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If the attacker can make related-key chosen-plaintext queries, then there is a generic attack that can break any block cipher with $n$-bit keys in $2^{n/2}$ time, using $2^{n/2}$ related-key queries and $2^{n/2}$ memory. So against a related-key attacker, the effective strength of a block cipher can be no more than half the key length. However, the ...


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Your question here has two answers, depending on what you mean. The first is the distinction between birthday attacks and exhaustion attacks. In a birthday attack, the attacker wins if he gets two messages that have the same key. And in that case the security is proportional to half the key length. In an exhaustion attack, the attacker has a specific ...


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You run the algorithm with two different plaintexts (whose difference is usually small, just a few bits, everything else being equal). Whereever these plaintexts lead to different inputs to an S-box (in any layer/round of the algorithm), we call this S-Box active (since the other S-boxes produce the same result for both plaintexts, they are called "passive" ...


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You are essentially asserting that if $k \equiv 1 \pmod N$, then $a^k \equiv a \pmod N$. This is false in general. The correct assertion is the following: $a^k \equiv a^\ell \pmod N$ if $k\equiv \ell \pmod{\phi(N)}$. In more general group-theoretic terms, if $a$ is an element of order $n$ in a group $G$, then $a^k = a^\ell$ if and only if $k \equiv \ell ...



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