On Provable White-Box Security in the Strong Incompressibility Model


  • Estuardo Alpirez Bock Xiphera LTD, Espoo, Finland
  • Chris Brzuska Aalto University, Espoo, Finland
  • Russell W. F. Lai Aalto University, Espoo, Finland




White-Box Cryptography, Incompressibility, Bounded-Retrieval, Leakage Resilience, Impossibility, Provable Security


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.




How to Cite

Alpirez Bock, E., Brzuska, C., & Lai, R. W. F. (2023). On Provable White-Box Security in the Strong Incompressibility Model. IACR Transactions on Cryptographic Hardware and Embedded Systems, 2023(4), 167–187. https://doi.org/10.46586/tches.v2023.i4.167-187