A fantastic facet of Birchas Kohanim is in the Seifer Ha’Pardes from Rashi. Either from talmidei Rashi, or Beis Midrasho shel Rashi. B’kitzur, from Rashi. In Hilchos Rosh Ha’Shana he says the following. After takanas Rabi Avahu that we blow three sets of tashrat, tashat, and tarat, and we also have two times that we do this set – tekios d’meyushav and tekios d’meumad, which he holds was also part of takanas Rabi Avahu, the total number comes out to sixty. This corresponds to the sixty letters of Birchas Kohanim, and each of these sixty are the shishim giborim saviv lah…kulam achuzei cherev (Shir Ha’Shirim 3:7-8). Even in the Diaspora, where Kohanim do not duchen every day, there still is this power of shishim giborim, because the pasuk says ha’shochein itam b’soch tumosam – once Klal Yisrael was exiled, the Shechina is with them wherever they are. This is accomplished by the Shaliach Tzibbur saying Elokeinu v’Elokei avoseinu barcheinu ba’bracha…and the pesukim of Yevarechecha, etc. Ha’Kadosh Baruch Hu agrees with the Kohanim and silences the Satan.
You see from this – from Rashi! – that every letter and every word of Birchas Kohanim is a weapon that delivers a powerful blow against the Satan v’chayalosav, the same way tekias shofar does – which is more effective than a powerful weapon. Also, you see that it is not just a zeicher what the Shaliach Tzibur does in chutz la’aretz, rather it effects the same koach of shishim giborim.
(Audio recording available here)