Midrash su Esodo 12:13

Another explanation: "And it was in the middle of the night" - this is [the meaning of] that which is written (Psalms 119, 62), "At midnight I arise to praise You for the judgments of your charity (mishpetei tzidkecha):" "At midnight I arise to praise You for" the judgments You enacted upon the Egyptians, and [that] for us You enacted charity. How is this? Rather, once Moshe said (Exodus 12:12), "and I will smite every firstborn," some of them began to fear, and there were [also] from them who were not afraid. One who was afraid would take his firstborn to a Jew and say to him, "I request of you, take this one and he will lodge with you." When the middle of the night arrived, the Holy One, blessed be He, killed all of the firstborn. And [concerning] those that were placed in the houses of the Jews, the Holy One, blessed be He, would skip between the Jews and the Egyptians and take the soul of the Egyptian and leave the soul of the Jew. And the Jew would wake up and find the Egyptian dead between all [of the Jews around him], as it is stated (Ibid. 13), "and I will skip over you and there will not be a plague among you." The Jews [then] began to say, "At midnight I arise to praise You." Thus is it written (Psalms 119, 160), "all of the judgments of your charity."

So Joshua did as Moses had said to him … and it came to pass, when Moses held up his hand (Exod. 17:10–11). Could the hand of Moses actually wage war or cause a war to cease? This indicates that whenever the Israelites glanced upward and directed their hearts to their Father in Heaven, they were strengthened, but if not, they were defeated. Similarly, And the Lord said unto Moses: “Make thee a fiery serpent, and set it upon a pole; and it shall come to pass that everyone that is bitten, when he seeth it, shall live” (Num. 21:8). Can a serpent of bronze cause death or life? This, likewise, indicates that whenever the Israelites looked upwards and expressed their devotion to their Heavenly Father, they were healed, but if not, they were destroyed. Similarly, in the verse And the blood shall be to you for a token (Exod. 12:13), did the blood help the angel of destruction or the Israelites? The fact is that at the time the Israelites smeared blood upon their doorposts, the Holy One, blessed be He, revealed Himself and had pity upon them, as it is said: And when I see the blood, I will pass over you (ibid.) i.e., the angel of death will not be permitted to come to your homes to smite you.

The Israelites took the blood of the covenant of circumcision, and they put (it) upon the lintel of their houses, and when the Holy One, blessed be He, passed over to plague the Egyptians, He saw the blood of the covenant of circumcision upon the lintel of their houses and the blood of the Paschal lamb, He was filled || with compassion on Israel, as it is said, "And when I passed by thee, and saw thee weltering in thy (twofold) blood, I said unto thee, In thy (twofold) blood, live; yea, I said unto thee, In thy (twofold) blood, live" (Ezek. 16:6). "In thy blood" is not written here, but in "thy (twofold) blood," with twofold blood, the blood of the covenant of circumcision and the blood of the Paschal lamb; therefore it is said, "I said unto thee, In thy (twofold) blood, live; yea, I said unto thee, In thy (twofold) blood, live" (ibid.).