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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 ...


1

The bottom of page 3 of your second link (the specification for LED) seems pretty clear: "Note that for a 64-bit key $K$, all subkeys are equal to $K$, while for a 128-bit key $K$, the subkeys are alternatively equal to the left part $K^1$ and to the right part $K^2$ of $K$." Basically, the input master key is split into a sorted list of nibbles, and ...


1

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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