We're very fortunate to have Sheldon as the Vice-Chair of the Libertarian Party, and as our speaker here tonight. Join me in welcoming Sheldon Richmond, please. I have to make two corrections. Number one, I never wore a return Vietnam button, and if I did, it didn't specify which side. And ordinarily you would have been correct that you were the person who's known me longest, except my parents were in the room. I'm Dave Touche. I got you. Well, thank you very much. It's very nice to be in Maryland. And Maryland is a great LP state, and you all saw the rundown of the Mathers campaign, and I think Tom deserves all the credit in the world for what he did. And we're looking forward to a great campaign from Jerry. Yeah, there it is. So it's nice to be here. Now I've titled this talk, this is sort of a title that's guaranteed to put you all to sleep after dinner. The spontaneous order and its value to liberty. Great lively year. And I knew this title was going to scare people, especially applied to an after-dinner speech. So I figured I would find a humorous story to open up with. Unfortunately, there aren't many jokes being written about the spontaneous order. Or at least there are not many clean jokes being written about the spontaneous order. So I'll have to forego the intended humor with the hopes that there will be some unintended humor. And that is really subtle. Now, actually I came to the conclusion that it's symbolic that there aren't too many jokes about the spontaneous order. Because when a conscious understanding of this important topic filters down to the joke smiths, we'll be much closer to the libertarian society. It's kind of the point of the whole talk tonight. Now, I don't want anybody to be alarmed about the title, because I don't intend to give a heavy lecture on the meaning of the spontaneous order. There are many other people who are better equipped at that, and there's plenty of writing on the issue, and I urge you all to go out and read it, dating back to Adam Smith and even earlier than that. But what I want to discuss briefly is the role this concept should play in our strategic activities. This role was emphasized in a lecture this summer by Walter Grinder of the Institute for Humane Studies. Grinder struck a responsive chord in me and some others in this room when he said that we won't succeed in abolishing stateism unless many people grasp the meaning of spontaneous order. And I hope this will become clearer as we proceed here. Now, to start off with an understatement, advocates of the free market are badly outnumbered these days. And you can just look at the results in Washington Tuesday for some empirical evidence. There are a lot of reasons for this, ranging from ignorance to semi-conscious aversion to outright power lustful hostility. For many people, unspoken ethical principles automatically condemn any system that allows people the freedom to pursue their own ends. And this applies even to many self-styled advocates of capitalism. I have George Gilder in mind. To George Gilder's self-interest and ambition are so objectionable he has had to devise a contorted gift-based rationale for capitalism that most people to their credit have found hard to accept. Gilder has gone so far as the right quote that with friends like Adam Smith, businessmen hardly need enemies. Now, whatever the reason, most people have it in for the free market. And over the years, every ill or alleged ill has been attributed to it. Mises has a marvelous opening paragraph in his little 1947 book, Plan Chaos, that reads, Nothing is more unpopular today than the free market economy, that is capitalism. Everything that is considered unsatisfactory in present-day conditions is charged to capitalism. The atheists make capitalism responsible for the survival of Christianity. But the papal encyclicals blame capitalism for the spread of irreligion and the sins of our contemporaries and the Protestant churches and sects are no less vigorous in their indictment of capitalism's greed. Friends of peace consider our wars as an offshoot of capitalist imperialism. But the adamant nationalist warmongers of Germany and Italy indicted capitalism for its bourgeois pacifism, contrary to human nature and to the inescapable laws of history, sermonizers accuse capitalism of disrupting the family and fostering licentiousness. But the progressives blame capitalism for the preservation of allegedly outdated rules of sexual restraint. Almost all men agree that poverty is an outcome of capitalism. On the other hand, many deplore the fact that capitalism, in catering lavishly to the wishes of people intent upon getting more amenities and a better living, promotes crass materialism. These contradictory accusations of capitalism cancel one another. But the fact remains that there are few people left who would not condemn capitalism altogether. Well, I think you get the point. My focus tonight is on the people who oppose the free market, not out of informed hostility, but out of ignorance. And my particular point is on... I have a particular kind of ignorance in mind. The ignorance of the essential orderliness of a market society. And perhaps it's a subtle point. But fundamental to the very concepts of society and market is the idea of self-generated orderliness. If you think about it, you can't conceive of the concept of market or even society without some sense of there being an order involved. Not an imposed order, but an order that comes out of it, you know, from within. In fact, it's the very element that drew the attention of Adam Smith and others to study these things. The fact that they looked out there and they noticed regularity in order. Now, given this ignorance, it is unsurprising that people oppose the market. After all, it's understandable that people want to live in an orderly environment by which I mean an environment where they generally know what to expect of other people under many kinds of circumstances, however complex. Imagine the problems of living in a society in which you'd never know how people will react when you say, good morning, or where the phrase, have a nice day, could get you a punch in the nose. Of course, considering the sappiness of that cliche, you're likely to be punched in the nose today and you may deserve it. The desire for order, then, is not objection. But, in fact, entirely fitting for rational beings. Now, probably the person who's done most of the writing, explicit writing and thinking about this is F.I. Hayek. And he's described two kinds of order in human affairs. The imposed order and the spontaneous order. And what he pointed out, and what I think must inform our strategic considerations, is that in the view of many people, there are only imposed orders. The idea of spontaneous or self-generated order has never occurred to them. This is ironic because they act within spontaneous orders all the time without realizing it. For example, even in a highly interventionist society, there is a large degree of predictability in people's everyday actions. To take a simple example, when you say good morning, most people respond in kind. The same applies to very highly complex exchanges. These rules of conduct, or customs that are more complex than they may appear at first, were not decreed by any law giver. They evolve through the ages, just through the individual acts of people seeking to better the condition. They comprise institutions that are, in Adam Ferguson's immortal phrase, the product of human action, but not human design. But I'm getting ahead of myself. When libertarians argue against the idea of a planned economy, we are arguing really two things at once, and unfortunately we don't separate the two as clearly as we should. The easier of the two arguments is the idea that planning is a bogus issue. As Mises put it, the alternative is not plan or no plan. The question is who's plan? Should each member of society plan for himself, or should the paternal government plan for all? The issue is not automatism versus conscious action. It is spontaneous action of each individual versus the exclusive action of the government. It is freedom versus government omnipotence. Now this argument, I think many non-libertarians will readily grasp, even though they still may choose omnipotent government, but they still can understand the idea that the issue is not between no planning and planning, but rather who's going to plan. So it's the next point that may evade them, and unless we are very careful and confident about making this argument, they'll never discover the point. Since it is such a critical point, I highly recommend that libertarians study the subject so that they can be conversant in it. You don't have to be a full-time libertarian scholar to pursue this subject so that you can better argue to the people you meet every day. Now here's the point. Once having grasped the idea that the free market means that the individual plans for himself or herself, the non-libertarian will likely ask, okay, what prevents, though, the countless individual plans, this pursuit of countless individual plans from turning into chaos? I'm sure you've all heard the people tell you that well, the market's okay for small primitive societies, but not for huge complex ones. We're way beyond the time when we can have a free market. So this is where the concept of spontaneous order comes in. Now it has gone under many names, undesigned order, unintended order, unplanned order, automatic forces, harmony of interests, and Adam Smith's immortal, the invisible hand. All of these names have merits and drawbacks. To the extent that they distract us from the fact that individual actors plan their actions, they're deficient. In other words, if we talk about spontaneous order, we don't mean people are acting only spontaneously. It doesn't mean that people don't plan their own actions. It has nothing to do with that aspect of it. But the merit of these various terms lies in their indicating that some web of consequences emerges that is orderly and yet unintended. Nozick in his book, Anarchy, State, and Utopia, wrote, quote, that an invisible hand explanation explains what looks to be the product of someone's intentional design as not being brought about by anyone's intentions. Thomas Sowell, in his book Knowledge and Decision, says that the mutually constraining complex of relationships whose results, excuse me, he refers to the mutually constraining complex of relationships whose results form a pattern not necessarily similar to the intentions of any of the individuals involved. And even Engels, Frederick Engels, was aware that quote, what emerges is something that no one will. Now let me quickly retreat from Engels, this is not the group