This is not a research question. Merely observe that $2^{2n} = 4^n \equiv 1^n\equiv 1 \mod 3$ and $10^n \equiv 1^n\equiv 1 \mod 3$. The relevance of $2^{2n}$ is that exchanging two characters (stored in bytes with even numbers of bits) amounts to multiplying one part of a key by $2^{2n}$ for some $n$, and dividing another part by a like amount. (Also note, powers of 3 ($3^k$ for some $k$) are multiples of 3 ($3\cdot m$ for some $m$ if $k>0$) but multiples of 3 are much more common than its powers.)

Observe that $2^{2n} = 4^n \equiv 1^n\equiv 1 \mod 3$ and $10^n \equiv 1^n\equiv 1 \mod 3$. The relevance of $2^{2n}$ is that exchanging two characters (stored in bytes with even numbers of bits) amounts to multiplying one part of a key by $2^{2n}$ for some $n$, and dividing another part by a like amount. (Also note, powers of 3 ($3^k$ for some $k$) are multiples of 3 ($3\cdot m$ for some $m$ if $k>0$) but multiples of 3 are much more common than its powers.)