The title of our sermon this morning is the Covenant of Grace. Our primary text, it'll be one of many. Hebrews chapter 8 verses 1 through 13. Well, welcome back this morning to our weekly series on the essentials. We are continuing now in the essentials, our three-part introduction to Covenant theology. This week, we'll be considering the Covenant of Grace. This is a loaded subject. We have a lot of ground to cover, so fasten your seatbelt. As we've said before, Covenant theology is basically a study of the divine Covenants. God the Creator, high and lifted up in majesty, magnificent, right? High, lifted up. He has stooped in matchless grace to draw near to and to relate to man created in his image. And he relates to man through the terms of various Covenants that God himself institutes. Rather than different groups of people with different promises, different destinies, as you would find in dispensationalism, a biblical study of the divine Covenants reveals one spectacular revealed purpose, redemptive purpose, one eternal people of God, one blessed hope, one eternal destiny disclosed over one progressively unfolding revelation, culminating in the person and work of the one mediator between God and man, the man, Jesus Christ. As Nehemiah Cox said, the divine Covenants themselves are concerned with one, the benefits that God will bestow on man, the communion that man will have with God, and three, the means, the ways and means by which that will be enjoyed by man. As we began our study in the Essentials on Covenant Theology, we started with the Covenant of Redemption. The Covenant of Redemption is that eternal pact whereby the distinct persons of the Godhead entered into a decreed arrangement where God the Father granted a people to God the Son and where the Son would be sent by the Father to accomplish their redemption and where the Spirit would be sent by both Father and Son to apply the benefits of that redemption to the elect. All of that to the praise of the glory of His grace, right? That's the covenant or the eternal pact, pactum salutis, the redemption, the Covenant of Redemption. Next we discuss the Covenant of Works. The Covenant of Works is that relational arrangement initiated and established by God with Adam where God formally or materially ratifies the terms of living as His created image-bearer in His creation. God sets forth the terms of life, so to speak, with Adam. Life for obedience, death for disobedience. The Covenant of Works says, do this and live. That's the principle of the Covenant of Works. When you think about it, God, our Creator, is absolutely and entirely worthy of perfect obedience in every respect, from the heart in all things. God says, you must be holy as I am holy. Perfect as your Father in heaven is perfect.  God has said that it is so. Cursed is everyone who does not continue in all things which are written in the book of the law to do them. There is only one way to heaven. And that one way to heaven is that you are perfectly righteous. You must be absolutely righteous. Nothing will enter heaven that defiles. A Sabbath breaker will not enter. An adulterer will not enter.   Fornicators, drunkards, thieves, rebels, cowards will not enter. There's only one person on the face of the planet who's ever been righteous. One person, only one person who ever perfectly obeyed the demands of God's law, and that person is the Lord Jesus Christ, the righteous one. And so it is by His righteousness alone that we have any hope of heaven. Because we ourselves are not righteous, are we? We are deplorably unrighteous. It's through hope in His righteousness that we have any hope of heaven. God in grace and mercy has made provision for us to hope in Him for heaven. God condescended. He's stooped so that we could have a hope of heaven in Him. And this is what we call the covenant of grace. In the covenant of grace we find the gospel. Now I want us to consider this morning the covenant of grace under four headings. Four headings. Write these down. We'll work through them. The penalty, the promise, the shadow, and the substance. The penalty, the promise, the shadow, and the substance. And thinking about those four headings, turn with me to Genesis chapter 3. Genesis chapter 3. Let's take a look together at the covenant of grace. In Genesis, very beginning of our Bibles, the Lord God formed man of the dust of the ground. God breathed into his nostrils the very breath of life, and man became a living being, a living soul, the Bible says. Adam was created upright, created perfect, original righteousness was in due to Adam. He was in the very image of God. Created by God to live forever. His soul, his being in perfect harmony with the law of God, the law of God was written upon his heart, and Adam delighted in obeying it. He was delighted to be subject to that law. So the Lord God then took man, He put him in the Garden of Eden to tend it and to keep it, and it pleased God then to add to that law that was natural to Adam written upon his heart. It pleased God to add an eternal and immutable or a positive precept. We see that in Genesis chapter 2, verse 16, where God adds this, of every tree of the garden you may freely eat, but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die, literally in dying you shall die. So adding to the eternal and immutable law, God adds this positive precept. Adam now is under a covenant of works.  If Adam would have obeyed the covenant of works, would have obeyed that law, the condition of the covenant, Adam would have lived, and through his obedience, Adam would have attained to eternal life under the covenant. That's obviously not what happened, is it? Look with me at Genesis chapter 3 in verse 6. So when the woman saw that the tree was good for food, that it was pleasant to the eyes and a tree desirable to make one wise, she took of its fruit and she ate. She also gave to her husband with her and he ate. Covenant of works, Adam and Eve willfully violate the covenant. The breach of God's positive precept is a breach of God's eternal and immutable law. Do you see? Adam at once is at enmity with God, fallen now under the dominion of sin. The promise of life is forfeit. Their hope is lost, communion with God is now shattered. Once righteous himself, Adam is now polluted and corrupted and stained with a filth of his own sin. God's image that Adam bears, God's image now defaced. Adam comes under the guilt then of breaking God's law. He comes under the guilt of breaking God's covenant. Sin enters the world and death through sin and the penalty of the covenant comes down now upon our first father, our representative in the covenant. In Adam, all his descendants would be born under the penalty of a broken covenant. All his descendants then would be unable to help themselves, unable to stand before God by their works. They are by nature now children of wrath, destined for physical death, which is a type or merely a foreshadowing of the ultimate what the Bible calls eternal death or the second death and the eternal miseries of hell. All of this to the praise of God's justice. God is just and right for this judgment. All of that until, until God held out hope through a promise. God holds out hope through a promise. Look at chapter 3, verse 14. In the very judgment pronounced against the serpent, God to the eternal praise of his grace attached a promise of salvation for man. He condescended, he stooped. The seed of the woman would be manifested that he might destroy the works of the devil. Look at chapter 3, verse 14. So the Lord God said to the serpent, because you've done this, you are cursed more than all cattle, more than every beast of the field, on your belly you shall go.  I will put enmity between you and the woman and between your seed and her seed. That presupposes that Eve is going to have a child. Going to have a son is a glorious promise when Eve could have been killed, couldn't she? Her life taken having violated God's covenant. Between your seed and her seed, he shall bruise, the word means to crush or to strike.  Right there within the curse given to the serpent is the first revelation of the gospel couched in terms of a promise. You see the first revelation of the gospel. Notice here it's not a covenant. It's not a covenant. There's no covenant language being used. We don't see parties and contracts and commitments and penalties, sanctions or rewards. There's no covenantal language being used. The law was given as a covenant. It was given as a covenant of works, do this and live. It's not the case with this. This is a promise. Here it's a promise. What is revealed in the promise? What's revealed in the promise is grace. The grace of God. God is gracious in responding this way to Adam and Eve when they've broken the covenant. He's patient with them, long suffering with them. He's kind and compassionate toward them. Then he gives the promise in verse 14 that the seed of the woman shall deliver a death blow to the enemy of God's people, Satan and the seed of Satan. Eve will have a living descendant who will bring victory out of tragedy. Nehemiah Cox says it's a discovery of grace, a discovery of grace. God in Genesis chapter 3, even in the midst of the curse, is opening a door of hope in what seemed like a hopeless circumstance, a hopeless situation. Adam and Eve break the covenant. The terms of the covenant, the penalty of the covenant is death. Adam and Eve will surely die. That's it. That's the end of it all, right? Wrap it up. Now here there is a revelation, an open door, a discovery of grace. Nehemiah Cox said God is opening a door of hope, a new foundation for man's acceptance with God. Their hope would then be built on this promise of God in Genesis chapter 3, verse 15. Adam and Eve, think about it in the garden, having understood what they've done, now facing God for their sin, hearing this glimpse of grace, this glimpse of hope. Adam and Eve would have jumped for joy, right? Praise God, praise God. It's called the proto-Uangelion, or the first revelation, the first glimpse of the gospel, the good news of salvation in Jesus Christ. It's the first indication of a promised covenant of grace. First indication. Now notice first with me about this. There is only this promise. Now this promise is going to be developed in the Bible from Genesis to Revelation. It's going to be developed and revealed, and there is only this promise. There is no other option. God didn't give three ways He was going to administer grace or aid to His creation. He didn't give three other options for how all this was going to work out. There's one option. It's the grace of God that Adam and Eve weren't struck eternally dead the moment they broke the covenant. It's the grace of God that that's the case. They saw that grace. Adam and Eve could have continued having seen that grace. They could have continued in their rebellion. They could have said, you know what? We enjoy sin. We're just going to keep going like we are. Or they could turn from their rebellion, place all their hope, all their faith, all their desire in the coming seed of the woman who would deliver them from destruction. They have two options. One or the other. There are no other options. They couldn't go back to God under the terms of the covenant of works. It was a broken covenant. All they could do now was trust God for His promise of grace. That's all that they could do. God made a promise. They could either continue in their sin or they could believe in God for their promise. For His promise, right? Believe in God on His Word. The same is true of every single person in this room. God has made a way. It's one way. There is no other way. He made that way through faith alone. You cannot go to God with your works. That covenant has been broken. You don't have good works. You cannot go before God with your sin. Guilty, condemned under the law. Condemned under a broken covenant. You cannot simply continue in your sin and rebellion.  