to quote Engels in, I'm sure, by turning to Hyatt when he has a marvelous passage in the Constitution of Liberty, where I think he really gets at the whole point. He said, the enemies of liberty have always based their arguments on the contention that order in human affairs requires that some should give orders and others obey. Much of the opposition to a system of freedom under general laws arises from the inability to conceive of an effective coordination of human activities without deliberate organization by a commanding intelligence. One of the achievements of economic theory has been to explain how such a mutual adjustment of the spontaneous activities of individuals is brought about by the market, provided that there is a known delimitation of the sphere of control of each individual. And understanding of that mechanism of mutual adjustment of individuals forms the most important part of the knowledge that ought to enter into the making of general rules limiting individual action. The Hyatt, this was the critical thing you had to teach people that there could be order without a designer. One of the things we have to do is communicate this to people through examples, concrete examples that they will grasp first in the particular case and then generalize. For instance, the language is something that has arisen as a result of what we're calling here the spontaneous order. No one invented language, no one sat down and said, okay, let's have language and rules of grammar and words that refer to different things. It evolved just through people's actions, through their seeking to achieve ends, which evolved communication. Language grew out of that. Money is another example. If you read Mises or Manger on the evolution of money, you get a good concrete example of how the spontaneous order works. No one invented money. But it was a result of people attempting to make exchange easier and out of that you've got a system that no one sat down to design. Same thing with the price system, standardization of parts, years and whatnot. No one decreed that there should be standardized parts. Again, it was the result of people seeking to better their condition through individual acts and not overall design. A very simple, simplistic, really, example that you can use to get through to people. See, I'll give just a path through some uncharted woods. If someone walks through woods for the first time, seeking to do nothing but to get to the other side, he will have, without intending it, have begun the process of creating even a permanent path because just by walking through, he downs some bushes and grass. The next person to come along may choose that path because it already looks easier because the first person has pushed down some of the brush. Before you have a path, even though no one of the person is crossing it, perhaps no one of them had in mind the actual creation of the path. Now, that's a very simplistic example and you can't leave it at that because in fact the path can be created by deliberate design. These other things though, language and economy, economy that serves human wants, those things cannot be created. It can't be designed by a single mind because the information just isn't available. In teaching people about spontaneous order, it is critical that we point out that there's nothing mystical or automatic or mechanistic about it. It is rooted in human action and human planet, but at the same time it is fantastically complex and so impossible for any one person to grasp in its entirety. This is so because of what Hayek calls the division of knowledge, the fact of life that knowledge necessarily is scattered and incomplete and therefore unavailable in its totality to any one mind. And one of the most ludicrous objections to the free marketing, you've all heard this, to the free market solution of anything is that it's quote simplistic. Okay, we've all tried to have unanimity. In fact, there is nothing more complex in the world than the free market and nothing can be more simplistic than the view that social problems can be solved by decree, by decrees of rulers who are necessarily ignorant of what matters in each situation. And equally absurd is the view that the market is suitable only for small, simple society. As you all know, I don't have to tell anyone here, it's the very opposite of the case. There's a much better case for planning, sort of central planning in a society of five people, but they all know each other. Not that it would be moral, but as far as just strictly speaking in economics, you have a lot more chance of pulling off central planning than we have in a family. In fact, we have central planning for a family, but as soon as the group is big enough that you can't have personal relations with all the people, then central planning has to fall on its face because the information just is not available to the planner. So we sometimes kid ourselves about our stock solutions and social problems, namely that answer, well, the market will take care of it. You've all heard the light bulb joke, right? Do I need to tell anyone here? The question is how many libertarians, he knows it all, number five. How many libertarians does it take to screw on a light bulb? Okay, the answer is none, the market will take care of it. Okay, now I have my own version of that. This is the revisionist joke.  And the answer is we can't make quantitative predictions. Okay, now while this may not be a sufficient reply to the uninitiated, namely the market will take care of it, that may not be enough for most people. It does get at the truth. The market does take care of things. But when we say the market, we don't mean a thing, you know, a single institution, an object out there that you can point to. As Thomas Sowell put it, the market is nothing more than an option for each individual to choose among numerous existing institutions or to fashion new arrangements suited to his own situation and pace. In other words, the market is just not a set, even a set group of institutions. In light of this sensible description by Sowell, the phrase market failure becomes nonsensical, something we're always arguing at the Council for Competitive Economy. There's no such thing as a market failure, doesn't it? There's not a thing out there called a market that can fail, and people can individually fail in their own plans, but that's very, very different. I was taking a Soviet history course last year, and the professor who was very anti-communist ridiculed the Soviet economic system as too complex because to get a simple production decision made, somebody down on the low level of the production structure had to send the requests all the way up to bureaucracy to some commasaur, and then the commasaur had to make a decision of course he was far removed from the problem area, had to send his answer all the way down and took months and all that. But anyway, he was ridiculing this as being horribly complex, and that was the reason the system was such a failure. Well, while in physical terms, you may call this complicated, I wondered out loud in the class whether the problem was not that it was, aside from ethics now, but in economic terms, the problem was not that it was too complicated, but that it was too simple. After all, here was a huge society of millions of people being run on a Robinson Crusoe model, as if there was only one end seeker and one decision maker. By the way, the professor agreed, I got an A in that course, so he never thought of that before. Now, this point about the market not being a concrete thing is an obstacle to us, because we can't point to the market, say there's the market connection. How often have you been told after reposing some government program, well, what do you propose? What do you want? You don't just say the free market, that's not a proposal for many people. The many people advocacy in the market is pure negativism without a constructive alternative. William Raspberry in the Washington Post criticized Thomas Sowell for the very thing. He outlined all Sowell's criticisms against schools and this and that, affirmative action, and then said, well, the man never proposed anything. So what uses he as a social company never tells us what he wants. Now, this is a silly criticism, and I've tried to illustrate it with this analogy. You're welcome to all of you use this.  Now, you walk up to him and you're the citizen type and you say, that's not the right way to get money. You should not be taking this man's mugger. And the mugger turns you and say, what do you propose? And you say, well, you know, there's a free market. Go find a job. He said, well, that's not a proposal. Now, as long as you can't give me a proposal, I'm going to continue with this concrete act, which I can see is very visible. Well, it's the same problem. We'd all agree that the mugger was being irrational. Mugger qua mugger. Now, in strategic terms, in strategic terms, the markets in corporeal nature, the fact that it's nothing to point to, requires us to be patient in making our case because we were asking people to think in a way that they haven't thought before. So we have to remember that. Now, there are other aspects of the spontaneous order that ought to be emphasized. First is synonymous with cooperation. The enemies of liberty have a stake in making the market appear anti-cooperative. Of course, this is nonsense. How could a system whose foundation is the division of labor be anti-cooperative? No one has better illustrated this than Leonard Reed in his essay, Eye Pencil. If you haven't read it, please look it up in the Freeman, Right to the Feet in Irvington, New York, and get a copy of it. It's fantastic. No one can make a pencil. No one person can make a pencil. And yet, the simple thing which costs very little, even with inflation, is made by millions of people, strangers to each other, scattered throughout the world, without central direction and without coercion. That's a great way to impress on people what the spontaneous order is. The cooperative nature of the market is deeply related to its benevolence and its humanity. Its enemies are to be admired, the market's enemies, are to be admired for their perceptiveness. They have known what they have to gloss over in people's minds in order to smash the market. They have to get, they understood the essential benevolence and humanity of the market, and they knew that this was what had to be blotted out if they were going to turn people toward status. If we are to triumph, we must teach people the causal link between the market and what they value about social life. Murray Rothbard, I think, describes this very well in the man-economy and state. I want to read a short paragraph