Abstract
In this work, we tackle the problem of estimating the security of iterated symmetric ciphers in an efficient manner, with tests that do not require a deep analysis of the internal structure of the cipher. This is particularly useful during the design phase of these ciphers, especially for quickly testing several combinations of possible parameters defining several cipher design variants.
We consider a popular statistical test that allows us to determine the probability of flipping each cipher output bit, given a small variation in the input of the cipher. From these probabilities, one can compute three measurable metrics related to the well-known full diffusion, avalanche and strict avalanche criteria.
This highly parallelizable testing process scales linearly with the number of samples, i.e., cipher inputs, to be evaluated and the number of design variants to be tested. But, the number of design variants might grow exponentially with respect to some parameters.
The high cost of Central Processing Unit (CPU)s makes them a bad candidate for this kind of parallelization. As a main contribution, we propose a framework, ACE-HoT, to parallelize the testing process using multi-Graphics Processing Units (GPUs). Our implementation does not perform any intermediate CPU-GPU data transfers.
The diffusion and avalanche criteria can be seen as an application of discrete first-order derivatives. As a secondary contribution, we generalize these criteria to their high-order version. Our generalization requires an exponentially larger number of samples, in order to compute sufficiently accurate probabilities. As a case study, we apply ACE-HoT on most of the finalists of the National Institute of Standards and Technologies (NIST) lightweight standardization process, with a special focus on the winner ASCON.
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Notes
- 1.
We can provide the source code to the reviewers if requested.
- 2.
A certain threshold has to be fixed.
- 3.
We recall that we report on the minimum value of each metric. This is why all metrics are monotonically non-decreasing.
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Bellini, E., Grados, J., Rachidi, M., Satpute, N., Daemen, J., El Hirch, S. (2023). ACE-HoT: Accelerating an Extreme Amount of Symmetric Cipher Evaluations for (High-order) Avalanche Tests. In: Aly, A., Tibouchi, M. (eds) Progress in Cryptology – LATINCRYPT 2023. LATINCRYPT 2023. Lecture Notes in Computer Science, vol 14168. Springer, Cham. https://doi.org/10.1007/978-3-031-44469-2_2
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