Abarim Publications' online Biblical Greek Dictionary
The adverb ενεκα (heneka), or ενεκεν (heneken), means since, owing to, because of, thanks to, by reason of, due to, in regard to, as far as such-and-such is concerned. It naturally generates a genitive.
To the eye it seems that our adverb has something to do with the particles εν (en), meaning in, and εκ (ek), meaning out. Its nature is mainly associative (such-and-such is happening because of, i.e. since so-and-so — kids are out playing 'because' the sun is shining), with less causative power than the comparable and much more common δια (dia), which often indicates direct causation (such-and-such is happening because, i.e. as a consequence of, so-and-so happening — it's hot 'because' the sun is shining).
This difference may seem subtle but it really isn't. Matthew 5:10 does not speak of clearly defined bad guys who persecute clearly defined good guys on account of the righteousness of the latter, but rather of the general reality of complex webs of pushing-and-shoving that will ultimately allow humanity to mature and attain righteousness in matters of science and statecraft. Until that happens, even humans with the best intentions are doomed to speak falsely of the Word of God, which describes the now not fully known natural and observable reality through which humans may know God (Matthew 5:11; see Romans 1:20 and Hebrews 1:3).
Our adverb is used 25 times in the New Testament; see full concordance.