about this. He says, in explaining the origins of society, there is no need to conjure up any mystic communion or sense of belonging among individuals. Individuals recognize, through the use of reason, the advantages of exchange, resulting from the higher productivity of the division of labor, and they proceed to follow this advantageous course. In fact, it is far more likely that the feelings of friendship and communion are the effects of a regime of contractual social cooperation, rather than the cause. Suppose, for example, that the division of labor were not productive and that men had failed to recognize its productivity, or that men had failed to recognize its productivity. In that case, there would be little or no opportunity for exchange, and each man would try to obtain his goods in autistic independence. The result would undoubtedly be a fierce struggle to gain possession of scarce goods, since in such a world, each man's gain of useful goods would be some other man's loss. On the other hand, in a world of voluntary social cooperation through mutually beneficial exchanges, where one man's gain is another man's gain, it is obvious that great scope is provided for the development of social sympathy in human friendships. It is the peaceful, cooperative society that creates favorable conditions for feelings of friendship among men. Very important that we get across the idea that the market is the maker, not only of order, but of cooperation, benevolence, peaceful exchanges. Now, if cooperation is so important, what about competition? Aren't they opposites? Well, here's another notion of the effectiveness of Liberty's foes. Again, if they could paint cooperation and competition as being opposites and show that the market is based on competition, they're able to drive home the point to people that the market has nothing to do with cooperation and therefore score another point for status. Far from being opposites, though, competition and cooperation entail each other. Now, being methodological individualists, we know that society can't cooperate. Only individuals can. And since an individual cannot cooperate with everyone at once on particular projects, he must choose whom he will cooperate with. The result is competition. If I need to choose, and I want to cooperate with someone in providing shoes, and two people want to cooperate with me, I have to choose which one I'm going to buy the shoes from. The byproduct there is competition, to do the cooperating. The stifling or prohibition of competition, then, is not a blow for cooperation, but a blow to cooperation. The eloquent libertarian writer, Albert J. Nock, made a wonderful contribution to the subject in his book, Our Enemy to State, in which he shows the incompatibility of social power and state power. What Nock tells us is that in human affairs, there are two vast networks of relationships. The network of voluntary relationships, society, and that network of coercive relationships, the state. Society is the realm of production, exchange, cooperation, competition. The state is the realm of expropriation, slavery, war, mass murder, and general misery. This is what he meant when he wrote, quote, taking the state wherever found, striking into its history at any point, one sees no way to differentiate the activities of its founders, and beneficiaries from those of a professional criminal class. Close quote. Nock's theme, brimming with benevolence, is that the free market generates a social bond of spontaneous order of cooperation that is undermined by state power.  The state tears the fabric with each act, and Nock summed this up when he wrote, quote, but it may be asked where are we to go for relief from the misuses of social power if not to the state? What other recourse do we have? It must be pointed out that this question rests on the old, inveterate, misapprehension of the state's nature, presuming that the state is a social institution, whereas it is an anti-social institution. That is to say the question rests on an absurdity. Therefore, an appeal to the state on the ground of justice is futile in any circumstances. For whatever action the state might take in response to it would be conditioned by the state's own paramount interest and would hence be bound to result as we see such action invariably resulting in as great injustice as that which it pretends to correct or as a rule greater. The question thus presumes in short that the state may on occasion be persuaded to act out of character, with the levity of those quotes. My message in closing is that the libertarian candidate is not that libertarian candidates should campaign as philosophers or that we should nominate Hayek for president. What I am recommending is that all of us become familiar with the rich subtleties of libertarianism and then find ways to make them clear and easy to our lay audience. We have to do this to overcome hundreds of years of prejudice against liberty and this is hardened into unquestioned, blind feeling that the free market is at best simplistic naive and contrary to human nature. What we must do if we are to have liberty and abolish the statism is teach this lesson to people and there is no greater cause. I don't usually go on for bumper sticker philosophy but I'll make an exception here and recommend that to open the subject with people you could hardly do better than to quote Crudone's brilliant formulation which is liberty is the mother, not the daughter of order. Thank you.


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This is Jeff Deist and you're listening to the Human Action Podcast. Ladies and gentlemen, welcome back once again to the Human Action Podcast. Happy 2021 to all of you. It's the first show of the year. We'll be doing it generally on Friday afternoons from here on out. As most of you know, this is one of the few podcasts which is not afraid to read books, to discuss books, and mostly in the area of dense economics, but also sometimes in related fields like history and philosophy and logic and politics. So we had a great 2020, went through some very serious books, had a lot of good back and forth with the audience, and we're really excited about a new year. So all that said, we're going to start off with a book that I mentioned in my last show with Tom Woods, The Ethics of Money Production by Guido Halsman, who many of you know is one of our senior fellows, who is originally from Germany but teaches and runs a PhD program at the University of Angers in France. And I thought there'd be nobody better to help me work through this book than a friend of mine, Stefan Lavera. Many of you know him from his Bitcoin podcast. He lives in Sydney, Australia, so he's joining us from a different time zone. And Stefan, I'm going to tell you this. I don't sort of live day to day in the Bitcoin community to put it mildly. And there's so much white noise. There's just so many people talking, so much crosstalk that to make my life easier, you and Safi and Amus are the two people that I really rely on to help me understand and to basically sift through everything out there. Yeah, well, thank you very much, Jeff. It's an honor. I'm a big fan of you and of the Mises Institute. So very excited to chat with you today about, truly, the ethics of money production. It is one of my favorite books. And I often talk about it on my podcast. I often recommend it to my listeners who are trying to learn a little bit more about what has government done to our money, just like the Murray Rothblood book. Well, and it's because I've heard you mention it that I thought of you for this show. Does that mean that this book has some purchase or some resonance in the Bitcoin community? Do you think it's reasonably well known out there? Because the Bitcoin community and the Austrian community have a lot of overlap, but they're not contiguous necessarily. Of course. Yeah. So I think to some limited extent, a lot of people coming into the Bitcoin world, because they listen to my show, I've been promoting Austrian economics to them. And so some of them, as they come down that Bitcoin rabbit hole, some of them also go down the Austrian rabbit hole. And so they typically DM me and ask me things.  Go and read this book. And once you read it, it really does set things in a new light for you. And so for me, I mean, my experience reading this book was just, it was just, it was a real page turner. I actually remember the night I was, I've read it for the first time, like my friend, Bittstein, Michael Goldstein had recommended it to me. And I was traveling for work at the time. And I was, you know, had finished work for the day and I was back in my hotel and I was reading this book online. And I remember literally just reading it in one night. And it was just a phenomenal experience. I really, really enjoyed it. Well, and Stefan mentions reading it online. You can find it for free at mises.org to read. Just type in the ethics of money production in the search bar. It's not super long. It's about 240, 250 pages. So it's a bit of a slim volume in hardcover. Came out in 2008. And one of the things that struck me reviewing the book again, Stefan was that in the introduction, he talks about how it's really an ontology of money. In other words, it's a book broadly about the actual metaphysical underlying nature of money itself. And I was struck that there's a little bit of an analogy to Safedin's Bitcoin standard book because even though the title is the Ethics of Money Production, a lot of the book is not directly about that. It's about the broader history of money, about banking practices, about fiduciary media, about fractional reserve, about historical gold standard. So it really is a great overall money book, even for a novice. Exactly right. And I think it, as you say, it just places so much of the context, whether that is from a legal perspective, an economic perspective, a historical perspective, and also in the Ethics of Money Production, some element of religious perspective as well, where there's some level of situating it amongst Christian and Catholic thought also. And yeah, just for me, it just really clarified so many things and stated them in a very clean and precise way. So you, as you read this book, you really start to understand a range of things and you might have heard them elsewhere, put them put in another way as I had also. But I think it was just the way that Dr. Holzman puts it in this book that to me was just so magical. It was such a great experience to read it and just have it all laid out so clearly. Like there are certain ideas, for example, that no fiat money had ever existed without kind of first being linked to natural and commodity money such as gold. And so it's kind of like a really nicely cleanly put way of trying to understand how money originates and then how it is essentially the process of it's getting co-opted by the government. Well, and the other thing is since there's so much history in here, Holzman's not the kind of person to shy away from acknowledging that there are moral and ethical components. And as a result, we need to bring in, let's say, the scholastics, Thomas Aquinas, traditional Catholic intellectualism, and he's not scared of that stuff.  