The books of Kabbala discuss the two parallel brisos that Hashem made with the Jewish people. There is the Bris Hamaor, the covenant of skin [the Bris Mila] and the Bris Halashon - the covenant of speech. The word מילה and פה have the same gematria of 85. How fascinating that the word for circumcision - "Milah", means "word", alluding to this dual bris .
Let us explore the connection of the brisos to Mitzrayim: The Zohar famously teaches that in Mitzrayim, "speech" was in galus. That is why we speak so much at the seder, for it is an expression of our new found freedom of speech. ברית הלשון. The galus was only able to begin after Yosef passed his test of the Bris Hamaor with the wife of Potiphar. That gave us the foundation to remain spiritually alive in the "land of nakedness". ברית המעור. [Incidentally, Yosef had the status of one of the Avos who paves the way for his descendants, in addition to being one of the bonim, as explained beautifully by the Pachad Yitzchak]. In order to be connected we must carefully and vigilantly guard both brisos.
Says the pasuk in Tehillim [45/ 2-3] יפיפית מבני אדם הוצק חן בשפתותיך וכו' חגור חרבך על ירך - You are more handsome than other men, charm is poured upon your lips etc. gird your sword upon your thigh. The lips refer of course to speech and the "sword upon your thigh" to the bris milah. One who guards his מילה will reach great spiritual heights מי יעלה לנו השמימה - who can climb up to heaven, is an acronym for Milah.
כל ארחות ה' חסד ואמת לנוצרי בריתו עדותיו - All of the paths of Hashem are kindness and truth to those who guard His bris and His testimonies [Tehillim 25/10]. Chesed goes in a straight path and not to the "dark side" [sitra achra] for those who guard Hashem's Bris [Milah] and His testimonies [testimony is given verbally, so this is referring to the bris halashon].
To return to the aforementioned pasuk: "A charm is poured upon your lips" this means that our tefillos will be answered positively, if we "gird your sword upon your thigh" - if we guard our bris kodesh. The Zohar teaches explicitly [Parshas Vayechi Page 240] that this pasuk refers to the Bris Milah.
[Tiferes Shlomo - Shaar Hatfilla Page 52]