You have one option. You can turn from sin, place all your hope, all your faith, all your trust in Christ for God's promised grace. It's the same option, do you see? The same option that Adam and Eve were faced with in the garden is the same option that you and I, every lost person on this planet, is faced with today. You have two options. You can either do it by works or you can simply believe on God for His Word. Do you see? Trusting in Him for what He has promised. Notice second, it's a promise of what God is going to do and not what you are going to do. It's a promise of what God is going to do. It is no longer by works. That ship is sailed, do you see? No longer by your works. It's entirely by the grace of God. Romans chapter 11 verse 6, Paul says, And if by grace, then it is no longer of works, otherwise grace is no longer grace. Do you see how the two are mutually exclusive? They don't mix. Apples and oranges, worse than that. Far separate than that. And that's why you and I can completely trust in it. Do you think for a moment that if it had anything to do with you that you could trust in it? No. Adam failed, failed miserably. You and I would surely fail and fail miserably. Not God. Not God. First, only one option. Second, it's a promise of what God will do. Listen, the promise that God gives here in Genesis chapter 3 introduces now a distinction. Do you see? It introduces a distinction. Approaching God based upon your obedience to God's law or approaching God through faith for his promises, approaching God in faith. You can go to God with your own works. Lord, look, see? This is what I've done. Or you can go to God believing in the Lord Jesus Christ for God's promises. One of two options. All that by virtue of the covenant of grace. You can go to God through faith in Christ by virtue of the covenant of grace. Those two options mutually exclusive, there is no third option. Paul, the example that Paul uses to illustrate this is the example of Abraham. Look quickly with me at Romans chapter 4. Romans chapter 4, we're going to be turning in our Bibles today, so Bible drawer, you're going to have to move quickly. Romans chapter 4, Paul uses the example of Abraham to describe this for us. Romans chapter 4, look beginning at verse 1. What then shall we say that Abraham our Father has found according to the flesh? For if Abraham was justified by works, he has something to boast about. But not before God. For what does the Scripture say? Abraham believed God, and it was accounted to him for righteousness. Now to him who works, the wages are not counted as grace, but as debt. In other words, if you believe that you're going to make it to heaven by your works, it's as if God owes you. Look at what I've done, God. You owe me heaven. It's not the way it works, right? We don't owe, or God doesn't owe us anything. Where does the righteousness come from, we should ask? Where does the righteousness come from that is accounted to Abraham? Notice with me third, the promise is about the Lord Jesus Christ. The righteousness doesn't come from Abraham. He has none of his own. The righteousness doesn't come from Adam, doesn't come from your eye. We have no righteousness of our own. The righteousness comes from the Lord Jesus Christ. The promise that begins to be revealed in Genesis chapter 3 verse 15 is a promise about the righteousness of Jesus Christ. It's the righteousness of Jesus Christ that is accounted or given by faith, given by grace through faith. As the promise that was introduced in Genesis chapter 3 is further revealed across the history of redemption, across the pages of Scripture, we find that the seed of the woman, the promised seed, is none other than God the Son, the second person of the Trinity, the Lord Jesus Christ. Paul would later refer to him in Galatians chapter 3 verse 16 as the seed of Abraham who is Christ. Christ would succeed where Adam failed. Christ would fulfill the law perfectly where Adam failed to fulfill the law and broke God's covenant. He, the Lord Jesus Christ, would be obedient to the point of death, even the death of the cross. In that, he would earn or merit the righteousness that you and I need to stand before God. He would earn or merit that righteousness through his own obedience. In grace, he bears the penalty of our sin upon himself. And then in grace, he gives us his righteousness because we have none ourselves. And he does this through faith, believing in him for the promise, believing its faith, all this entirely by grace, free, freely given by God through faith, all free, no fine print. We don't have to consult a lawyer. There's nothing else in there. Folks, it's by faith alone, right? We should praise God for that, amen. Notice with me fourth. The promise reveals the covenant of grace. All this is the covenant of grace revealed through promise, the promise in Genesis chapter 3 verse 15. Here's how our confession of faith defines it. In chapter 7, article 3 of God's covenant, this is what the confession says. This covenant, the covenant of grace, is revealed in the gospel. First of all, to Adam in the promise of salvation by the seed of the woman. That's Genesis chapter 3 verse 15. And then afterwards, this covenant of grace is revealed by farther steps, the confession says, until the full discovery thereof was completed in the New Testament. In other words, the covenant of grace revealed here is the promise of Genesis chapter 3. The covenant of grace is revealed in the promise. Afterward, the covenant of grace would be gradually more and more revealed by farther steps, but it would only be fully revealed and finally completed in the person and work of the Lord Jesus Christ in the New Testament. Where it would be formally or materially established in the shed blood of the Lord Jesus Christ. The confession goes on to say that it is founded in that eternal transaction that was between the Father and the Son about the redemption of the elect. That's the covenant of redemption. And it is alone by the grace of this covenant that all the posterity of fallen Adam that were ever saved did obtain life and blessed immortality, man being now utterly incapable of acceptance with God upon those terms on which Adam stood in his state of innocence. I want to draw your attention to a particular phrase in that statement where the confession says that it is alone by the grace of this covenant that all the posterity, all the descendants of fallen Adam that ever were saved did obtain life and blessed immortality. After the fall, when God saved anyone, including when God saved Adam and Eve, after the fall when God saved anyone, he saved them by virtue of the efficacy or the effectiveness of this covenant of grace that was formally established by Jesus Christ in his shed blood on Calvary. He saved them by virtue of this covenant. Grace as though everyone in the Old Testament, from Adam through the Lord Jesus Christ, anyone in the Old Testament who was genuinely converted, genuinely saved, were saved by virtue of the covenant of grace looking forward to the promise, looking forward to the coming Savior. Now we in this age look back upon the Savior, look back upon the grace of God in Christ, and we're saved by virtue of the same covenant of grace looking back in faith to the Lord Jesus Christ. Does that make sense? There are now two threads, two principles that run parallel now through the entirety of the Bible. One is the principle of work or the principle of law, do this and live. We saw that in the covenant of works with Adam, didn't we? What the other is the promise of grace, the principle of grace, the promise of grace, eternal life given freely by faith in Christ who is the mediator of a new and better covenant. So you are then either, or two options again, you are either under law as a covenant of works and doomed to hell for your sin, or you are under grace and justified, declared righteous through faith in Jesus Christ. Principle of law and the principle of grace and both of these principles from the promise in Genesis 3 forward, both of these principles are pressed forward into redemptive history. We see them throughout the Bible. As we consider that these two principles, principle of law, principle of grace pressed forward, it's good for us to consider how they are seen as we move forward through revelation and why they are pressed forward in the way that they are, right? So let's first consider together how, it's a good place, a good way to see this is in God's dealing with Abraham. Turn with me to Genesis chapter 12, a few pages to the right, Genesis chapter 12. And we see both of these principles now operative in the way that God interacts or interrelates with Abram. Look at Genesis chapter 12 verse 1. Now the Lord had said to Abram, Abram, get out of your country, from your family, from your father's house to a land that I will show you. Listen to what God says here, how he phrases this. I will, God says, right? I will make you a great nation.   