And what strikes me is that I think if you went to the average Econ PhD out there, they would readily say that there is something, there's an element of justice to how money is distributed in society. But they'd rarely say that there's an element of justice to how it's produced. And that's, I think, one of the really big revelations of this book. Exactly. And I think that's one of the things that perhaps is difficult to communicate to somebody who's not in our world, let's say, of the Austrian world of thinking that there really is a justice component to this as well, that it really is about what is the right way that money should be created and whether it needs a central planner or whether it can be determined. The supply of that money can actually be determined on the market itself. And so that's a very challenging, I guess, question for people who are not already in the Austrian sphere. But I think when you read the book and you sort of take in that perspective, it really, yeah, it just really changes your perspective on things. Well, what's been interesting for me is sort of a bit of an outsider to observe in the Bitcoin Twitter sphere is how people talk about time production and people talk about saving and people talk about applying thrift in their own lives because obviously they're big believers in Bitcoin and so instead of buying that, you know, 35 bucks worth of sushi and cocktails tonight, they'd rather have a tiny bit more Bitcoin. And it strikes me that whether it's intentional or not, whether it's conscious or not, whether it's because of Austrian principles or not, that there's something about Bitcoin and a super hard currency which is hopefully gaining value over time that teaches the lessons of thrift, which is sort of the opposite of fiat. Exactly right. And this is a point that safety makes. I want to make this and a bunch of the other guys in the Bitcoin world who are into Austrian economics were talking about how society as Hans-Hermann Hopper says its capital accumulation is what sets off society and by enabling this process with savings, that is really what enables us to be so much more productive. And so I think this is something that has spilled over into the Bitcoin world and people will generally, they will genuinely be talking about time preference and why we should try to lower our time preference. And this is like a good thing for us and for our own behavior and to think more about our families and what we're going to leave behind after we're gone, which is also an expression of a lower time preference. Well, and of course in an inflationary environment where interest rates are low or even nominally negative and certainly negative in real terms compared to inflation, saving is for chumps. Exactly. Yeah, that is unfortunately the hard reality. And I think it's okay. So for me, I'm in my early to mid 30s and I remember even when I was young, there was a bit more of a culture of, hey, you save in the bank account and you get some interest. But nowadays you don't even really get any interest. Savings accounts in banks are just getting completely, you're just getting annihilated in there. And so now I think that is also what this whole Bitcoin movement is about. It's actually trying to bring back the idea of saving. It's making savings cool again. And we have to really set everything right again where the world has come into this perspective of putting the cart before the horse of consuming first. We have to now reorient ourselves and think more, okay, no, it's about savings, building our capital, using technology so that we can produce and then we can consume. That's actually the way it should be. Yes, it is the way it should be and it feels like we're so far from that. When I look at the way this book is structured at the beginning part of the book, the natural production of money, a question that struck me that I would ask you in particular is, is Bitcoin natural? Would it have arisen regardless of central bank depredations or is it sort of a reactionary force against fiat? I do think of it as a reactionary force. I think of it like all these prior attempts at money were tried and failed. Now, and in fairness, it's not that gold itself failed. It's more just like the folly was trusting the government. And so there were earlier attempts at money, whether they were in a crypto form or whether they were in a more just a business form, right?  And in the crypto world, it was things like hash cash, B money, bit gold, all of none of those worked. Basically, all of them got shut down for one reason or another. But Bitcoin has been around for now for 12 years and it continues to rise. And I see it as essentially it achieves what human institutions could not because I think part of it. And this is also coming back to the book as well. I think part of it, Dr. Hausmann talks about how some of the different forms of money in history, they relied to some level on the credibility of their issuer.  And then talking about how it transitioned forward into, oh, okay, now we're going to have, you know, paper money, but it's like by this person in some sense, Bitcoin is like the durability, if you will. Like if we're thinking of the durability of money, I think Bitcoin achieves that in a certain way because we know that the issuer can't be corrupted. It's a program that we all run when we run our Bitcoin node and our Bitcoin software. So, yeah, but I think you're right that it doesn't evolve as like, you know, it's not like gold. It's not just like naturally existing. It had to be created and it has to be maintained. But I think taking some of those lessons allow us to understand that money doesn't necessarily have to be tangible. Well, the notion that is today, of course, completely lost. And by today, I mean in the era of unbridled central banking is that money should gain purchasing power over time. And this is considered anathema for a number of bizarre reasons. I guess chief amongst them is that expansionary monetary policy benefits governments. And so governments and central banks work together to make each other happy. But I want to direct your attention and listeners attention to page 65 of this book because in just a little four or five page section, subsection of the book, Guido Halsman gives an absolute masterclass on the benefits of deflation and takes a sword to, I believe, six different rationales for why deflation is a bad thing. And it struck me as something that we should put out maybe as a separate article or something. Just Halsman disabuses the deflation myth because it was just... I mean, that's where this book really shines because it's a short readable track. But man, oh man, do you get something out of those five pages? Yeah. So in the fighting deflation section, I actually was... So I was reviewing last night as well and there are six arguments here. One is this idea that deflation has negative repercussions on aggregate production and therefore on the standard of living. And then they also talk about how, oh, because of deflation, we're going to postpone our buying because everyone's speculating that's going to be lower. And he just absolutely just goes through and blasts away all of these different six justifications because he essentially firstly points out that deflation has no clear negative impact on aggregate production. And so it's not like we had lower growth rates under that kind of monetary order. And he even takes it to the extreme and says, okay, in the case where people are talking about delaying their production, even if you're a neurotic miser, you still have the constraint of the stomach. You still have to eat, right? We still have to live. And so even in that case, he's saying, look, hoarding is not necessarily... It's not per se a problem because there are all these other X, Y and Z downstream impacts of that if you will. And so as an example, to the extent that you and I hoard our money, it just raises everybody else's purchasing power because we're not buying anything with that money. We're giving up that, in some sense, we're relinquishing the ability to, or at least temporarily relinquishing the consumption that we could have had. And I think he also spells out some elements around servicing debt as well. So he's talking here a little bit about how you have to anticipate the inflation expectations. So that kind of is a theme in this book. But I think one really, really crucial point here that he also really drives home in this section is he's saying bank credit does not create resources, right? So the typical, like a typical argument we might hear from the mainstream is something like, oh, but we need lending so that businesses and entrepreneurs can go and get capital to run their business. But Dr. Holtzman here is pointing out that, no, no, hold on, that's not true. Well, that's not exactly right. Really, you can extend credit to somebody, but really all you're doing is you are channeling the existing resources into some other business than the one that would have already had it. And so I think that is a very, very kind of basic point, but it's so lost in today's mainstream commentary. And so that and that reflects when people say, oh, but if we didn't have fear money and fractional reserve banking and these cheap interest rates, then entrepreneurs would not be able to borrow to get the resources they need. And it's just, it's like, no, that's just fundamental misunderstanding of what's going on here. And of course, nobody can provide a definition of hoarding. It just means too much, right? There's never as a percentage or anything else. And of course, by hoarding what we're doing, what we should really say is maintaining larger cash balances than we otherwise would. But hoarding just means that we are voluntarily shrinking the money supply. And sure, if there's less, you know, if there's sort of less demand for money, then interest rates might fall and people who have borrowed money at 3% and now earning 1%, they may be in trouble. But as Halsman points out that, you know, that just changes who owns the resources. It doesn't provide any diminution in them. And so I thought that was just such a masterful little section of the book that everyone would benefit from. And he alludes to a point which Rothbard makes very succinctly in what his government done to our money, which is we don't care about the money supply per se, right? The total amount of money in society because as long as it's infinitely divisible, we can always readjust prices. So, you know, I'm struck by some criticisms of Bitcoin in the sense that the ultimate limit in the number of bitcoins minable at 21 million, somebody would say, well, that you're setting an artificial ceiling on the money supply. Right. And so it's the same answer essentially. Those 21 million bitcoins are divisible down to 100 million satoshis or sats for short. And with other technical ways of doing this, it could be subdivided even further. So essentially the price would just rise to adapt for these things. And so, yeah, certainly I think that is a point that Halsman really drives home here in terms of the ability to, you know, around how wide the supply of money per se doesn't matter. And I think it's also really another point is that he raises in deflation and liberty as well. So that's also another really nice short version articulation of many of these points also. You know, Bob Higgs uses the term regime uncertainty. But when we have these hiccups every 10 or 12 years, members central banks were supposed to smooth out the booms and busts while we just had one in 07 or 08. Now we're having one in 2020. It strikes me that regime uncertainty could apply to central banking too because when you have crazed fiscal and monetary policy, you know, wow, imagine being out there and trying to plan your business.  