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The condition is that: $$g(0, x_2, x_3, ..., x_n) \ne g(1, x_2, x_3, ..., x_n)$$ for all $x_2, x_3, ..., x_n$ This can easily be derived from the condition that implies bijectivity of $f$; that is, $f(x_1, x_2, ..., x_n) = f(y_1, y_2, ..., y_n)$ implies that $x_1 = y_1$, $x_2 = y_2$, ..., $x_n = y_n$


For any fixed $x_2, \ldots, x_n$, $g$ must be a surjective function of $x_1$ (i.e. onto).


There is a known distinguisher on SEAL presented here that works with about $2^{43}$ bytes of known plaintext. As breaks go, this is on the academic side of things; it requires almost as much known plaintext as you can possibly encrypt with a single key, and all it does is distinguish; it tells you nothing about what the key might be (and very little about ...


Say you have the value $n$ which is the size of the alphabet (i.e. the range of characters that make up your plaintext and ciphertext). And say $m = x \times n$ is the largest value you have that is not higher than $y$ where $y$ is the largest size produced by your random number generator. For each character: Take values from the random number generator ...


The biggest reason is performance. Stream ciphers are generally faster than block ciphers and perform fewer operations. Stream ciphers only need to generate a pseudorandom output while block ciphers need to be pseudorandom permutations. So when you create a steam cipher out of a block cipher, you are doing a lot more work to get the same effect. To get an ...


There are two answers, really depending on your specifications and how your generator will be evaluated. If all you need is to have a PRNG with statistically excellent random, but really don't care about predictability or cryptographic considerations, go for something simple like a Mersenne Twister. If you actually need some effective stream-cipher, look ...

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