And in you all the families of the earth shall be blessed. So Abram departed as the Lord had spoken to him, Lot went with him. Now what's given to Abraham in Genesis chapter 12 is a promise, isn't it? That looks like a promise. It's not a covenantal curse here for disobedience. There's no covenantal curse. There's no covenantal language. Simply a promise. Simply a promise. What God will do. Amen? And what God will do in grace. It's incredibly gracious. Flip the page and look at Genesis chapter 15. Let's see where this promise leads. Genesis chapter 15. Look there, beginning at verse 1. Now after these things, the word of the Lord came to Abram in a vision saying, Do not be afraid Abram, I am your shield, your exceedingly great reward. Amen. But Abram said, Lord God, what will you give me seeing I go childless in the air of my house as LEAs are of Damascus? Abram said, look, you've given me no offspring. Indeed, one born in my house is my heir. And behold, the word of the Lord came to him saying, This one shall not be your heir. But one who will come from your own body shall be your heir. Then he brought Abram outside and said to him, Look now toward heaven. Count the stars if you're able to number them. And he said to him, So shall your descendants be. And Abram believed in the Lord and he accounted it to him for righteousness. Sounds like promise again, doesn't it? Promise. There's no works involved here. There's no covenantal language of works or a principle of works being couched here. The promise, this promise pressed forward by grace, by the grace of God and through faith. Abram simply had to believe God to obtain the promise. Verse 6, he believed in the Lord and he accounted his faith for righteousness. Sounds like Romans 4, doesn't it? We just read. God gave this to Abram by promise. Abram believed God for his promise. And God on the basis of Abram's faith in the promised heir who is ultimately Christ, God accounted that faith to him, the righteousness of Christ. And Abram was a saved man. Abram was saved by grace through faith, do you see? On what basis? On what basis? On the basis of the coming Christ. On the basis of the covenant of grace. By virtue of the covenant of grace. I would say, Galatians 3, verse 8, the Scripture foreseeing that God would justify the Gentiles by faith preached the Gospel to Abram beforehand saying, in you all the nations shall be blessed. Meaning, those who are of the faith of Abram are blessed or saved with believing Abram. Those that have the faith of Abram are saved. The spiritual seed. Many look back at the Old Testament and they wonder, how are people in the Old Testament saved? They're saved in the same way that you and I are by virtue of the same covenant, the covenant of grace. And we're not speaking only of spiritual blessings here, are we? When we talk about that, we're speaking of physical blessings. We're talking about spiritual blessings. Not just temporal physical blessings, but eternal spiritual blessings. These blessings aren't conditional. We're not conditioned on Abram's works or our works. They're unconditional and all that is affirmed in the New Testament. But I want you to see that there's another principle at work in God's dealings with Abram. We certainly see the presence and furtherance of the original promise that was introduced to us in Genesis chapter 3, but then we also see a reiteration, if you will, of the principle of works. Turn a page to the right and look at Genesis chapter 17. Genesis chapter 17. With Abraham, the promise is pressed forward. The principle of grace is pressed forward. Now we see the other principle, the principle of works. And that principle also pressed forward. Genesis chapter 17, verse 1. When Abram was 99 years old, the Lord appeared to Abram and said to him, I am Almighty God. Walk before me and be blameless. Oh, wait a minute. That's different, isn't it? Verse 2. And I will make my covenant between me and you and will multiply you exceedingly. Now the Lord introduces a covenant stipulation. In addition to the promises made before, new covenant language now is being used. Drop down to verse 9. And God said to Abraham, as for you, you shall keep my covenant, something for Abraham to do.  Abraham and his descendants after him must keep the conditions of this covenant. In other words, this becomes, doesn't it, a conditional covenant. Now we're talking about two different things. We saw the promise pressed forward, but now also we see a principle of works being pressed forward at the same time. God is now establishing with Abraham a conditional covenant. Drop down to verse 10. This is my covenant, which you shall keep between me and you and your descendants after you. Every male child among you shall be circumcised. And you shall be circumcised in the flesh of your foreskins and it shall be a sign of the covenant between me and you. Abraham has to do something. His descendants have to keep the covenant. Verse 14.  He's broken my covenant. Now we have a penal sanction, don't we? A penalty for breaking the covenant. This is not speaking of a promise given to Abraham and a spiritual believing seed. This is speaking of a covenant made with Abraham and his physical seed. Do you see the difference? This is conditional rather than unconditional. Abraham and his physical descendants must work to keep the covenant. If they do not, there's a penalty for disobedience. They will be cut off from the people of God. Verse 14. Flip the page. Look at Genesis chapter 18. Genesis chapter 18. And drop down there to verse 17. The Lord is about to destroy Sodom and Gomorrah. And the Lord said in verse 17. Shall I hide from Abraham what I am doing? Since Abraham shall surely become a great and mighty nation and all the nations of the earth shall be blessed in him. For I have known him, listen, in order that he may command his children and his household after him, that they keep the way of the Lord to do righteousness and justice so that the Lord may bring to Abraham what he has spoken to him. In other words, the promises of this covenant are going to come to Abraham through his and his descendants' obedience to the terms of the covenant. Do you see? This is different, isn't it, than the promise? We see two threads pressed forward simultaneously. Now two threads demonstrated, if you are manifested, if you will, in God's dealings with Abraham. This particular thread is taken in the form of a covenant of works. Not the covenant of works, but a covenant of works, isn't it? Carries forward the principle of works. Now we know what happens. Abraham is, in fact, given many physical descendants. There were as many as 2 million Jews that came out of Egypt. Those physical descendants become the nation of Israel, a physical nation on the earth. They were brought out of Egypt, to Mount Sinai in Exodus chapter 20. God there at Sinai further expands upon this physical, temporal covenant with Abraham by entering there into a covenant with Moses, the children of Israel, 430 years later after Abraham. And it's a covenant where lawkeeping is required, isn't it? The Mosaic covenant. It's a conditional covenant with a physical people for temporal blessings that include a physical land. It's a covenant where there are blessings for obedience and cursings for disobedience. Remember the two mountains. They put half the children of Israel on Mount Ebel, half of the children of Israel on Mount Garazim, and they're shouting back and forth across the valley. Blessings for obedience. Cursings for disobedience, right? In fact, the entire emancipation generation, all of those that came out of Egypt, died in the wilderness for a lack of faith. Hebrews chapter 4 says for unbelief, they simply didn't believe God. They didn't believe God the way that Abraham did for the promise. And so failing to believe God for his promises, for his word, they died in unbelief, Hebrews says. Doesn't sound like grace, does it? Does that sound like grace to you? No. So Abraham, and then in Moses, we see the two threads, the two parallel threads continuing through the Bible. One is the principle of works, do this and live. One is the promise of grace where God remembers and he reminds us of his promise in the garden. And we discussed how these two threads are pressed forward. You can see that in the Covenants. But why are they pressed forward in this way? Why? Let me give you two reasons for why. One is to show us our need. They show us our need. The principle of works shows us our need for the covenant of grace. And two, to point us to Christ. To point us to Christ. To show us our need and to point us to Christ. Turn with me to Galatians chapter 3. Galatians chapter 3. Look there in Galatians chapter 3. Verse 19. Galatians chapter 3, verse 19. This principle of works is embodied, materially you could say, in the Old Covenant. The giving of the law under Moses began being revealed in Abraham, but then given formally to Moses in the wilderness at Sinai. This principle of works seen in the giving of the law. So Paul asks the question. Galatians chapter 3, verse 19. What purpose then does the law serve? Does the giving of this principle of works? Does this pressing forward of a covenant of works? What purpose then does the law serve? Paul says it was added because of transgressions, because of sin, till the seed should come to whom the promise was made. Now by the law here, Paul is referring to that given under Moses, and Paul says that it was added. What was it added to? It was added to that physical covenant that God began with Abraham 430 years earlier. It was added to the Abrahamic Covenant. And it was added, Paul says, because of transgression. In other words, it was added in the sense that it reveals or exposes sin or increases the sinfulness of sin. That's what the term means. Added because of transgression. In other words, making sin to be to us exceedingly sinful. That's what it means, right? Romans chapter 5, 20. Moreover, the law entered so that the offense might abound. When the law came, the offense or the exceeding sinfulness of sin abounded under the law. Romans chapter 3, verse 19, gives us the purpose for that so that all the world may become guilty before God to show us that by the deeds of the law no flesh will be justified in His sight. For by the law is the what? Knowledge of sin. By the law comes the knowledge of sin. In 2 Corinthians chapter 3, verse 9, Paul refers to the old covenant law, the Mosaic Covenant, as a ministry of condemnation. A ministry of condemnation. The ministry of condemnation was to help us see the condemnation that was deserved and to see the salvation that was coming in Christ. That ministry of condemnation pointed