Or if you're Michael Saylor even exchange cash for Bitcoin on your balance sheet.  I mean, central banks to me are exceedingly volatile. Yeah, of course. And I think that this comes into this whole question around monetary stability as well. So, and I think Gitter-Hosman explains this in the book as well. He talks about two forms of it. He talks one about stability of physical integrity and then stability of purchasing power. And the stability of the purchasing power part is something that we can never really have because really the world is always changing. There's always some errors being made somewhere or some changing condition and people's desire to hold cash will raise, you know, rise that will go up or down. But in terms of us knowing what the final supply of this thing is, well, at least in a Bitcoin sense, we do know that. And in a gold sense, we know that there are certain natural checks, if you will, on the creation of new gold, the mining of gold to produce it into gold coins and so on that we could use theoretically if we were to live under a gold standard. And so I think that is a real benefit there for those people who are using market chosen money such as gold or Bitcoin, that they are not as susceptible or vulnerable to the vagaries of what's going on with central banking. Certainly, I think central banks have put us into a very weird situation where people are now, as Michael Saylor would put it, we're sitting on a melting ice cube and now we all have to think about what to do about that. And even in ethics of money production, there's discussion about how for many people when they want to save and especially towards the end of their life, they might need a financial advisor, they might need a tax planner and they might need to watch the financial markets. And even then, if they're unlucky, they might still end up with a lot of their life savings getting inflated or lost because of having been pushed into playing the financial markets. So that's a real shame. It is a shame, especially at a time in people's lives where they should be out of markets and just sort of living off of capital and interest. And one of the things that this book I think lays out equally well is the case against inflation. In other words, if deflation is not the boogeyman we thought it's actually a desirable state of affairs then it follows that inflation must be an undesirable state of affairs. And I like the way that Halsman separates between what he calls private inflation and fiat or state inflation. So talk about that a little bit. Oh, of course. Yes. So I guess if I had to maybe summarize into maybe I'm maybe I'm not as precisely stating it, but it's sort of like in a fully free market, there would be some level like a natural level of inflation that might occur as people go and mine new gold. And there would be a normal, almost like a countervailing balance factor where if too much of that gets mined, well then the return for going and mining new gold goes down as such that there would be a level over time of natural production. And I think historically, as people like safety pointed out, that level is something like one and a half to 2% inflation of gold per year hypothetically. But what happens in the fiat world, once the government co-ops the money and puts in its monetary interventions such as legal tender laws, central banking, the lender of last resort, you know, implicit and explicit bailout guarantees, all of these things that essentially cause what calls a race to the bottom that they essentially create this scenario for fiat inflation, which now we get a bit more technical and it's kind of how much of that is directly printed by the central bank versus how much of that is printed by the commercial banks, but in a central banking regime in a fundamental fraction reserve banking regime where this is permitted. And so historically, we find the inflation rate in that kind of scenario to be a lot higher. That's more like 7% or 8% or depending on what country, you know, you might be paying 15% or 20% in a kind of inflation hidden tax and that's fiat inflation. Well, and so one thing that commercial banks do within that central bank regime as you describe is they issue fiduciary media or what we would call unbacked money substitutes and the extent to which they do this depends on a lot of things. It depends on their capital constraints. It depends on the lending market. It depends on the credit worthiness and demand for credit borrowers and that sort of thing.  But we have something even beyond that where a degree of money-ness, I guess we could call it, it becomes in a de facto way assigned to things even like U.S. Treasury debt or maybe certain Goldman Sachs bonds. I mean things that almost seem so liquid that they become money substitutes of a sort. And so when we start to think about the monetary base or M1 or M2 or what we used to call M3 before the Fed stopped tracking it. In fact, this sort of ticking time bomb out there in the form of claims to real money which cannot be satisfied might be far, far larger than we imagine. And we've had glimpses of this with collateralized debt obligations, tranches sliced up around housing for example in 2008. And today we have a word for the shadow banking. And so if you listen to people like Caitlyn Long, the real nuclear weapon out there might be all of this stuff that is awfully akin to money out there but which doesn't have any real money underlying it. Precisely. And I think it's what we have to look at is the overarching conditions under which we live under. It's that because of these initial conditions that the government has done because the government wants to control the money, right? Legal tender laws, blah, blah, blah. We live in this world of cheap debt. And I think the system evolved in that way or it kind of grew up in that way. And because of that, now we have these huge markets for debt and for bonds. And that obviously helps the government because the government relies on that for debt funding as opposed to fully tax funding everything. And then as you were saying, then we've got this whole weird, crazy scenario where there are like corporate treasurers out there who are looking out for these kinds of risks and thinking, well, maybe I'm better off. Even though I know I'm going to lose money, I'll hold some US treasuries because that is that for me is quite unquote safer than leaving it in these banks where the deposit guarantee only goes up to a certain level. So it's kind of a it's a confusing and very technical world with all these weird little nooks and crannies. And so what we historically thought of is, okay, it's just M zero and then it pyramids up and M one and M two. And it's like now it's more just like there's all this money out there and people like Jeffrey Snyder and Caitlyn Long and others are kind of helping point out that, well, maybe the Federal Reserve doesn't actually have the best picture of what's going on out there because there are people trading, if you will, a synthetic dollar around and about. And so I think all of this is, we've been put into this scenario, I think under a natural order of, you know, economics and money, we would, I think, tend towards a full reserve system where people would demand higher level assurances over their money whereas now, because we've been pushed into this fractional reserve system and part of that was government influence right it's legal tender laws it's forcing us to treat these inferior. As you said for do you share a media, these substitutes for money that they're not as though they were real US dollar. And so I think it that it we've been pushed into this system because of that and that's what we've that's now why we're seeing this kind of outgrowth of excesses of that system. Well, imagine that we have all this weaponized unbacked money out there. And imagine furthermore that we don't even know the number because some of it is sort of traded privately and it's not easily accessible, you know, in the Wall Street Journal or something to figure out where it all is. And so some of the estimates of total worldwide debt sovereign otherwise might in that sense be a skew because some of this money, some of these money substitutes are basically claims that look a lot like debt. So you put it all together and you say what if there was a big crash someday and the US dollar lost its status and what would things look like afterwards. You recently had a guest on your own show, an important guest, a famous guest, Niall Ferguson, and he laid out some monetary scenarios, one of which would be, you know, some sort of ugly hyperinflation and a few others. One that he didn't mention and Halsman alludes to some sort of international system potentially, you know, that would replace Bretton Woods or post Bretton Woods in his book here. But I'm sure you've heard of the idea of the IMF becoming the backstop to central banks. So just as central banks were originally designed, at least allegedly, to back up commercial banks, then there would be a central bank for central banks and in under the auspices of the IMF. And they would issue what are called SDR special drawing rights, which at least at the beginning and they exist already. But at least under some new regime would consist of a basket of currencies to make a bunch of countries sort of comfortable and willing to go along at first. Maybe it would contain the U.S. dollar and the Chinese Yuan and the Swiss franc and maybe it would contain a few commodities like gold and men's solely over time. These SDRs would sort of become their own money. They would take on money-ness characteristics without having necessary underlying value. And this is something people like Jim Rickards have talked about and you can say it's slightly conspiratorial or you can say, no, no, no, that's exactly what world leaders will rush to and clamor for. If there is some sort of currency breakdown.  