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There are two major problems with this method. The first problem is that Susan is likely to be able to recover significant amount of data from a series of such blocks. For example, if Susan knows $subkey_1$, then she could recover the value $subblock_1 \oplus subblock_2 \oplus subkey_2$; if a single block is encrypted with this key, she can't deduce ...


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 $x_1 = y_1$, $x_2 = y_2$, ..., $x_n = y_n$


It depends greatly on what form and mode of encryption you use. For any stream cipher or a block cipher used in a psuedo-stream mode such as CTR or GCM then reusing a key/IV pair even once is absolutely fatal. Never, ever use a static key with them, and if you do, never, ever reuse an IV. They are strictly for one time use keys negotiated via a key exchange ...


In short, yes, key re-use will eventually lead to a growing vulnerability to a persistent and dedicated attacker over a very large data set. Depending on what encryption method you are using, the details get a very complicated very quickly. I believe in a standard AES CBC implementation with a random IV a key change is recommended after 264 bytes of data. ...

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