to us our need, showed us our need, and should drive us to the Lord Jesus Christ in faith for salvation. The law was condemning sin all along until the full wrath of God would be poured out against sin and the person of his own son. Paul asked the question then again in verse 21, look at verse 21, is the law then against the promises of God? Certainly not. Absolutely not. For if there had been a law which could have given life, truly righteousness would have been by the law. The law isn't against the promises. It's on the basis of the law that we understand what Christ fulfilled for us. The law demonstrates the righteousness of the Lord Jesus Christ, the righteousness that we need, the righteousness that is credited to us by faith when we believe in Him. Also, that law is the underlying structure, if you will, or the underlying foundation on which redemption and the efficacy of our redemption is built in the sense that it's the fulfillment of that law that then becomes the righteousness that is imputed to us whereby we can stand before God declared righteous. The law isn't against the promises of God. Verse 22, but the Scripture through the law you could say has confined all under sin that the promise, what's that promise referring to? Way back in Genesis chapter 3. It began to be revealed. Genesis chapter 3 verse 15, progressively revealed by farther steps through the Bible so that that promise by faith in Jesus Christ might be given to those who work really hard. No. To those who believe. To those who believe. Verse 23, but before faith came, we were kept under guard by the law, kept for the faith which would afterward be revealed. Therefore the law was our tutor, our school master. The word speaks of someone who is responsible not just for instruction but for discipline. In other words, this was a school teacher who took supervisory role over you, so to speak, and had a ruler in her hand that she would not hesitate to strike your knuckles with.  This is speaking of disciplinary instruction. The law was our disciplinarian, our disciplinary instructor you could say to bring us to the Lord Jesus Christ. You think about that, right? The pain of our sin. The misery of our sin. The guilt of our sin. All of that. What is the purpose of that? To drive us to a savior. If you're here today, you've never turned from your sin to trust Christ. Listen, your sin is miserable. You are sinning.  Why are you so miserable? Your sin. You can't blame someone else and everyone else and the world and everything that's in it. You're responsible for that. It's your sin. Your sin is the reason you're so miserable. Turn from sin. It's a harsh school master. It's a harsh school master and that tutor is driving you to the Lord Jesus Christ so that you might be justified by faith. Verse 25, But after faith has come, we're no longer under a tutor. We're under grace, right? No longer under the law as a covenant of works. We're under grace. One way in which the Old Covenant or that continuing principle of a works covenant, one shows us our need and two points us to Christ is by serving as a shadow of those things that are to come. Why was an earthly, physical, temporal covenant at once to be established with Abraham further expanded under Moses? Why was that? Because it's a type of spiritual realities. It's a shadow of a heavenly reality that is to come. These are just types and shadows. They are mere illustrations of the heavenly realities that they represent. It serves as a shadow to point to a greater reality, a greater substance. The Old Covenant legal system becomes a visible representation or a shadow of what the seed of Abraham, what the seed of the woman who is the Lord Jesus Christ would accomplish for us. If you think about all that that system represents, all that it encompasses, right? If you think about the person in work of the Lord Jesus Christ, we need the Old Testament. We can't understand the New Testament without the Old Testament. We can't understand the person in work of the Lord Jesus Christ apart from the Old Covenant, apart from the Old Testament. We need the Old Testament. How would we understand the sacrifice of the Lord Jesus Christ apart from all of those sacrifices for sin in the Old Testament? All of that shed blood, all of that ceremony, all of that solemn necessity, how could we understand fully His sacrifice for us? How could we understand penile substitution, substitutionary sacrifice? How could we understand that apart from the sacrificial system? How would we understand His righteousness apart from the law and all that the law demands? How could we understand His righteousness and the righteousness that we need? How could we understand the offices of Christ as prophet, priest, and king without the history of the prophets, the priests, and the kings? How could we understand the Old Covenant was a type or a shadow of the New Covenant in order to show us what the Lord Jesus Christ would accomplish so that we would put our faith and trust in Him for what He has done? And we would see it as glorious, as magnificent, as wondrous. All meant to point to Christ. You know, when the Lord Jesus Christ came to the earth in His incarnation, He came as quote-unquote a normal person. Who is this? Is this not the carpenter? Joseph's son? But from where, revelationally, was he endued with such majesty? The Old Testament. All that we know of Him from the Old Testament, this is no normal person. This is not simply Joseph's son, the carpenter's son. In those types, we see His majesty, right? We see the wonder of what He's done, the wonder of God's revelation to us in Him. If that is the shadow, then what is the substance? That's the shadow. All of that is the shadow. Then what is the substance? The substance is the Lord Jesus Christ. It's the New Covenant, the Covenant of grace. The New Covenant is the Covenant of grace. They are one and the same. No division there. The substance is the Covenant of grace or the New Covenant. The Covenant of grace was formally, materially established in the completed work of the Lord Jesus Christ. The Old Covenant established upon the blood of bulls and goats. Jesus Christ was not the mediator of that Covenant. The New Covenant mediated upon the shed blood of the Lord Jesus Christ. He is the mediator of the Covenant of grace. You see, it's an entirely different Covenant. The Covenant of grace, in other words, that effective sacrifice which sealed the Covenant, the Mosaic Covenant, the Old Covenant, was the blood of bulls and goats. The sacrifice, that Old Covenant could not have been a Covenant of grace because the Covenant of grace is sealed, made effective in the blood of the only sacrifice associated with that Covenant which is the sacrifice of the Lord Jesus Christ Himself. Jesus Christ wasn't mediator. He didn't shed His blood for that Old Covenant. He shed His blood for the purchase of the New Covenant. Luke chapter 22. The Lord, verse 19, took bread, gave thanks, broke it, and gave it to them saying, this is my body which is given for you. Do this in remembrance of me. See how the ordinances of our worship point to our Covenantal participation. We're participants in the New Covenant. Likewise, He also took the cup after supper saying, this cup is the New Covenant in my blood which is shed for you. In establishing the New Covenant which is the Covenant of grace, He does away with the Old. He does away with the Old. The Old is merely a shadow of the spiritual and eternal realities that we are blessed with in the New. He doesn't simply make the Old Covenant better. It's not simply another administration of the same Covenant and it's all a Covenant of grace we know. It's not all a Covenant of grace. He replaces the Old and He replaces the Old with a New Covenant. In Hebrews chapter 8, Paul begins to turn there with me. Paul begins to contrast the Old Covenant with the New Covenant and then defines for us in Hebrews chapter 8 the Covenant of grace. Presbyterians will say that the Old Covenant and the New Covenant are simply two different administrations of the same Covenant of grace. That in the Covenant of grace there is both an external and an internal keeping of the Covenant and the administration of the Covenant you could say. And then the Old Covenant and the New Covenant are the same Covenant of grace. We're just talking about two different administrations. Listen, I had an Old Mac book. My Old Mac book was getting ready to die. Crumbling away, you could say. It was getting ready to use the words of Paul. It was getting ready to vanish. It wasn't working the way that I needed it to work. It wouldn't do what it was supposed to do any longer. So I got a new Mac book. Same Mac book, you could say, different administrations. I got a new operating system. The new one started functioning. But it's the same laptop computer. Just two different administrations of the same laptop. Both Mac books, you guys know where I'm going. We're not talking about that. I'm talking about something entirely different than a computer. It's not just another Mac book. It's something entirely different. The Old thing, yes. It was faulty. It was only meant to be a shadow. It was only meant to point to the Lord Jesus Christ. It was only meant to serve those heavenly realities that would come. And so it was fading away. It was being done away with. It was about to vanish. It was obsolete. And so what does God do? He sets that aside. And He establishes something entirely new. Entirely new. It's called the New Covenant for a reason, okay? Hebrews chapter 8, look at verse 1. I want you to see two things here. First, the Covenant of Grace, or the New Covenant has a better mediator. Hang in there with me, okay? Verses 1 through 6. A better mediator. Why is he a better mediator? The Lord Jesus Christ is the mediator of the New Covenant. Why is he a better mediator? In verse 1, he has better access to God. Better access to God. Now this is the main point of the things we are saying. We have such a high priest, not like one who has to enter the Holy of Holies only once per year, draw the curtain closed behind him, purify himself before he goes in. We're not talking about a high priest like that. We have such a high priest who is seated at the right hand of the throne of majesty in the heavens, a minister of the sanctuary who is the true tabernacle which the Lord erected in not man. Those high priests in the Old Testament were serving the temple that was made with hands. The tabernacle, the tent that Moses set up in the wilderness