What operations provide perfect secrecy other than modulo addition
Any group operation works for a one-time-pad if you can shoehorn a message uniquely into a group element—addition modulo $n$, multiplication modulo $n$ if you can uniquely encode a message block as an integer coprime with $n$, addition or multiplication in finite extension fields, invertible matrix multiplication over finite fields, whatever group you want—and can be extended by a direct product to arbitrary-length messages: if you have a group operation $m \oplus k$, then you can extend it to an $\ell$-block message $(m_1, m_2, \dotsc, m_\ell)$ with an $\ell$-block key $(k_1, k_2, \dotsc, k_\ell)$ by $(m_1 \oplus k_1, \dotsc, m_\ell \oplus k_\ell)$.  Conventionally we talk about addition modulo 26 in English, or use addition modulo 2 for computers, of course.

Going beyond the one-time pad approach, to encrypt a $t$-bit message, you could choose a permutation $\pi$ uniformly at random from all $2^t!$ possibilities; then the one-time cipher $m \mapsto \pi(m)$ has ‘perfect secrecy’ too.  Of course, it's tremendously inefficient even compared to a one-time pad!  (Bonus: You could get built-in authentication with forgery probability bounded by $2^{-f}$ by using $m \mapsto \pi(m \mathbin\| 0^f)$.  Of course, still much cheaper to compose a one-time pad and one-time authenticator…)