Author: lukas

The best solution I found was:

pip3 install-i https://pypi.tuna.tsinghua.edu.cn/simple the-library-you-want-to-install

Most likely you already read this account in elementary school, for it is perhaps the best introduction to the concept of what is fiat currency and why we might use it. Read it again. It’s incredibly short and captures the idea well which underpins the most powerful political forces today, so this reading assignment is mandatory.

It’s worth pointing out that while Marco Polo hadn’t heard of them before, fiat currencies had been used in China for centuries already, and others had brought this news to Europe. However Marco Polo’s widely read books contributed to everyone finding out about how fiat worked, and thus to the kings and queens of the rest of the world adopting it to their purposes, leading to the rise of fiat empires in which you dear reader are likely a subject. Take a look at the footnotes here for more background on this translation by Henry Yule. Now without further ado:

• 

How the Great Kaan Causeth the Bark of Trees, Made Into Something Like Paper, to Pass for Money All Over his Country

Now that I have told you in detail of the splendour of this City of the Emperor’s, I shall proceed to tell you of the Mint which he hath in the same city, in the which he hath his money coined and struck, as I shall relate to you. And in doing so I shall make manifest to you how it is that the Great Lord may well be able to accomplish even much more than I have told you, or am going to tell you, in this Book. For, tell it how I might, you never would be satisfied that I was keeping within truth and reason!

The Emperor’s Mint then is in this same City of Cambaluc, and the way it is wrought is such that you might say he hath the Secret of Alchemy in perfection, and you would be right! For he makes his money after this fashion.

He makes them take of the bark of a certain tree, in fact of the Mulberry Tree, the leaves of which are the food of the silkworms,–these trees being so numerous that whole districts are full of them. What they take is a certain fine white bast or skin which lies between the wood of the tree and the thick outer bark, and this they make into something resembling sheets of paper, but black. When these sheets have been prepared they are cut up into pieces of different sizes. The smallest of these sizes is worth a half tornesel; the next, a little larger, one tornesel; one, a little larger still, is worth half a silver groat of Venice; another a whole groat; others yet two groats, five groats, and ten groats. There is also a kind worth one Bezant of gold, and others of three Bezants, and so up to ten. All these pieces of paper are [issued with as much solemnity and authority as if they were of pure gold or silver; and on every piece a variety of officials, whose duty it is, have to write their names, and to put their seals. And when all is prepared duly, the chief officer deputed by the Kaan smears the Seal entrusted to him with vermilion, and impresses it on the paper, so that the form of the Seal remains printed upon it in red; the Money is then authentic. Any one forging it would be punished with death.] And the Kaan causes every year to be made such a vast quantity of this money, which costs him nothing, that it must equal in amount all the treasure in the world.

• 

With these pieces of paper, made as I have described, he causes all payments on his own account to be made; and he makes them to pass current universally over all his kingdoms and provinces and territories, and whithersoever his power and sovereignty extends. And nobody, however important he may think himself, dares to refuse them on pain of death. And indeed everybody takes them readily, for wheresoever a person may go throughout the Great Kaan’s dominions he shall find these pieces of paper current, and shall be able to transact all sales and purchases of goods by means of them just as well as if they were coins of pure gold. And all the while they are so light that ten bezants’ worth does not weigh one golden bezant.

Furthermore all merchants arriving from India or other countries, and bringing with them gold or silver or gems and pearls, are prohibited from selling to any one but the Emperor. He has twelve experts chosen for this business, men of shrewdness and experience in such affairs; these appraise the articles, and the Emperor then pays a liberal price for them in those pieces of paper. The merchants accept his price readily, for in the first place they would not get so good an one from anybody else, and secondly they are paid without any delay. And with this paper-money they can buy what they like anywhere over the Empire, whilst it is also vastly lighter to carry about on their journeys. And it is a truth that the merchants will several times in the year bring wares to the amount of 400,000 bezants, and the Grand Sire pays for all in that paper. So he buys such a quantity of those precious things every year that his treasure is endless, whilst all the time the money he pays away costs him nothing at all. Moreover, several times in the year proclamation is made through the city that any one who may have gold or silver or gems or pearls, by taking them to the Mint shall get a handsome price for them. And the owners are glad to do this, because they would find no other purchaser give so large a price. Thus the quantity they bring in is marvellous, though these who do not choose to do so may let it alone. Still, in this way, nearly all the valuables in the country come into the Kaan’s possession.

When any of those pieces of paper are spoilt–not that they are so very flimsy neither–the owner carries them to the Mint, and by paying three per cent, on the value he gets new pieces in exchange. And if any Baron, or any one else soever, hath need of gold or silver or gems or pearls, in order to make plate, or girdles, or the like, he goes to the Mint and buys as much as he list, paying in this paper-money.^[

Now you have heard the ways and means whereby the Great Kaan may have, and in fact has, more treasure than all the Kings in the World; and you know all about it and the reason why. And now I will tell you of the great Dignitaries which act in this city on behalf of the Emperor.

• 

There are two very important factors which make the reveal in this post possible:

1. You won’t believe me
2. You won’t think that I believe it myself

If it weren’t for these things, this blog post would not be here.

• 

Of course we are all familiar with Asimov’s classic novella, widely acclaimed as the best time travel story of all time.

Long story short: the secret society of “eternals” who are capable of time travel which Asimov presents in his classic book “The End of Eternity) (pdf) (epub) is actually a real thing, with some modifications.

The real time travellers themselves are known in the society of eternals as “grandmasters” and have learned through intense study how to spread their consciousness over many variable timelines, enabling the use of other chess matches in other times as endpoints for a projection time travel technique. These guys are really travelling in time.