But apart from that, what do you think about the concept of internationalization of currencies? Because now we have sovereign countries issuing their own currencies, their own debt. And since everybody's got their own self-interest, you could see a really nasty global worldwide recession being used as justification. I'm going to say, no, no, no, we need one overarching monetary body. Right. I think if it was going to be that sort of system, yeah, I think this whole IMF SDR thing, maybe that's a possibility. I see it like a lot of central banks around the world now are experimenting and doing trials on this idea of central bank digital currencies. So potentially they try to make an SDR that is some kind of CBDC and they try to placate the different powers of the world, essentially based on their political or military might and say, OK, USA or OK, China, you get this much of the basket and to try to give them some level of power at the, give them a seat at the table and so on. I think maybe that's if anything, that's kind of like what happened with Facebook and Libra and how they sort of got really smacked down hard because they were essentially challenging the power, openly challenging the power of governments and their money. So I think potentially the CBDC kind of thing is an avenue that they try to go down. I think what we will see, though, and I think this very much reminds me of a point I read from Hunterman Hopper's article, how is fiat money possible? Because I think he takes it back to saying, well, hang on, why do we use money? We use the most saleable one. And if we were to use a basket of commodities, then the basket of commodities would not be saleable as the most saleable one inside that basket. So I see it like we're probably likely to just limp along for a little while on the US dollar for a while until the world chooses something better. But I think, of course, the governments around the world will try. I think they will try central bank digital currencies. I just see it like we're just going to kind of limp along for a while. And I don't know if it will be like a big, great crash. I just think it would just be like a Japanification of the world that we just kind of... Because I guess the way I see it is, and I'm pretty sure you would agree, is that many of the governments and central banks have painted themselves into a corner. They, under their own kind of frameworks, theoretically, they should be thinking, oh, we need to raise the rates, but governments are in massive, massive debt. They can't afford that kind of thing. So the best they can do is to try to just eek it out for as long as they can. And I think that's probably the reality for a lot of this is we might think, oh, look, this system is unsustainable. It's going down, but we don't know when it's going down and they can just kind of eek it out for as long as they can. Yes, I think that's probably a likely scenario that we all just become zombies like Japan and people would sort of get used to the idea that you don't earn interest on money. And we would sort of limp along and we'd have declining economic fortunes. And maybe all of that could just happen slowly over decades so that we don't scream too loudly. I hope that's not the case here. It's frightening. But what this book is about, I guess, on some level is that all of this makes us worse people. It makes us present oriented. It makes us gloomy about the future. It makes us not save and put away for future generations. And you don't even have to have a family. You just understand civilizationally, we're all standing on the shoulders of previous generations that helped create all the material wealth and abundance that those of us who are fortunate enough to live in places like Australia and the United States enjoy every day. And the idea that that material wealth will continue to organize itself around us, regardless of incentives, regardless of the quality of money, and that we can degrade our money without degrading ourselves societally, I think is just crazy. You're right. And I guess to put it simply, regress is possible. I think we have become so, what's the word, entitled, and we have become so as a society, right? We've become so entitled and we think everything is just going to be progress. There's always this kind of upwards arc of history and so on. I guess that's more of a progressive idea. But still, people just do not appreciate how fragile society can be and how things could break down if we don't appreciate the things that make our humanity great and our ability to trade and transact and to save across time and space and all of these things. And Dr. Holzman points out in the book that there's spiritual casualties of fiat inflation. And he points out that it changes the way people act. It makes people act in a more materialistic way. It means they are less able to perhaps care for their own families and societies. And to some extent, that makes them less of an independent man able to help their family and friends. And they become more dependent and they become more submissive. And they become more, you know, pliant and willing to do what the state and docile. And perhaps that is also part of the reason we have not seen as much of a pushback against all of this, you know, hysteria 19 government stuff is that people have had their financial self-reliance taken from them. Now they are more dependent on the being in the good graces of the people around them and they don't want to say anything bad in case they get fired or in case they, you know, lose their ability to feed their family. And so there really is this kind of spiritual and cultural consequence of inflation. And I think Giddo Holsman does a great job in this book trying to tease that out and explain that to people because I think to a person in the mainstream media, they may look at this and think, what do you mean like fear money can cause degenerate behavior? But it really can if you actually look through and trace through the implications of fear money. Well, we saw an example of that on this show just a few weeks ago when we covered Adam Ferguson's When Money Dies. And he talks about the period of hyperinflation of Weimar Germany, Weimar Germany and the, you know, the depredations that caused the privations that caused the rape, the prostitution, the, you know, the theft, the creating orphans. I mean, it was really something and we tend to view central bankers, Stefan, as these sort of dry technocratic guys who went to Wharton or something or Oxford. Yeah, yeah. And, you know, we tend to think that they're just dialing knobs around and looking at spreadsheets all day and that they exist in an ethical vacuum. Exactly, exactly right. And so I think there really is a moral element to using and promoting sound money. Well, we'll finish with this, the conclusion, the final chapter of this book is just fantastic. And again, Halsman, who happens to be a devout Catholic, you know, he quotes John Paul II here with a really great definition of capitalism. And I just want to, I'm just going to read John Paul II's quote here because I think it's great. Because oftentimes even people in the libertarian sphere say, no, no, no, we shouldn't use the term capital. That's a slur. Marx created it. It implies the untoward accumulation of capital in the hands of a few people. Whereas, you know, Mises used that term to mean private ownership. He used that term to mean social cooperation and markets, that it was really the best system for well-being throughout society. So here's, here's John Paul II. He says, if by capitalism, it's meant an economic system which recognizes the fundamental and positive role of business. I don't think we'd hear Francis say that, by the way. The market private property and the resulting responsibility for the means of production as well as free human creativity in the economic sector, then the answer is certainly in the affirmative. So I thought that was interesting.  He says, that's not what I mean by capitalism. So, you know, it's just, it leads Halsman to say that in this regard, as we have shown, there's no fundamental disagreement between the views of the Austrians and the Catholic moral concerns. So, you know, I guess some people don't want to see that sort of thing in a book about money and economics. I understand that. But the flip side is that I think everything needs to be placed in the context. And you can't understand the history of where we, how we got here without understanding some of the religious and ethical components of, you know, the drove people's worldviews for centuries. Of course, yeah, I think so. And I think we, you know, we grew up in this society with these kinds of values. And this was the way we, this was the, yeah, this is the way it evolved. And I guess, you know, whether you're religious or not, I think you certainly will take a lot from this book. I think even on my reading of it, I really don't see, you know, if you're not a Catholic or not a Christian, that you would still not learn a great deal from reading this book. Well, we're going to leave it at that. Again, ladies and gentlemen, you can find this book at Mises.org just in the search bar type in the Ethics of Money production. It's available free there in PDF form. If you want to purchase it from the Mises.org store, use the code HAPOD for Human Action Podcast and get 10% off. Before we go, I want to thank our guests, the great Stefan Lavera for joining us. Stefan, just real quickly tell people how they can follow you, how they can find you on Twitter and find your podcast. Oh, of course, just look me up Stefan Lavera and my website is StefanLavera.com and thank you very much, Jeff. It's been an honor to chat with you. Same here. I wish you everything for the best in 2021 and I hope Sydney remains a great city to live in. Thank you, Jeff. And same to you. And find more content like this on Mises.org.


