Abstract
The output of modern cryptographic primitives like pseudorandom generators and block or stream ciphers is frequently required to be indistinguishable from a truly random data. The existence of any distinguisher provides a hint about the insufficient confusion and diffusion property of an analyzed function. In addition to targeted cryptoanalysis, statistical tests included in batteries such as NIST STS, Dieharder or TestU01 are frequently used to assess the indistinguishability property. However, the tests included in these batteries are either too simple to spot the common biases (like the Monobit test) or overly complex (like the Fourier Transform test) requiring an extensive amount of data. We propose a simple, yet surprisingly powerful method called BoolTest for the construction of distinguishers based on an exhaustive search for boolean function(s). The BoolTest typically constructs distinguisher with fewer input data required and directly identifies the function’s biased output bits. We analyze the performance on four input generation strategies: counter-based, low hamming weight, plaintext-ciphertext block combination and bit-flips to test strict avalanche criterion. The BoolTest detects bias and thus constructs distinguisher in a significantly higher number of rounds in the round-reduced versions of DES, 3-DES, MD5, MD6 and SHA-256 functions than the state-of-the-art batteries. Finally, we provide a precise interpretation of BoolTest verdict (provided in the form of Z-score) about the confidence of a distinguisher found. The BoolTest clear interpretation is a significant advantage over standard batteries consisting of multiple tests, where not only a statistical significance of a single test but also aggregated decision over multiple, potentially correlated tests, needs to be correctly performed.
The BoolTest implementation and paper supplementary material can be found at https://crocs.fi.muni.cz/papers/booltest2018.
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Notes
- 1.
This is extended version of the paper ‘The Efficient Randomness Testing using Boolean Functions’ [1, SeCrypt].
- 2.
In most cases distribution D(x) is given.
- 3.
\(f_1\), \(f_2\), \(f_3\), \(f_4\), \(f_5\), \(f_6\) are particular boolean functions.
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Acknowledgements
We acknowledge the support of the Czech Science Foundation, project GA16-08565S. Computational resources were provided by the CESNET LM2015042 and the CERIT Scientific Cloud LM2015085, provided under the programme “Projects of Large Research, Development, and Innovations Infrastructures”.
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Sýs, M., Klinec, D., Kubíček, K., Švenda, P. (2019). BoolTest: The Fast Randomness Testing Strategy Based on Boolean Functions with Application to DES, 3-DES, MD5, MD6 and SHA-256. In: Obaidat, M., Cabello, E. (eds) E-Business and Telecommunications. ICETE 2017. Communications in Computer and Information Science, vol 990. Springer, Cham. https://doi.org/10.1007/978-3-030-11039-0_7
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