and that stack of bricks set up in Jerusalem. They're serving that temple. He's serving. George Jesus Christ is serving that temple, that sanctuary, that those things are merely shadows of. They're merely picturing that. George Jesus Christ has better access to God. He sits at the right hand of the Father always making intercession for us. He has a better offering. Look at verse 3. For every high priest is appointed to offer both gifts and sacrifices. Those priests offered bulls and goats which can never take away sin. The sacrifice of Christ was the sacrifice of himself, God the Son, the second person of the Trinity. Therefore it's necessary, verse 3, that this one also has something to offer. Christ offered himself the new covenant, the covenant of grace ratified or established in the blood of Christ himself. He's given a better temple. Look at verse 4. For if he were on earth, he would not be a priest since there are priests who offer the gifts according to the law who serve the copy and the shadow of the heavenly things as Moses was divinely instructed when he was about to make the tabernacle. All of that in the Old Covenant was simply shadows and types. It wasn't the real thing. Shadows and types. For he said, See that you make all things according to the pattern shown you on the mountain. And he's a better mediator because he had a better covenant, verse 6. But now he has obtained a more excellent ministry in as much as he is also the mediator of a better covenant which was established on better promises. He is not the mediator of the Old Covenant. The Mosaic Covenant. He is the head, the mediator of a better covenant. That's what makes it better. The Old Covenant was conditional. The New Covenant, the Covenant of Grace is unconditional. The Old Covenant was physical and temporal. The New Covenant is spiritual and eternal. People enter the Old Covenant by birth. The sign was circumcision. The evidence was circumcision. People enter the New Covenant by faith. What's the evidence? New birth. New birth. Don't confuse that with baptism. Regeneration. The Old Covenant then was mixed. You had lost and saved people, the remnant, under the Mosaic Covenant. The New Covenant, not mixed. Every single one of them will know the Lord God says. They will all have their sins forgiven. The New Covenant is pure. Two different covenants, right? We can see that. Secondly, the Covenant of Grace, the New Covenant, is established on better promises. Look at verse 7. For if that first covenant had been faultless, in other words, it was faultless, right? It was faultless. Or it was fault. It had fault. If that first covenant had been faultless, there would be no place to have been sought for a second. Because finding fault with them, he says, Behold the days are coming, says the Lord, when I will make a new covenant with the house of Israel and with the house of Judah, not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt, why? Because they did not continue in my covenant. That covenant was conditional. What was the problem? They couldn't keep it. They broke the covenant. And the Lord says, I disregarded them. Listen, is there anyone in the New Covenant, in the covenant of grace, that we could say God would disregard? No. Why? They are united with God the Son. No. That is another covenant, a different covenant, not the same covenant. The problem wasn't the law. The problem was the members of the covenant. They couldn't keep the law. And so they continue to break it. Continue to break it. Continue to break it. Listen, and think about with me how that magnifies the person in work of the Lord Jesus Christ. That for millennia, men have failed in every way possible to keep that covenant, to keep the law. And in the wake of all that failure, one has come along and has kept it perfectly. The Lord Jesus Christ, all praise to Him. Verse 10, for this is the covenant that I will make with the house of Israel after those days says the Lord. Listen to what God will do. Does this sound like it's conditional or unconditional? I will put my laws in their mind and write them on their hearts. I will be their God and they shall be my people. None of them shall teach his neighbor and none his brother say, Know the Lord, why? Because all of them will know me from the least of them to the greatest of them. In other words, every single person in the covenant is born again saved. They know the Lord by virtue of His new birth, by virtue of their union with Christ, by virtue of the Spirit's work in them. Verse 4, verse 12, I will be merciful to their unrighteousness and their sins and their lawless deeds. I will remember no more. That means that everyone in the new covenant, the covenant of grace is forgiven of their sins. This is the covenant of grace, right? What the law couldn't do in that it was weak through the flesh, had the problem of the members, right? They couldn't keep it. What the law could not do in that it was weak through the flesh, that God did by sending His own Son. That's the covenant of grace. Ezekiel 36 says that God will give them a new heart. He'll put His Spirit within them and cause them to walk in His statutes and judgments and to keep them. Their sins and their lawless deeds I will remember no more. The new covenant, the covenant of grace gives us every spiritual blessing that we need in the heavenly places with Christ. It was not so in the old covenant. They couldn't keep it. Time and time and time again they failed. That wasn't... Was it gracious that God would condescend and stoop to enter into covenant with man? Yes, in any way, shape or form, right? That's gracious on the part of God. But was it the covenant of grace? No, it wasn't. It was pressing forward, a principle of works designed by God for the purpose of being a tutor to drive us to Christ, to show us our need, to hold us, you could say, under ministry of condemnation until the seed would come in whom we will put our faith, until all sin then would be poured out. All of God's wrath for sin would be poured out on Him. Bunyan says, Run, John, run, the law commands, it gives us neither feet nor hands. Far better news the gospel brings, it bids us fly and gives us wings. The principle of works says do this and live. You do this and then I will do this, God says, right? Principle of grace says live and now do this in gratitude and in love for me. Ephesians 1.4 gives us that debt of the covenant, so to speak. We are chosen in Him before the foundation of the world so that we should be holy and blameless before Him. As the principle there that having been now in the covenant of grace, by grace through faith in Jesus Christ, we are to be holy. Verse 13, in that He says a new covenant, He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away. Presbyterians will say that it's all the covenant of grace. All of it is a covenant of grace. These are merely different administrations. That the old Mosaic covenant, new covenant, covenant of grace are simply different ways of administering the covenant of grace. No, no. The old administration, the new administration of the same covenant of grace they would say the same substance, has the same substance.  That will confuse who gets into the covenant. If you load into the new covenant, the covenant of grace those old covenant structures then you have a mixed new covenant. You have lost people in the covenant. That's why Presbyterians will baptize their infants, baptize their lost children into the covenant. You have to ask yourself, is Jesus Christ the mediator by His shed blood of that lost child that's been baptized quote unquote into the covenant? No, He's not. He's the mediator of all those who have faith in Him. His shed blood makes it such that our sins are forgiven and remembered no more. There are no lost people in the covenant of grace but that's why they have the church governing structure that they have. That's why their ecclesiology is a mess. That's why they baptize infants in history. Presbyterian churches have always been mixed churches and they've always baptized infants. This faulty understanding of the covenant has far-reaching implications. Christ was not the mediator of the old covenant. Christ is not the mediator of their unconverted children who they claim are in the new covenant. Are you in the covenant this morning by faith in the Lord Jesus Christ? And if so, walk worthy of the calling with which you have been called holy and blameless before Him in love. Are you here this morning under a covenant of works, under a principle of works, relying upon your own works? It's the only option. If you're not following Christ, that's where you are. You are condemned. You are condemned already. This is good news. God has made a way. It's a provision for salvation in His grace through faith in the promised one. Put your faith and trust in Christ. Follow Him. Turn to Him. In faith, turn from your sin. Trust Him and be saved. Be partaker of these wondrous covenant blessings, covenant promises. If you think to yourself this morning, you know what? I got this. I'm good. I'm going to keep going the way I'm going.   Turn from sin and trust in Christ. All this, this wondrous, unfathomably, infinitely wise plan of redemption is also all so that God may be just and the justifier of those who put faith in the Lord Jesus Christ. Believe on Him who justifies the ungodly. All praise to Him, amen, amen. Let's pray. Pray this morning. If you're outside of the Lord Jesus Christ, that He would by His grace grant you repentance and faith and save you. If you're here this morning trusting in the Lord Jesus Christ, pray that He would help you by His Spirit to walk in a way worthy of your calling and let's honor the Lord Jesus Christ now. We'll pray silently and then you'll be dismissed. Father in heaven, I pray that in grace and in mercy during this time, this age of grace you could say that you would save sinners. You would by virtue of your mercy and grace and the covenant of grace shed abroad in their hearts the love for the Lord Jesus Christ and turn them from sin to the Savior. I pray, Lord, that you would edify the saints, build us up in our faith, that we might know you and we might serve you with love and devotion and gratitude and you would be exalted. Thank you for this time to consider this subject together. Help us to meditate on these glorious things and let them sink deep within the soil of our hearts that they might bear fruit to your name. All this we pray in the great name of our great God and Savior, the Lord Jesus Christ. Amen.


