t. the specification, an obfuscation does not leak any ``useful'' information, even though it may leak some ``useless'' non-black-box information. Our main result is a negative one - for most interesting programs, an obfuscation (under \emph{any} definition) cannot satisfy the WBP for every specification in which the program may be present. To do this, we define a \emph{Universal White-Box Property (UWBP)}, which if satisfied, would imply that under \emph{whatever} specification we conceive, the WBP is satisfied. We then show that for every non-approximately-learnable family, there exist certain (contrived) specifications for which the WBP (and thus, the UWBP) fails. On the positive side, we show that there exists an obfuscator for a non-approximately-learnable family that achieves the WBP for a certain specification. Furthermore, there exists an obfuscator for a non-learnable (but approximately-learnable) family that achieves the UWBP. Our results can also be viewed as formalizing the distinction between ``useful'' and ``useless'' non-black-box information.
BibTeX
@misc{eprint-2008-17950,
  title={On White-Box Cryptography and Obfuscation},
  booktitle={IACR Eprint archive},
  keywords={foundations / obfuscation, white-box cryptography, white-box property, universal white-box property, virtual black-box property},
  url={http://eprint.iacr.org/2008/273},
  note={none amitabh123@gmail.com 14050 received 12 Jun 2008, last revised 20 Jun 2008},
  author={Amitabh Saxena and Brecht Wyseur},
  year=2008
}