Hi, so together with Sunil Boubier we recorded this brief presentation for our 2020 PKC paper, so hopefully it's somewhat watchable. So the context of this talk is integer factorization. As you may know, the best known algorithm when you want to factor a very big integer is the number field sieve. The current record from February 2020 is a 250 digit RSA number. That was factor using the open source software CAD-1FS. So the number field sieve algorithm has different steps. One of the first steps is called the sieving phase. And part of this sieving phase consists of breaking into primes, millions or even billions of, say, medium-sized integers. This step is called cofactorization. And the time spent in cofactorization is rather important. We estimate that it was about one-third of the time for a previous record of RSA 768. So when you want to do that, the usual method that you pick to find those prime factors of medium-sized integers is the elliptic curve method. So I will not enter into the details of ECM by lack of time. But the only thing you need to know to understand the rest of the talk is that the step one of ECM simply consists of computing a very big scalar multiplication k times p, where p is a point on an elliptic curve. And k is a special number. That is the product of all the primes up to some predetermined bound b1. And all the prime, actually, we mean all the prime powers. So as you can see on the example, if we pick b1 is 32, then the scalar k is going to be 225 times 3 to the 3 times 5 squared times then all the primes of b1. So in order to do that, to compute k times p, we can think of two rather naive options. The first one is to evaluate the integer k and then to compute the scalar multiplication k times p. Or we can take the primes one after the other and accumulate the result in the current point. And the best option out of these two is, well, it depends on the way you perform this scalar multiplication, either k times p or the prime times p. So when we want to do that as part of co-factorization in the number of felsives context, what do we have? We usually know that the integer that we want to break into primes have a size of roughly 150 digits. Of course, it depends on the size of the integer you want to factorize using NFS, but this is more or less what you expect. We also know that these integers have no small factors. They have been eliminated by the sieving phase. And usually we expect numbers to have three or four factors. What do we know also is that the bound b1 are usually rather small and fixed. That's important. They can be fixed in your implementation. For example, if you use the Kado NFS, b1 values go from 105 to 8192. So the result is that k, the scalar in all k's for all these b1 values, k is not in advance. So the goal is to design some kind of optimal algorithm for computing k times p for those b1 values. So the first algorithm that used something rather different than the two naive options I mentioned before is due to Dixon and Leistra. Their idea was to regroup some of the primes into what we're going to call blocks for the rest of this talk. In order to reduce the number of addition. For example, in the formula you see that you can write k as a product of some of the products of well-chosen primes. And the best is to show an example. I pick three primes, p1, p2 and p3, and give their hamming weight. Because, for example, if you use the double in algorithm for this kind of application, you know that the number of addition is equal to the hamming weight minus 1. So the first prime has hamming weight 10, the second 16 and the third 11. But if now you consider the product of those three primes, then you can see that the hamming weight of the product is only 8. So it's much more efficient to compute p1 times p2 times p3 and then multiply this number by p, then taking the primes one after the other. So that was the idea of Dixon and Leistra. They implemented this algorithm, but of course finding the combination of all the primes was way too expensive. That's the limitation what they only consider block of at most three primes. Some years later, Boss and Klein Jung proposed a nice improvement. As I just said, it was just not possible to consider blocks of more than three primes. It was way too expensive for practical p1 values. So instead they used the opposite strategy. They generated a huge number of integer with very low hamming weight because they knew that the corresponding scalar multiplication will have a small number of addition. And for those numbers, they checked for smoothness. Let's pick an example with the small value of p1 of 32. The first one has hamming weight 3 and as you can see, if you evaluate the integer that corresponds to this binary string, you can see that it's b1 smooth value, meaning that all the prime factors of this number are less than b1. So we save this number and we hopefully can use it for the algorithm. The second binary string has also hamming weight 3 but this time it's not b1 smooth because one of the factor is greater than 32. So we don't keep this one. And of course we can also consider sine representation as we have with the NAF for example and the third example has hamming weight 2 and is also b1 smooth. So we keep this one. So the idea of Bosz and Kleinum was to generate a huge number of that form, check for smoothness, keep those that were smooth and try to recombine everything in an early optimal way. So another parameter that is important when you implement ECM is which curve model do you want to pick? Well, it's not clear. It depends on different things. We usually have two competitors, the original Montgomery option using the Montgomery curves as different advantages. For example, you can represent the point using only the X and Z coordinate. It has very efficient doubling. You can enjoy tripling if you want. A bad point is that we don't have a usual addition. We only have what we call differential addition. We'll get back to that in a few minutes. Then because of this restriction on addition, the scalar multiplication is also somewhat constrained and we need to generate something that is called LucasChain. On the other hand, Edward's curve has very good arithmetic, doubling, tripling and addition. You can use the algorithm of your choice for scalar multiplication and the best choice between the two is not clear. In this work, we used a theorem that says that every Edward, tweet to the Edward curves, is rationally equivalent to a Montgomery curve. So we try to use the best of both words. So what is the contribution of this work? So as I just said, we try to use a good mix of Montgomery and Edward's curves. And for that, the algorithm works as follows. We start the computation on a twisted Edward curve. At some point, we'll see later, we switch to the equivalent Montgomery curve. And for that, we introduce a new operation that is called addM, given two points in Edward's coordinate. We can compute the sum p1 plus p2 on the corresponding Montgomery curve in x, z coordinate only. And this operation costs only four multiplication. This operation is partial, but that is sufficient for this context. And then we can finish the computation on the Montgomery curve, including the step two of ECN, which we're not going to talk about in this presentation. And then for the scalar multiplication, we have proposed an extension of Boss and Kleinung's algorithm in two ways. The first is with the generation of blocks of various types, beyond the usual enough, and also a better combination algorithm. Alright, so block generation. So in order to take advantage of faster plane operation on Edward's curve, we consider double base expansion and double base chain. In that form, a number is written as a sum of mixed powers of two and three. In the picture below, the dots are represented according to the corresponding powers of two and three. You have the powers of two on the x-axis, the power of three on the y-axis, and each dot corresponds to a term of this sum. And as an example, I give you an integer that can be written as a sum of three terms of that form. And if you use this representation to compute your scalar multiplication, you will need eleven doubling. That is the largest power of two, seven triplings, the largest power of three, and only two addition. And you may need to pre-compute three points. Double base chains are subsets of double base expansion. It's the same representation as a sum of mixed powers of two and three, but you have extra divisibility conditions on the terms. That allows to compute without pre-computing points. And in this example, we have a double base chain with only two terms. That requires twelve doublings, eight triplings, and only one addition. So that's for Edward's curve. On Montgomery curve, we do not have a classical addition. We only have a differential addition, meaning that if you want to compute p plus q, you need pq, but you also need a difference between p and q. And if you want to use this differential addition to compute your scalar multiplication, you need to use what is called Lucas chain. This is exactly a chain that satisfies the above condition. A term in the sequence is defined as the sum of two previous terms, but you also need to ensure that the difference of these two terms belongs to the chain. One way to produce Lucas chain was proposed by Peter Montgomery in the PROC algorithm. I'm not going to explain the PROC algorithm here, but you can see this algorithm as a big switch algorithm. You have a rule A, given according to some invariance, and you can have a corresponding sequence of operation, and then rule B, etc. And you have a sum number of rules. The way we produce Lucas chain in the same vein as before, we simply generate short words on the alphabet A, B, C, F, 2, J that correspond to the rules. That means that we generate some short Lucas chain, then we compute the corresponding integer and test for smoothness as we did before. So for the overall block generation, we use a strategy that was similar to bus and client new by considering the reverse approach. We consider a very large number of blocks of each type, double base, expansion, chains and Lucas chain. We eliminated the blocks that did not correspond to smooth integers. And also if, for example, we had a block of a double base expansion and a double base chain that represented the same integer, we only kept the double base chain because we had no pre-computation involved. So in total, we generate quite a lot of numbers, as you can see on this table. And it took about 10,000 hours of intensive computation to produce all these blocks. When you compute such a big amount of objects, especially computational, combinatorial objects, you want to make sure you do not compute the same object twice. So that's what we did and no block was generated more than once. So for the rest of the talk and the block combination and the result, I will give the screen to Cyril that will finish his presentation. Thank you. We are now going to see how to use a block that was just generated to compute the scalar multiplication in ECM. So for small value of b1, like in the example b1-32, it's quite easy to find a way to use them to compute the scalar multiplication. For example, by using eight blocks and one block on the one double base chain on the twisted order squares and seven Lucas chains on the corresponding Montgomery curve. So the goal here is to find, given a b1 value, the subset of all the generated blocks with the smallest cost such that the product of the integers represented by those blocks is exactly k, which means that the subset of the block allows us to compute the scalar multiplication in ECM with the given value b1. So here by the cost, we mean the sum of the arithmetic cost, which is just counting the number of multiplication and squaring that are needed. In their paper, bus and canyons propose a greedy algorithm to combine the blocks. Their algorithm is very fast. It generates good solutions, but not optimal ones. In order to do that, they use two values to choose the best block that they add in the current solution set. So the first value is the ratio between the number of doubling and the number of addition. And the second value is a score function that they design to fiver blocks