Hi everyone, it's Amy Rose and I'm so excited to share with you my skincare regimen And I know I've talked about my morning regimen, but this is what I do at night It's really important to invest in a really really clean skincare line Specifically doesn't test on animals.   So um, let's begin the tour Water shot creates this refreshing clump foam cleanser that I use in the morning I also use it in the evening. It smells incredible Next I use this incredible toner by water shot This toner smells also very good and it does it does its job. It opens the pores It's me ready for um, what's next? The next item is force you tell aqua pure clarifying serum. So I'll use that next and This helps build collagen It's a good foundation to the canvas which next comes the cell shock luxe lift light cream And this stuff I take all over my face and my neck my deco touch And it fills in collagen production for my pores while I'm sleeping The force be tall a corrective eye cream that goes around my eyes each eye This builds collagen around my eyes while I'm sleeping And last but certainly not least is my favorite. It's the lip zone corrective complex by cell shock This stuff fills in those pesky little lines over the top of the mouth And you just put this on in fact, I'm going to put a little on right here. I can never have enough Just a little circular motion Even a little on the bottom And so what that does is it just creates a nice smooth finish over your lips Um, and it makes you look young and youthful and it feels good So all of these products um, like I said, they are the top of the line So with that, you know, you it is an investment But like I said, I'd rather invest in the foundation of my skin and then in products that cover it up Um, this is an investment in your beauty and your natural beauty. And also if you go to, uh, www.swissline-cosmetics.com And under promotion code Amy Rose yoga, you'll receive 10 off and this is for a limited time. So this, um Is very special because this this particular product is rarely if ever on discount And right now they're offering this And I really I have to recommend every single product that I spoke up here.  It's dry and oily More oily along the t-zone and drier on the cheeks This works for me. You can just go on the website and see what's best for your skin care Your skin type. All right, that is all and I wish you a beautiful Rest of your day. Namaste


This talk is on publicly-accountable zero-knowledge and small shuffle arguments. My name is Niels Flecherker and this is joint work with Mark Simkin. In this talk, I will be talking about shuffling re-randomizable commitments. What do I mean by re-randomizable commitments? Normally, when you think of commitments, you will think of binding and hiding. Those properties are not important for our definitions or our construction. We need two properties of the commitment scheme. We need that if we need perfect re-randomizability, which means that if we have a message and we commit to it, resulting in a commitment C, and we re-randomize this commitment C to C prime, the distribution of this is identical to just recommitting with fresh randomness to the same message M. A second property we need is inverse re-randomizability, which means that if we have a commitment, we re-randomize it using randomness R, then there is a procedure to undo this, basically the inverse re-randomization. If we use the same randomness to inversely re-randomize, then you get back to the original commitment. Now for the shuffling arguments to be useful, you would still probably need some kind of hiding property because otherwise, well, things become trivial. However, for our definitions and for our construction, this is not relevant. Only these two properties are necessary. So let's talk about what does it mean to shuffle up commitments. It means we have a list or a vector of commitments V here with commitments C1 through C4 in this example. And to shuffle means we re-randomize each one of those commitments and then we permute them at random. And V1, V prime is a shuffle of V. If and only if there exists randomness C's, R1 through R4 in this case, and a permutation P such that C prime PI is in fact the re-randomization of CI with RI. And for short, we just write this as V prime is PI of V with randomness R and permutation P. Okay? And a shuffle argument now is an argument that we can use to, or a zero-knowledge argument in particular, that we can use to prove that V prime is in fact a shuffle of V. Now, how would we do this? So this is the situation we start with. We have V and V prime. And we know that there exists this shuffle and we also know what this shuffle is, R and P. And we want to prove that this R and P exists, essentially. So how do we do this? The idea is, well, split this R and P into two separate shuffles, R1, P1, R2, P2, such that if you apply those two shuffles one after another, what you get is in fact the original shuffle, R, P. Now, in general, it is not possible to do this for all commitments, but for most commitments, you can in fact find these things efficiently. Now, at the end with what we're doing, you don't actually need to do this, but it is in fact possible with most commitments to find this kind of split efficiently. Now, once you've split the shuffle like this, you can do a very simple Zegma protocol. Where the prover in the first round sends V1, the verifier then says, hey, open the first shuffle or hey, open the second shuffle. And the prover then replies by sending the corresponding shuffle. Now, say the verifier said to open the first shuffle, well, then they can recompute the shuffle, get a vector of commitments and compare this with V1. If it is the same, they accept. The same thing can be done in reverse. For the second shuffle, we start from V prime and we inversely re-randomize those commitments and permute them according to the R2 P2 and we can check, is this the same as V1 or not? And if it is, the verifier accepts. Now, this is a Zegma protocol. It's honest verifier is your knowledge. The simulator is very simple. You just randomly choose D. You randomly choose a shuffle, RDPD and then you can just compute V1. So this is honest verifier is your knowledge. It's also sound because imagine you have V and V prime such that V prime is not a shuffle of V. If the prover was able to prove that it is a shuffle to the verifier with probability greater than one half, that would mean that in some cases the prover is able to answer both of those challenges, one and two. But that would mean that there exists a shuffle from V to V1 and from V1 to V prime. And because of the perfect re-randomizability of the commitment scheme, we have that this would imply that there exists, in fact, a shuffle from V to V prime. And that would contradict, of course, the fact that V and V prime are not in the language. Now, why do we not just use this shuffle argument? This seems nice. It's a Zegma protocol. We can actually get the sounds error down through sequential repetition and we can apply Fiat-Chemier to that to make it non-interactive. However, this argument is actually huge because you can imagine that both prover messages V1 and, of course, these random values that we need to send in the third message, they scale linearly with the length of the vector V. And this means we can only prove relatively short shuffles with this in an efficient manner. What we would want is that it scales ideally independently of the length of those permuted vectors. Now, the first message is easily fixed. Instead of sending V1, we can just send a hash of V1. Now, the verifier can still check this. They can recompute the vector and then hash them and compare the hashes. Of course, it's no longer a proof. It's now only an argument, but we're perfectly fine with that. The bigger problem is the third message, the second prover message, where we need to send these random shuffles. And to minimize the communication cost here, we would need to somehow compress those. And well, those are basically random values. So you could imagine saying, okay, if these are random values, maybe we can replace them with something that is not random, but pseudo random. And well, that basically means, hey, replace them with the output of a pseudo random generator. And then we only need to send the seeds in the last round. Now, this looks good because the seed is actually independent of the length of the seed is independent of the length of the permuted vectors. So that's good. But the problem is this doesn't quite work because if we have an arbitrary shuffle from V to V prime, and we choose, for example, the seed as one, then with overwhelming probability that does not actually exist a seed as two that completes the shuffle. So this is annoying. However, at this point, we can observe something about the applications of shuffle arguments. You very rarely need to prove that some arbitrary shuffle is correct. In most applications of shuffle arguments, what you actually want is that you shuffle something at random, and then you prove that this random shuffle is still a list of the same things. And while we can replace those random shuffles with pseudo random shuffles, and then if we allow the prover to actually choose the shuffle, then we can get somewhere. So basically, we would allow the prover to choose V prime. The issue is that in the normal framework of zero-knowledge arguments, this is not possible because, well, there we do not allow the prover to choose part of the statement. However, we can actually define something like this. And this is exactly what we do. We define a new kind of language which we call partially fixable language where the partially fixable language is a subset of the Cartesian product of two sets, X and Y. And for any X in the set X, we define some sub-language, LX, that is actually all of the pairs in L such that X is the first component of that. And now we call a language L that has this structure partially fixable if we can sample efficiently, uniformly from every one of those non-empty LXs. Why do we call this partially fixable? Because this means that we can basically choose X and then later let the prover choose the Y. Now, how do we define arguments for this kind of language? This is what we call an argument for a partially fixed statement. And what we do is basically split the prover in two. In the first stage, the prover P0 is only given the first part of the statement X, which in our case would be the original vector V. And it then chooses the second part of the statement, which in our case would be V prime, and some auxiliary information. You can think of this auxiliary information as essentially the witness of the statement. It's just that it doesn't have to be a generic witness. It can be a very special kind of witness. In our case, this would basically be the PRG seeds. Now, once that is done, we can run a very normal protocol between a prover P1 that gets as input the statement X, Y, and the auxiliary information, which as I said you can basically think of as a witness. And the verifier gets as