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Statistical testing is used to estimate the likelihood of a hypothesis given a set of data. In cryptanalysis, statistical testing is commonly used to detect non-randomness in the data, e.g. distinguish the output of a PRNG from a truly random bitstream or to find the correctly decrypted message among several incorrect decryption attempts.

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Why did NIST remove The Lempel-Ziv Compression test from the Statistical Test Suite?

According to the paper On Lempel-Ziv Complexity of Sequences by Doganaksoy and Gologlu, A test based on Lempel-Ziv complexity was used in the NIST test suite, to test the randomness of sequences. …
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