[Jesus Christ], who gave himself for us to redeem us from all lawlessness. (ESV)
[Jesus Christ], who gave himself for our sins (Gal 1:4 NIV)
Take a few minutes and reread that small phrase in each of these verses, “who gave himself for us” (Titus 2:14), and “who gave himself for our sins” (Gal 1:4). Dwell on those words. If you didn’t know the Gospels, what would these words mean to you? It sounds like a hostage exchange. He gave Himself and in exchange for Himself, someone got us and our sins. Looking at it as an exchange, who received Jesus? There are some that say that Satan got Jesus because we were captive to him because of our sins (2 Tim 2:26). Satan exchanged his rights of bondage over us for the death of Jesus. This fits with the concept of redemption where a price is paid to redeem a slave from captivity. This concept of redemption is ingrained in the Law of Moses where the Lord redeemed Israel from Egypt at the cost of the firstborn (Ex 6:6), also the redemption of slaves was proscribed in the Law (Lev 25:47-49). However, it grates on the nerves of theologians who view this as Satan having some power over God to demand or accept the ransom.
However, the Bible also explains that the sacrifice was given to God, “Christ also loved you and gave Himself up for us, an offering and a sacrifice to God as a fragrant aroma” (Eph 5:2 NASU). The sacrificial sin offerings in the Law of Moses prefigure Christ’s death for our sins. This is clearly explained in the book of Hebrews. Chapters 9 and 10 retain the concept that Jesus’ death brought about our redemption (Heb 9:12) but it clearly explains that the sacrifice was in no way associated with a payment to Satan. Rather, Jesus offered the sacrifice of his blood to God (Heb 9:14).
But now the righteousness of God apart from the law is revealed, being witnessed by the Law and the Prophets, even the righteousness of God, through faith in Jesus Christ, to all and on all who believe. For there is no difference; for all have sinned and fall short of the glory of God, being justified freely by His grace through the redemption that is in Christ Jesus, whom God set forth as a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed, to demonstrate at the present time His righteousness, that He might be just and the justifier of the one who has faith in Jesus. (Rom 3:21-26 NKJV)
Redemption is expounded in Romans 3:21-26 without one word regarding Satan. It is all about God’s righteousness and His justifying us. In Titus, Paul says we were redeemed from lawlessness. Whether we were aware of the law or not, we were all sinners. The only way out of the prison of sin was for someone to redeem us. It had to be someone who was right with the law otherwise, he would be in prison with us. God’s righteousness had to be satisfied and Romans 3:25 says that the blood of Jesus Christ was the propitiation, the appeasement to God for breaking His totally righteous law. Note also that set the blood of Jesus as the propitiation, not Satan. So the payment wasn’t to Satan for release but it was the payment to God as required by the Law. As Romans 3:26 says, this demonstrated God’s righteousness because He is the one who “might be just and the justifier of the one who has faith in Jesus.” This brings all the glory back to God and Jesus completely eliminating any concept that Satan was anything other than a jailer who had to release us from his powers not because he got anything from it, but because the price was paid to God’s justice system.
Therefore they said to Him, "What shall we do, so that we may work the works of God?" 29 Jesus answered and said to them, "This is the work of God, that you believe in Him whom He has sent." (John 6:28-29 NASU)
So the door to the jail is open. The blood of Jesus paid the price for our sins. What is left for us to do? Simply believe and have faith in Jesus (Rom 3:22). Without faith in Jesus, that door looks like it is still closed. Is walking through the door into Jesus’ arms works that we have to do to be saved? Only if it is in belief. We must remember that it is by God’s grace that we are justified (Rom 3:24) and His grace is a gift that enables us to have faith (Eph 2:8). In this way, our salvation is then completely dependent upon God and nothing of ourselves.
 The Greek word for “lawlessness” is anomia according to Thayer's Greek Lexicon s.v. “NT:458,” (Biblesoft, 2006), its meaning is:
1. properly, the condition of one without law -- either because ignorant of it, or because violating it
2. contempt and violation of law, iniquity, wickedness.