with a large number of large factors. They also propose a randomized version of their algorithm in which they only choose the best block with a given probability or else they choose the second block or the third block, etc. It's all of them to generate lots of solutions and to keep the best one. When we try to adapt bus and canyons algorithm to our setting, we encounter multiple problems. First, we look at the ratio between the number of doublings and the number of addition that they use to sort the blocks. The first problem was that we use triplings. So we need to add this in the ratio. But also, we use both twisted dwarf and mongom records, where the cost of addition and doubling are different. So it was not easy and straightforward to find one single value to replace this ratio. We also observe that the score function does not always achieve its goal to fiver blocks with large factors. We were able to find examples where their score function was fivering blocks with smaller factor or less factor. Like the ratio between the number of addition and the number of doubling, we were not able to find a suitable replacement for the score function. We first try to sort the block by arithmetic cost per bit, but it does not yield better result. Here, by arithmetic cost per bit, we mean that we divide the arithmetic cost, the number of multiplication and squaring needed to compute the block, by the number of bit of the integers that the block is representing. So we wanted to do something more exhaustive, but a complete exhaustive search is totally out of reach, even for small b1 values. So we try to reduce the enumeration, the exhaustive search. So first, we shrink the enumeration depth by using an upper bound on the number of blocks in a solution set. So here we lose solutions, but we hope that the best solutions and the good solutions have a small number of blocks. Then we find a way to reduce the enumeration width at each step using the knowledge of an upper bound on the minimal cost. Using this, we do not lose any solution. First, note that an upper bound on the minimal cost can be found with any method, like Boston-Clenion's algorithm or the double-node method. Using this knowledge, at each step of the exhaustive enumeration, we are able to compute an upper bound on the arithmetic cost per bit of a block that can be added to the current set if we want to obtain a solution with a smaller cost. So now we can describe our algorithm. First, we sort the set of all generated blocks by increasing value of the arithmetic cost per bit. Then we enumerate depth first all subsets of blocks of size less than a given bound. At each step of the enumeration, we use the upper bound on the arithmetic cost per bit to discard inadmissible blocks. The bound on the arithmetic cost of the best solution can be updated throughout the algorithm, which means that as we obtain better solutions with smaller costs, we obtain a sharper bound for the arithmetic cost per bit at each enumeration step. Now let's look at results that we obtained with this algorithm. First, let's look at the best solution that we found for B1 equals 105, which is the smallest B1 value used by CADO and FS during the cofactorization step. Here we can see that with this solution, we use both the twisted Edwards curves and the Montgomery curves. We use double base chain and double base expansion with triplings on the twisted Edwards curves and we use Lucas chains on the Montgomery curves. Now let's compare our results with other implementation of ECM. We looked at the implementation of ECM in CADO and FS, which use Montgomery curves. Then we looked at other implementation of ECM using twisted Edwards curves like EECM and PFQ or ECM at work or an implementation of ECM on Calary. We compare using the number of multiplication needed to compute the scalar multiplication with what we call the arithmetic cost. For all B1 values that we looked at and for all small B1 values, we are always better by a few percent than all the other implementation of ECM. If we look at the graph for lots of B1 values of the arithmetic cost per bit of the solution that we found, we can see that with our method, we always found a solution with an arithmetic cost per bit between 7.6 and 7.7 and all the other solutions have higher arithmetic cost per bit. We then implemented our method in CADO and FS and we rerun some parts of the co-factorization step for RSA 200 and RSA 220. We observed that with our algorithm for the scalar multiplication and ECM for the co-factorization step, the time decreased by 5 to 10 percent, which correspond to what we estimate from our theoretical results. To conclude, in this talk, we proposed a new and better implementation of ECM in the context of NFS co-factorization. Following the idea from Dixon and Lengstra and Boston-Clanion, we generated blocks of various types, like double-base chains, double-base extensions and look-as-chain, and we combined them using a new quasi-exhaustive approach for values B1 values. Our ECM implementation used both twisted dwarf curves and Montgomery curves, used a new addition and switch operation to go from two points in a twisted dwarf curve to their addition on the Montgomery model, and used not only NAF, but also double-base extensions and chain, and also PROC generated look-as-chain. All our results and our source code are available at the following address. Thank you for your attention.


Okay, I think this should be a relatively short video, but it's important to get this information under your belt before we move forward. I want to talk about describing molecules and describing atoms. So not just molecules, atoms and molecules. And using the symbols for the atoms for describing molecules to other people. So this capital letter X here is supposed to be a generic symbol. So there is no element with the symbol X, so I'm just using that. What I want to tell you is that when you write the symbol for an atom, like we have right here, there are four places where you can put a number next to the symbol. I'm writing four boxes for the four places. You can put a number in the upper left, in the lower left, in the upper right, in the lower right. And those positions, if you put a number in one of those positions, they mean different things. So for example, if you put a number over here, we're going to talk about this in more detail, it more or less means how much the atom weighs. More formally it's called the mass number of the atom. I'm cutting a big corner there, but more or less, if you put a number in the upper left of the symbol of an atom, it's roughly telling you how heavy or how light the atom is. We're not going to talk about this number until later in the course, so you can ignore it for the moment. Atoms can have electrical charges, which we will talk about later this week. And if you want to tell people what the electrical charge of your atom is, you write a number in the upper right. The one that I'm most concerned about now is the one in the lower right. If you put a number here, this number tells you how many of the X atom are stuck to each other, attached to each other. And I'm going to go into a little bit more detail on the next page about what I mean by that. So as an example, I want you to look at this little picture here. This is supposed to be the, let's call it the molecular formula for some molecule. And what it's supposed to tell you is it's supposed to tell you what the different types of atoms there are in this molecule and how many of each one of each type of atom are stuck to each other. So these are all more or less these are pretend names. But I want you to basically, in a moment, I want you to pause the video and tell me what types of atoms there are and then how many of each type you can pause right now. Okay, so the types of atoms that there are here are, there's a Y atom, whatever Y is, we might talk about that later. There's an X atom, there's also a Z atom. So those are all capital letters, which means these are all individual symbols for different types of atoms. And if you want to figure out how many of each one there is, you have to look in the lower right next to each symbol. Now in the lower right next to Z, there's a four. That means there's four Z atoms in this molecule. If you look at the X symbol in the lower right there, there's a two. That means there's two X atoms. And if you look at the symbol for Y, there's no number, no number. If no number is written, the implication is that there's only one of that atom. So there's one Y atom in this molecule. And basically what it means when you smush all of the symbols together and put a number, maybe, in the lower right is that all of these atoms are stuck to each other. So there's one Y atom. There's two X atoms. And there are four Z atoms all stuck to each other in this molecule. This is called a molecular formula. You should understand the basics of how to read it. This does not tell you how the order that the atoms are attached to each other in. All it tells you is that they are stuck to each other. But it doesn't give you enough detail about explaining how they're attached to each other. So keep that in mind. All this tells you is the different types and how many of each different type there exists. So if you don't understand that, here's a slightly different example. This is the molecular formula. This is the molecular formula for water over here. Many of you are probably familiar with this. You might have heard the phrase H2O, meaning water. But if you look at it, there's the symbol O. That is the abbreviation for oxygen. And there's no number in the lower right, no number, which means there's a 1 implied to be there. And if you look at the other symbol, it's a capital letter H, which stands for hydrogen. There's a 2 in the lower right with respect to the capital H. That means there's two hydrogen atoms. So if you see the formula H2O, it means two hydrogen atoms plus one oxygen atom stuck to each other. It doesn't tell you how they're stuck to each other. But all it really does is tell you how many there are and that they are stuck to each other. So keep that in mind. Here's a different practice problem. I want you to look at this. This is a formula of some pretend molecule. It doesn't really exist. I believe all of the symbols are fake. And what I want you to do is I want you to pause the video and basically tell me what types of atoms there are and how many of each type. This is a little tricky. So keep that in mind. You may be stumped. So all right, pause, unpause. Here are the different types. There is usually the way that I ask this to the on-ground students as I say, how many y atoms are there in this molecule? And this is actually a trick question, because there are no y atoms in this molecule. There are y a atoms, however. And the reason why I want you to realize this is just because you see a capital letter y, you have to look to the right and see if there's also a lower case letter. And this is a lower case letter a. So what this is saying is there are no y atoms, because you can't have another atom that starts with a lower case. So the y and the lower case a are stuck to each other. They are the symbol for some atom that has a symbol y a. And if we're counting the y a atoms in this molecule, there are three of them, three atoms. Then I might say how many x atoms are there? Here's our x. There are two of them, so two x atoms. How many z atoms are there? Well, this is a capital Z. There's no lower case letter immediately to the right of the z. So it's just a z atom, whatever z is. There's no number immediately to the right. So there's one. This should say two atoms for x, one atom for z. And then finally, there are r atoms in our molecule. And how many r atoms? There are four of them. So the reason why this slide exists is I want you to realize that if you see a lower case letter in a formula, that means that that lower case letter is part of a larger symbol. So there isn't a y atom in this molecule. There is a y a atom in this molecule, and there happen to be three of them. So in my pretend molecule, there's three y a atoms stuck to two x atoms, also stuck to one z atom, also stuck to four r atoms. So keep that in mind. You should be able to read molecular formulas like this. Oh.