f=v=b=p, g=k, d=t, y=o=u, e=i.
Cybernetics -> kupirnitics
Government -> kupirnit
It's probably also related to "operatus" (Latin for "work", things like cooperate and opera come from it) but I can't find sources. (co)operatus -> (k)upiratus
Another example is the famous "father" etymology:
Father/vader/pater -> patir (PIE *pH₂tér)
This happens a lot for third declension nouns where nominative ends in -s (opus is one such example)
Other examples of this pattern:
Corpus -> corporem (not *corpusem)
Venus -> Venerem (not *Venusem)
Flos -> florem (not *flosem)
Colos -> colorem (not *colosem)
Or more simply, we can look at opus and see it comes from a different PIE root from cyber. (When i look it up, the former has a root meaning "work", and the latter has a root meaning "turn")
The comparative method proves the original phoneme was /s/ in many cases:
generis - compare Greek gene(s)os, Sanskrit janasas
jus, juris - compare justitia where the /s/ was not intervocalic
robur (archaic robos), roboris - compare robustus
The 3rd declension has many s-stems like these though there are some original r-stems also like jecur (< PIE jekwor, compare Greek hepar).
We have a tendency to think of "cy" as an S followed by an "ai" diphthong. But if we consider the "c" as a hard /k/ and the "y" as a vowel similar to /u/, there isn't a huge difference between "cyber" and "guber", the latter form showing up in Latin and ultimately in English words like "gubernatorial".