To whom did Christ pay the ransom for our sins?

The church does not say it. There were theologians, some very early, who taught what is called the ransom theory, that God paid a ransom to the devil, but that theory of the atonement was shut down not long after it was popularized. The reason they brought in the devil is that a ransom is normally paid to someone, and the only one they could think of was the devil, because the devil appeared to have won in the garden of Eden and to hold the reins. But is it correct to say the atonement is God paying a ransom to the devil? No. By the time of St. Anselm you have a satisfaction understanding, that Christ gives a vicarious death to the Father, and the devil really has nothing to do with it; he is just a bit player. And in the end the atonement is not even a legal matter, not a price paid, because the whole thing is voluntary. Christ could have said, I am not going to become a man and die on a cross, and He could have done that freely; no law, no person, nothing required Him to do it. So it takes it out of the legal framework entirely, and out of the ransom framework. What Christ actually does on the cross is restore the honor of God that Adam besmirched, and appease the wrath of God, on a personal basis, because God is a personal being with personality, not a rock you can insult all day. That is why the ransom theory does not fit; there is no payment made to the devil.