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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. However the test had some weaknesses. First of all, the test could only be applied to data of a specified length: $10^6$ bits. Moreover, the test used empirical ...

By discarding values 252 to 255, you effectively avoid introducing any new bias; the generic method is expressed in many places, e.g. this article (page 3). To generate random values between $0$ and $d-1$ (inclusive) from a PRNG which produces bit, you do the following: Choose an integer $r$ such that $2^r \geq d$. Obtain a $r$-bit word $x$ from the PRNG. ...

Well, from your previous questions, I'm assuming that your writing a utility to brute-force decrypt a password protected file (encrypted with a certain encryption utility), and you're looking for a way to determine whether your trial decryption is plausible. Normally, when an attacker attempts to decrypt something, he has some idea about what it is (why ...

A quite common way to actually prove something is building a system on already known components, and then proving the security of the composed system, given the security of the components. Most often the paper has a theorem like If the function F has property Y, then this new function G has property X. The proof then shows that if someone can attack ...

Well, for one, SHA-2 (either SHA-256 or SHA-512) doesn't have a 'keyspace'; that's because it doesn't have a key. SHA-2 takes an arbitrary bitstring is input, and generates an output; while there are limits on how long the bitstring can be, those limits are so huge ($2^{64}-1$ bits for SHA-256, $2^{128}-1$ bits for SHA-512), those limits can in practice be ...

I'll assume that the objective is to assert if the distribution of the $f'_i/n'$ is sufficiently similar with the distribution of the $f_i/n$ to support that a substitution cipher (including Caesar cipher) with the same permutation table and same frequency of plaintext characters could be used in both case. If $n \gg n'$, $f_i \gg 5$ and ...

On the first glance, this base 36 key stream looks at least as secure as RC4 itself - you are simply discarding some of the output, and not introducing any bias. Note that there are some general weaknesses with in the start of the output of RC4, which means that it is normally recommended to discard the first 1000 or so bytes after initialization (I have to ...

The usual assumption is that the attacker knows a full plaintext block; that's what the EFF DES-cracking machine uses. That machine knows exactly 8 consecutive plaintext bytes and the corresponding ciphertext block; it stops when it finds a matching key. Since there are 256 possible DES keys, and 264 possible 8-byte blocks, chances are high that there is ...

The most important take-away is that if you are asking this question, you are almost certainly not qualified to design a secure cryptographic primitive. Sounds harsh, but I mean it in all earnestness. You wouldn't trust someone who hadn't been to medical school to do surgery on you. Similarly, we wouldn't trust someone who doesn't already know the ...

I can't give an example illustrating why leakage must be non-negligible for the utility of the mechanism, but I can give a proof of why leakage must be non-negligible for the utility of the mechanism. Let $\;\; U \: = \: \left\{\langle D,D'\rangle : D,D' \text{ differ in one element}\right\} \;\;\;$. By the triangle inequality, for all $D$ and $D'$, for ...

In addition, NIST Statistical Tests and Diehard Battery of Tests of Randomness are good tests.Some tests proposed here and here for stream ciphers. Passing these tests is essential but does not enough. For more information see introduction of first link. Also Provable security may be useful.