Abstract
In this work, we propose a new table-based block cipher structure, dubbed \( \mathsf {FPL} \), that can be used to build white-box secure block ciphers. Our construction is a balanced Feistel cipher, where the input to each round function determines multiple indices for the underlying table via a probe function, and the sum of the values from the table becomes the output of the round function. We identify the properties of the probe function that make the resulting block cipher white-box secure in terms of weak and strong space hardness against known-space and non-adaptive chosen-space attacks. Our construction, enjoying rigorous provable security without relying on any ideal primitive, provides flexibility to the block size and the table size, and permits parallel table look-ups.
We also propose a concrete instantiation of \( \mathsf {FPL} \), dubbed \( \mathsf {FPL}_{\mathsf {AES}} \), using (round-reduced) \(\mathsf {AES}\) for the underlying table and probe functions. Our implementation shows that \( \mathsf {FPL}_{\mathsf {AES}} \) provides stronger security without significant loss of efficiency, compared to existing schemes including \(\mathsf {SPACE}\), \(\mathsf {WhiteBlock}\) and \(\mathsf {WEM}\).
J. Lee was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (Ministry of Science and ICT), No. NRF-2017R1E1A1A03070248.
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Notes
- 1.
- 2.
It would also be possible to tweak the probe function when it is instantiated with a pseudorandom function such as \( \mathsf {AES} \).
- 3.
A table-based block cipher \( \widetilde{E} \) can be regarded as keyed since each table in \( \mathcal {F} _{s,t}\) can be indexed by \(t\cdot 2^s\) bits.
- 4.
We assume that \(0<(B/A)^{\frac{1}{d}}<rd2^s\). All the parameters in Table 1 satisfy this inequality.
- 5.
We let \(r'C(q/r')=0\) when \(r'=0\).
- 6.
The definition can be straightforwardly extended to \(s>16\).
- 7.
Any constant key will not affect the overall security (compared to \(\mathbf {0}_{128}\)).
- 8.
This is the table size of \(\mathsf {WEM}\) for their recommended parameters.
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Kwon, J., Lee, B., Lee, J., Moon, D. (2020). \( \mathsf {FPL} \): White-Box Secure Block Cipher Using Parallel Table Look-Ups. In: Jarecki, S. (eds) Topics in Cryptology – CT-RSA 2020. CT-RSA 2020. Lecture Notes in Computer Science(), vol 12006. Springer, Cham. https://doi.org/10.1007/978-3-030-40186-3_6
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