More on justification through the blood of Christ:
Chrysostom.
Writing On The Blood Typology
Let us then return from the [Communion] table like lions breathing fire, having become terrible to the devil; thinking on our Head [Christ] and on the love that He has shown for us.… Our Lord says:
“I feed you with My own flesh, desiring that you all be nobly born, and holding forth good hopes for your future.… I have willed to become your Brother. For your sake, I shared in flesh and blood, and, in turn, I give you the flesh and the blood by which I became your kinsman.” This blood causes the image of our King to be fresh within us. It produces beauty unspeakable and prevents the nobleness of our souls from wasting away.… It nourishes our souls and works in them a mighty power. This blood, if rightly taken, drives away devils, and keeps them far from us, while it calls the angels and the Lord of angels to us. For wherever they see the Lord’s blood, devils flee, and angels run together.
This blood poured forth and washed all the world clean.
St. Paul uttered many wise sayings concerning it in the Epistle to the Hebrews. This blood cleansed the secret place and the Holy of Holies. And if the type of this blood had such great power in the temple of the Hebrews, and in the midst of Egypt, when smeared on the doorposts, much more the reality! The type sanctified the golden altar. Without it [the blood of the sacrifices], the high priest dared not enter into the secret place. It even consecrated priests. It cleansed sins [in the Old Testament].
But if the blood [of the sacrifices] was but a type and had such power, if death so shuddered at the shadow, tell me how would it not have dreaded the very reality?
The blood [of Christ] is the salvation of our souls. By it, the soul is washed, is beautiful, and is inflamed! This blood causes our understanding to be more bright than fire and our soul more beaming than gold. This blood was poured forth and opened heaven.
—John Chrysostom , Homilies On the Gospel of St. John, Homily XLVI.3
St. Chrysostom refers to Hebrews 2. From Hebrews 2:
9 But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honor; that he by the grace of God should taste death for every man.
10 For it befitted him, for whom are all things, and by whom are all things, in bringing many sons unto glory, to make the captain of their salvation perfect through sufferings.
11 For both he that sanctifies and they who are sanctified are all of one: for which cause he is not ashamed to call them brethren,
12 Saying, I will declare your name unto my brethren, in the midst of the congregation will I sing praise unto you.
13 And again, I will put my trust in him. And again, Behold I and the children whom God has given me.
14 Since then the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil;
15 And deliver them who through fear of death were all their lifetime subject to bondage.
We become brothers of Christ when we partake of the same flesh and blood He Himself was, sharing in His death and resurrection. Thus are we justified through his blood, who by the grace of God was offered to the world on behalf of the many. God's gracefulness is him willingly sacrificing His own Son, and justification comes from becoming part of that Son, through his flesh and blood.
Hence why Jesus talks about this extensively in the Book of John. If you ever see "blood" and "Christ" mentioned by a writer before the 10th century, they were talking about the Eucharist. This goes doubly for St. Paul.