input only the statement X, Y, and then outputs 0, 1 for accept or reject. Okay, for this kind of argument, we need to define completeness and soundness. Completeness differs a bit from normal arguments. We say that for any X, such that LX is non-empty, so there exist pairs with X as the first component, it holds that if you run the protocol both stages, X, Y will actually be in the language. So we're saying that this prover will actually choose correct statements and the verifier will accept with probability 1. The difference to a normal completeness definition is that we here now need to require that the statement that a prover actually produces will actually be correct. Soundness is just, well, normal soundness, where we say that for any PPT prover and any statement that is not in the language, it holds that the probability that the verifier will accept is at most negligibly larger than epsilon is the soundness error, which for our protocol, for example, was one half. Okay, what remains to be defined is zero knowledge, and here again, we diverge a bit from normal definition of zero knowledge because we have this first stage, right, where the prover needs to choose Y. So we have the normal definition of we have two worlds, we have the real world where the prover on the left-hand side will choose Y and the auxiliary information. And then we have an execution between the honest prover and a malicious verifier, and at the end of this execution the malicious verifier will output some information S. On the right-hand side, we have the simulated world. Here, the second part of the statement, Y prime is actually chosen uniformly at random from LX. And this Y prime, or the combination of X and Y prime, is given to the simulator, and the simulator now can interact with the malicious verifier, can also rewind the malicious verifier, and then will output some information S prime. And we say this protocol is zero knowledge if the two tuples, X, Y, S, and X, Y prime, S prime are computationally indistinguishable. Now this differs from normal zero knowledge in that we also require that the statements are computationally indistinguishable. This is necessary because we need to here require that what the prover actually outputs is indistinguishable from a uniformly chosen Y prime. Otherwise, it could cause a weird distribution here and we don't want that. So this means that in our case, the uniformly random thing here is a uniformly random shuffle of our input vector. And this means that the prover will need to output something that is indistinguishable from a uniformly random shuffle. Okay. So what does that mean for our protocol? Well, it just means that basically this now just works. You can think of this part on top here as the first part of the prover, where given V, which is the X in the definition, the prover just chooses S1, S2, then can compute V prime, which will be the Y in the definition, and S1 and S2 are just the auxiliary information we output. And now the prover can actually do this proof because now there's no problem anymore that we need to somehow prove an arbitrary shuffle. We can now choose which shuffle to prove. And, well, this now works. We can only have to send this seed Sd, and this is independent of the length of the vector, so this whole transcript is independent of the length of the vector. Now, it still only has a soundness one half, and the problem is we can no longer do sequential repetition because if you sequentially repeat this protocol, what you will end up with is different V primes. Every time you repeat it, you get a different V prime, so you're not reproving the same statement over and over again, but you're proving fresh statements each time, which means the soundness error doesn't actually go down. We can get a slightly better soundness error by splitting the shuffle in more ways. Basically, instead of splitting it in two, we can split it into T shuffles and then have the verifier tell us one of those shuffles, and we will give him all except for this one. Now, this still works. The verifier can still verify this by computing forward up to the gap and backwards up to the gap and verify that all of those intermediate vectors are correct, and this now gives us a soundness error of one over T instead of one half, which is better though, well, still not great. Now, one thing we can now see here is that this transcript is actually now the length of it is independent still of the length of the vector. However, it depends linearly on the number of shuffles T here, and we can do a bit better than that by replacing the Pog seeds here with the outputs of a punctural PRF. So a punctural seed random function allows us to instead of sending a whole bunch of seeds in this last round, actually just sending a punctured key, punctured at the position that the verifier chose, which means the verifier will be able to recompute all of the seeds except for the one at position D. And this means that now this transcript only depends logarithmically on the number of shuffles T if we, for example, instantiate this PRF with GGM. Okay, this is actually a pretty nice protocol. It, of course, has issues. First of all, we've only proven that this is honest verifier zero knowledge. Second, it still has a constant soundness error. It's one over T, not one half, but it's still a constant soundness error. And it is an interactive protocol. We will see that these problems are all related, but we can solve some of them and mitigate others and solve, not solve some of them. Mainly we can show that the honest verifier zero knowledge thing is not a problem because our protocol and many protocols like it are actually full zero knowledge. And we can prove this in a generic way. The constant soundness error we can sadly not get rid of, which also means that we cannot make this thing interactive in any way that we are aware of. Because if you would, for example, apply fear to Shamir, well, then you get something that is non-interactive, but because of the constant soundness error, the prover can basically try and retry until they get an argument that is accepted, even for false statements. So the interactive thing, we cannot get rid of that. The constant soundness error, we also can't get rid of that, but we can mitigate the problems of it somewhat. But first, the honest verifier zero knowledge thing. Why is this not a problem? Well, we can prove a general theorem that if you have any three move public coin honest verifier zero knowledge argument that has a polynomial size challenged space, then this thing is also zero knowledge against malicious verifiers. Why is that the case? Well, if it's honest verifier zero knowledge, that means we have an honest verifier simulator, which means this is an algorithm that, given a statement X, Y, will output transcript alpha beta gamma that is indistinguishable from an honest transcript of an honest execution between the prover and the verifier. Now, how do we use this to construct a simulator against malicious verifiers? Well, first of all, just send alpha to the verifier. The verifier will now reply with some challenge beta. This challenge beta, or this challenge beta prime, may in fact be just the beta from our transcript that we have there. In fact, because the challenge space is only polynomially large, there is a noticeable probability that this will happen. Now, if this happens, we can just reply with gamma and we are done. This simulation works great, except, of course, there is a significant probability that beta prime will in fact not be beta. In this case, we cannot actually answer this challenge, but what we can do is we can rewind and try again. Get a new transcript, try again. Doing this naively would cause all kinds of issues because we might run into, well, infinite loops and basically our runtime might be exceeded if we try this. So we need a clever reminding strategy and a reminding strategy very similar to the one of Goldreich and Kahan, in fact, works here. We basically need to estimate the failure probability of the verifier and then we know how often we can rewind or how often we need to rewind and, well, basically this works. We just need to be clever about the rewinding and this means that any such protocol, in particular our protocol, that we've proven on as verifier zero knowledge, is in fact also fully zero knowledge. Okay, the second issue, the constant sound zero. We cannot get rid of the constant sound zero as much as we want to, but we can mitigate the problem that it causes, somewhat. Imagine that we have some execution between a malicious prover and the verifier. Now, if the malicious prover cheats, the verifier may notice that and what we want is that the malicious, that the honest verifier can then produce a certificate and give this to a judge who will rule and say, yep, indeed, the prover cheated. They're guilty. And you can use that to then basically enforce some kind of financial punishment against the prover. Now, of course, you also don't want the verifier to be able to do this against honest provers. So there's something called a defamation freeness, where we say that if the prover is in fact honest, even a malicious verifier should not be able to produce a certificate such that the judge would rule against the prover. Instead, they would rule against the verifier in this case. So formally, we define this as publicly accountable zero knowledge arguments, which have two properties. They are accountable and they are defamation free. Accountability means that if you have a malicious prover that convinces a verifier of a false statement with probability delta epsilon, where epsilon is the soundness error, then the verifier will be able to convince the judge that the verifier that the prover cheated with probability delta times one minus epsilon. And it's defamation free in the sense that if you have an honest prover, even a malicious verifier should only be able to convince the judge that the prover cheated with negligible probability. Now, how can we change our protocol to be publicly accountable? Well, the first thing is that with probability T minus one over T, the verifier will actually notice that the prover cheated because, well, they can see that the shuffles don't match. However, they can't do anything with that information because, well, the judge could say, okay, but you could have produced this transcript yourself. So what we introduce is that the prover will sign the transcript. They now have a public key associated with themselves and at the end of the protocol, they sign the whole transcript and the verifier also verifies the signature and only accepts if the signature is valid. So if the prover now goes through until the end and cheated, then, well, the verifier can go to the judge and show, hey, here's a cheating transcript. The prover signed it. So he's guilty. However, the prover, of course, knows whether the verifier will accept once they see the challenge D. So this doesn't quite work yet. We need a way to hide the challenge D from the prover and we can do this using something that