The teaching of the Orthodox faith regarding atonement of Christ is that Christ was ransomed by Satan. The so called “payment” that was given was not to God but to Satan. This was no compromise on God’s part. He was not giving power and authority to Satan. Satan had no idea what he was getting. God did not reveal to Satan that Jesus was God until he entered Hades. He had no idea that after the death of Jesus, Jesus would enter into Hades and destroy its bond, taking his people with him.
St. Chrysostom ca. 347-407
It took a body and, face to face, met God! It took earth and encountered heaven! It took what it saw but crumbled before what it had not seen! “O death, where is thy sting? O hades, where is thy victory?” (Paschal Homily)
St. Gregory of Nyssa ca. 335-394
”As the ruler of darkness could not approach the presence of the Light unimpeded, had he not seen in Him something of flesh, then, as soon as he saw the God-bearing flesh and saw the miracle performed through it by the Deity, he hoped that… if he came to take hold of the flesh through death, then he would take hold of all the power contained in it. Therefore, having swallowed the bait of the flesh, he was pierced by the hook of the Deity and thus the dragon was transfixed by the hook.” (The Great Catechetical Oration 22-24)
St. Augustine of Hippo ca. 354-430
The devil was conquered by his own trophy of victory. The devil jumped for joy, when he seduced the first man and cast him down to death. By seducing the first man, he slew him; by slaying the last man, he lost the first from his snare. The victory of our Lord Jesus Christ came when he rose, and ascended into heaven; then was fulfilled what you have heard when the Apocalypse was being read, ‘The Lion of the tribe of Judah has won the day’ [Rev. 5:5]. . . . The devil jumped for joy when Christ died; and by the very death of Christ the devil was overcome: he took, as it were, the bait in the mousetrap. He rejoiced at the death, thinking himself death’s commander. But that which caused his joy dangled the bait before him. The Lord’s cross was the devil’s mousetrap: the bait which caught him was the death of the Lord. (St. Augustine, Sermons, 261; trans. by Henry Bettenson, ed., The Later Christian Fathers: A Selection From the Writings of the Fathers from St. Cyril of Jerusalem to St. Leo the Great (Oxford: Oxford University Press, 1970, 1977), p. 222.)
Pope St. Leo the Great ca. 400-461
And in order that He might set the human race free from the bonds of deadly transgression, He hid the power of His majesty from the raging devil, and opposed him with our frail and humble nature. For if the cruel and proud foe could have known the counsel of God’s mercy, he would have aimed at soothing the Jews’ minds into gentleness rather than at firing them with unrighteous hatred, lest he should lose the thraldom of all his captives in assailing the liberty of One Who owed him nought. Thus he was foiled by his malice: he inflicted a punishment on the Son of God, which was turned to the healing of all the sons of men. He shed righteous Blood, which became the ransom and the drink for the world’s atonement. The Lord undertook that which He chose according to the purpose of His own will. He permitted madmen to lay their wicked hands upon Him: hands which, in ministering to their own doom, were of service to the Redeemer’s work. And yet so great was His loving compassion for even His murderers, that He prayed to the Father on the cross, and begged not for His own vengeance but for their forgiveness, saying, Father, forgive them, for they know not what they do Luke 23:34 . And such was the power of that prayer, that the hearts of many of those who had said, His blood be on us and on our sons Matthew 27:25, were turned to penitence by the Apostle Peter’s preaching, and on one day there were baptized about 3,000 Jews: and they all were of one heart and of one soul Acts 4:32, being ready now to die for Him, Whose crucifixion they had demanded. (Sermon 62)
The Venerable Bede ca. 673-735
A certain person has interpreted this passage as follows, that the saints resting in the lower world longed for that consolation about which the Lord say to His Apostles, Many prophets and righteous persons have longed to see what you see and did not see it and to hear what you hear and did not hear it (Mt. 13:17), about which the psalmist also says, My eyes have failed at your message, saying, ‘When will you comfort me,” (Ps. 119 (118):82) and that this consolation and encouragement was preached by the Lord when He went down into the lower world even to those who were in prison and were once in the days of Noah unbelievers. He may have aid this. But the Catholic faith holds that when the Lord went down into the lower world and brought his own from there, it was the faithful alone and not unbelievers whom He took with Him to the heavenly kingdom… (Commentary on 1st Peter)