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On Provable White-Box Security in the Strong Incompressibility Model

Authors:
Estuardo Alpirez Bock , Xiphera LTD, Espoo, Finland
Chris Brzuska , Aalto University, Espoo, Finland
Russell W. F. Lai , Aalto University, Espoo, Finland
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DOI: 10.46586/tches.v2023.i4.167-187
URL: https://tches.iacr.org/index.php/TCHES/article/view/11162
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Abstract: Incompressibility is a popular security notion for white-box cryptography and captures that a large encryption program cannot be compressed without losing functionality. Fouque, Karpman, Kirchner and Minaud (FKKM) defined strong incompressibility, where a compressed program should not even help to distinguish encryptions of two messages of equal length. Equivalently, the notion can be phrased as indistinguishability under chosen-plaintext attacks and key-leakage (LK-IND-CPA), where the leakage rate is high.In this paper, we show that LK-IND-CPA security with superlogarithmic-length leakage, and thus strong incompressibility, cannot be proven under standard (i.e. single-stage) assumptions, if the encryption scheme is key-fixing, i.e. a polynomial number of message-ciphertext pairs uniquely determine the key with high probability. Our impossibility result refutes a claim by FKKM that their big-key generation mechanism achieves strong incompressibility when combined with any PRG or any conventional encryption scheme, since the claim is not true for encryption schemes which are key-fixing (or for PRGs which are injective). In particular, we prove that the cipher block chaining (CBC) block cipher mode is key-fixing when modelling the cipher as a truly random permutation for each key. Subsequent to and inspired by our work, FKKM prove that their original big-key generation mechanism can be combined with a random oracle into an LK-IND-CPA-secure encryption scheme, circumventing the impossibility result by the use of an idealised model.Along the way, our work also helps clarifying the relations between incompressible white-box cryptography, big-key symmetric encryption, and general leakage resilient cryptography, and their limitations.
BibTeX
@article{tches-2023-33344,
  title={On Provable White-Box Security in the Strong Incompressibility Model},
  journal={IACR Transactions on Cryptographic Hardware and Embedded Systems},
  publisher={Ruhr-Universit├Ąt Bochum},
  volume={2023, Issue 4},
  pages={167-187},
  url={https://tches.iacr.org/index.php/TCHES/article/view/11162},
  doi={10.46586/tches.v2023.i4.167-187},
  author={Estuardo Alpirez Bock and Chris Brzuska and Russell W. F. Lai},
  year=2023
}