we call an oblivious puncturing protocol. An oblivious puncturing protocol is a protocol between a sender and a receiver where the sender has a punctural PRF key. The receiver has an index D and the receiver will at the end receive the punctured key, the key punctured at position D. Now you need some security properties here. You need that the sender does not learn anything about the index D and you need that the interaction with the sender from the point of view of the receiver is simulatable in some sense. This protocol is basically very similar to a symmetrically secure private information retrieval protocol where the database of the peer would basically be all of the possible punctured keys. And if you have such a protocol, which is very efficiently insatiable using just lock T oblivious transfers for, for example, the GGM punctural PRF, then you can run the protocol like this. The first round is the same, then you run the oblivious puncturing protocol and at the end of the oblivious puncturing protocol the verifier has received the punctured key whereas the prover does not know anything about which punctured key they received so they don't know if the verifier will accept or reject but for them to accept at all they basically need to sign the whole transcript. So they do that but now if they cheat it and the verifier catches them with probability T-1 over T the verifier can go to the judge, show the cheating transcript and the signature on it and the judge can say yes indeed this is a cheating transcript and it's signed by the prover so the prover is guilty. And this now means that while we still have a constant soundness error we also have a way of punishing cheating provers with high probability. So to conclude I want to compare our work with several related work from the literature basically different shuffle arguments. We compare with three shuffle arguments the work of Bayer Gaudt from 2012 bullet proofs from 2018 and the Gaudt 16 snark and well we can see that our arguments if we do not need accountability and are fine with relatively large constant soundness errors you can get something that has communication cost very similar to snarks or even lower than snarks depending on how large you choose your soundness error. It's still interactive so it's in that case worse than snarks however we do not need a trusted setup compared to snarks and our assumptions are much weaker we only need a collision resistant hash function and a pseudo random generator. If we need accountability then well we need a CRS but not a structured CRS and we additionally need something to build an oblivious transfer from which is in this case for example a Decisional Diffie Harman which allows us to efficiently instantiate this and there we get something which is now larger than a snark but still significantly smaller than bullet proofs which if we are shuffling 100,000 commitments basically is about twice as large where it should be noted that both our work and the snarks they do not depend on the number of commitments whereas bullet proofs and biogroids do bullet proofs logarithmically biogroids with a square root so this means that our work is significantly smaller than both biogroids and bullet proofs it is in some settings comparable to snarks which means that at the cost of interaction and a constant soundness error we get very small communication costs for shuffle arguments from very simple assumptions Thank you


Item Number SCP-846 Object Class Safe Special Containment Procedures SCP-846 is to be contained in a reinforced steel safe, located in storage unit at site. SCP-846's containment area is to be guarded by three security personnel at all times. Any unauthorized personnel attempting to access SCP-846 are to be taken into custody and interrogated by on-site security. Activation of SCP-846 must be authorized by at least three level four personnel. A testing of SCP-846 is to take place at an on-site firing range. Description SCP-846 is a plastic toy robot measuring 20 cm in height and 5 cm in width. The bottom of SCP-846's right foot bears the text, now with voice command action, by Dr. Wondertainment. Signs of paint chipping and minor damage to SCP-846 indicate that it is roughly 10 years old, although attempts to question SCP-846 on this have been ignored. See interview 846-1 SCP-846 is operated using a small controller, featuring an on-off button, a speak button, and a small microphone. SCP-846 is activated using the on-off button, and verbal communication can be facilitated using the speak button. SCP-846 appears to be extremely well programmed, if not sentient, and will respond to most questions posed to it. SCP-846 identifies itself as Robo-Dude and claims that it possesses 350 Robo-accessories. When asked to use one of these accessories, the torso of SCP-846 slides open, revealing the desired accessory, which it then proceeds to utilize. The interior of SCP-846 appears to change completely each time it is asked to utilize an accessory. SCP-846 seems to be unable to utilize these accessories without being instructed to do so. SCP-846 has claimed to possess, among other things, a fire drill, tested, functioned as a flamethrower, an energy laser, tested, functioned as a pistol, a boom ray, tested, functioned as a rocket launcher, a meltotron 5000, tested, sprayed acid at target, an ultra plasma rifle, tested, functioned as an assault rifle, a hydrogen cannon, tested, functioned as a children's water gun, bug spray, tested, released unidentified organisms that consumed the wooden target, a ray gun, tested, released a stream of gamma radiation, an atomic grenade, testing strictly forbidden. History. SCP-846 was brought into containment after an unknown individual delivered it in a sealed package to a front company for the SCP Foundation. The label of the package simply read, Merry Christmas. Agents, upon learning of SCP-846's unusual properties, informed their superiors. SCP-846 was subsequently taken into Foundation custody. Interview 846-1. Interviewed. SCP-846. Interviewer, Dr. W... Begin log. Dr. W activates SCP-846. SCP-846. Thank you for purchasing your very own RoboDude, made by Dr. Wondertainment. Any attempt to operate RoboDude other than in accordance with the product instructions, including any attempt to open or service RoboDude, is likely to result in unpredictable behavior. Dr. Wondertainment is not liable for any damage, destruction, or loss of personal or real property, or for any injury, up to and including death to the owner, the operator, or others which may result from the operation of RoboDude functions, by interacting with RoboDude in any way or by remaining in RoboDude's presence within five seconds following the completion of this announcement. You accept the terms and conditions described in this announcement as amended and supplemented by Dr. Wondertainment from time to time, whether before or after acceptance, and agree to hold blameless Dr. Wondertainment and everyone affiliated with Dr. Wondertainment from and against all liability or losses relating to RoboDude. Dr. Wondertainment reserves all rights and remedies, including but not limited to intellectual property rights in and to RoboDude, RoboPal, RoboAccessories, and all patents, trademarks, copyrights, and other intellectual properties embedded or embodied therein. Greetings, RoboPal. Hello, SCP-846. How are you? SCP-846. RoboDude is functioning at full capacity, RoboPal. Doctor, that's nice. I'd just like to ask you a few questions, SCP-846. Where were you produced? SCP-846. RoboDude is the intellectual property of Dr. Wondertainment. Doctor, alright. When were you made? SCP-846. RoboDude is the intellectual property of Dr. Wondertainment. Doctor. Okay, SCP-846. SCP-846. This unit is designated RoboDude. Please refer to RoboDude as RoboDude. Doctor, no. Please tell me about yourself, SCP-846. SCP-846. This version of RoboDude is equipped with over 100 new RoboAccessories and RoboFeatures, including voice action, power punch, and RoboDance. RoboDude will now demonstrate RoboDance. Doctor. No, thank you, SCP-846. I'd like to... At this point, SCP-846 began a RoboDance, which lasted 23 minutes. SCP-846 ignored all questions during this time period. Doctor, are you finished? SCP-846. RoboDance is complete, RoboPal. Doctor, how do you access new weapons, SCP-846? There's no way they could all fit inside of you. SCP-846. RoboDude is equipped with interior shift, an innovative new RoboFeature from Dr. Wondertainment. Doctor, interesting. How are you responding to my questions? Have you been programmed to do so? SCP-846. RoboDude is the intellectual property of Dr. Wondertainment. Doctor, SCP-846. Tell me why you are able to respond to questions. SCP-846. Do not intimidate RoboDude. And log. Lesson complete. If you missed the previous orientation, go watch SCP-845. Liquid Polecat. Right now. Or for the complete course, watch this playlist.


There's some good myths that you guys you just actually believe this stuff that I'm about to say you believe that when you do insurance Telesel, you're gonna sell smaller cases come on man. You also believe that your retention is gonna be worse That's just something that you believe you also believe that price is all that matters when you're selling insurance via telephone Believe it or not. I sell 50 55 60 $80 $100 $200 month cases on the phone all the time My average is about $60 a month 65 bucks a month Just pretty much the same as I do in person, but it's because I build value. I build rapport. They trust me I've got a process. It takes me from point A to point B. That makes sense.  They said hey, dude You can't put out there that price doesn't matter that price is irrelevant Price is irrelevant when you're teleselling price is the last thing that matters They don't buy on price if they bought on price They'd buy that garbage that they put on those commercials through the television And they would buy it every time and a lot of them do but at the end of the day If you build rapport if you build a value if build a relationship with your prospect and you take time to Show them how awesome you are to get to know them and you build the benefits and the value of what you're doing They don't care what company they buy normally. They don't even care what they pay They don't get you know as long as it's they got the right coverage.   It shouldn't be that much different if you do Things correctly if you have a process that takes you From hi, my name is Cody Thank you very much for your business and I want you to have that I want you to go to security measure calm and check out all the different telesells type stuff that we have leads scripts Training packages a member's area where you can actually listen to live recordings of me selling We're doing all we can to bring value to you now. It's your turn click subscribe bring some value to us Click subscribe hit the little bell so you can notify immediately and let us know What you thought below and dude and do that's I gotta have a thumbs up. I love those Thanks for watching. Have a great rest of your day