Unlike in Azimov’s story, it doesn’t appear that these time travellers can move physical goods from one century to another in arbitrage, however the ability to observe and even affect at reality in another time is already quite a shock.

Don’t believe me? Lets start with some incontrovertible facts:

1. Paul Morphy was able to travel to the future and learn chess from Alpha Zero.
2. Technicians in Azimov’s story of the eternal can make small minimal “adjustments” to timelines; Chess masters are told only to make minimal changes to the board without touching anything, unless they are technicians who announce “j’adoube”.
3. Historical scenes which have been “adjusted” are often seen with a chess board in the background.
4. Chess rules seem oddly stubborn to changes over millenia.
5. Timers stuck in predestined timelines are just pawns for the use of masters.
6. The mental projection of a single chess master can spread to allow an entire room or even those in a distant future to participate in the moment of time travel.
7. En Passant. Ok this doesn’t really prove anything but still, it’s kinda time travelly.

Another insight into the workings of this ultrasecretive society of time travellers (described as “eternals” in the Azimov book) comes from the gender inequality in chess masters. As Asimov puts it:

” Could he tell her that women almost never qualified for Eternity because, for some reason he did not understand (Computers might, but he himself certainly did not), their abstraction from Time was from ten to a hundred times as likely to distort Reality as was the abstraction of a man.”

Women are often simply too important in their influence on the future to be taken out of time to join the eternals and their chess time travel.

So that’s about the size of it. Look at some of the pictures of men standing around watching the highest level chess games… you will see it. Why are they there? Why the intensity? The threads of time are being smeared in that location and in effect, a certain kind of time travel I don’t understand is being enabled. The inaction in the present moment enables a smearing of Hamiltonians such the the wavefunctions can tunnel into the less probable tachyonic pathways.

Those who wish to understand further the method of time shifting via multiple lines of game progress are also advised to read Anathem by Neal Stephenson. The Mandela Effect is also relevant in the case of real timeline adjustments. (Since we’re there, lets promote this album.)

For those of you who are interested in more conventional time travelling methods, there is always the option of visiting China to see the future.

The harpers was the nickname of which British football team?

In Brief: A Harper is dedicated to three things:
– The freedom and autonomy of all living things
– The balance between the settled and the wild
– The preservation of knowledge

In short: we found this pamphlet discarded in the wild, here it is.

A “low protein” experiment on 3 million subjects, from Denmark 1920, M. Hindhede, Journal of the American Medical Association

hindhede1920

Download PDF

powers-of-2-flash-cards-final-1

How well do you know your powers of two? You gotta at least know the first ten of course. The first twenty is quite good. The first thirty? Better than me.

Print them out, label them, and go study up! The 2048 card is only there because there’s an extra spot to fill, when I have made these flash cards in the past we only went up to 1024.

Enjoy!

(By request, from Dmitry Orlov, reblogged here without apology or permission. Go buy his books or support his blogging on boosty, or feel free to complain about the errors in his opinionated prose on your own pages or in the comments)

• 

Many people around the world gaze in wonder and amazement upon the assortment of geriatrics atop the great American pyramid of power—the withered witches Nancy Pelosi (82), Maxine Waters (83) and Dianne Feinstein (88), the living cadavers Chuck Grassley (88), Jim Inhofe (87), Richard Shelvy (87), as well as quite a few others, and the obviously senile Joe Biden (80) who sits atop it all. How does a pile of oldsters, all of them obviously well past their prime, manage to control a great big empire, the biggest (strictly in budgetary terms) military power on Earth and the sacred keeper of the Holy Dollar Printing Press?

The people old Biden commands aren’t spring chickens either: Lloyd Austin at the Pentagon is 69, Janet Yellen at the Treasury is 76. If you look at the various powers behind the throne, there’s the Yoda-like Kissinger (99) and the moneybag George Soros (92).I don’t mean to be ageist, but it is simply foolish to ignore the toll time takes on our brains, as well as the rest of our bodies, as we age. It is not just our limbs that become less flexible (check if you can still touch your nose to your big toe) but our thinking becomes ossified as well. Our learning ability dwindles over time: short-term memory shrinks, long-term memory decays and receptivity to new concepts and ideas declines. We become emotionally attached to the past, comforted by our memories, shocked by an increasingly unfamiliar present and fearful of an unpredictable future.The political science term for such a system of government is gerontocracy. It can take many forms.

Its most benign form is the council of elders found in many traditional societies, who accumulate authority through experience and reputation and wield power through the unconditional respect that must be given to old people in traditional societies. In places where centralized authority is weak, repressive, remote or nonexistent, tribal elders are often called upon to help resolve conflicts that would otherwise give rise to violence, and political authority naturally accrues to those with a successful history of conflict resolution.

Obviously, this is not the case in a young country like the US: 236 years is a blink of an eye in historical terms compared to 6000 years for India, 4000 years for China, 2500 for Persia and 1000 years for Russia. Nor is gerontocracy a natural outcome for a system of representative democracy: why would young people ever choose their great grandparents to be their elected representatives? Also, why would crusty old greyhairs be a natural choice in a country undergoing rapid change that in a single generation experienced the end of the Cold War, the rise of new China and Russia, the development of the internet and now the proliferation of artificial intelligence applications and robotics? Obviously, something has gone seriously wrong with the succession of political authority in the US if old people can’t retire from power and younger people aren’t allowed to advance and take their place.The most malignant form of gerontocracy is rule by an oligarchy of the aged. Imagine a small clique of elderly men and women tenaciously clinging to power, protected by a powerful police state and many layers of yes-persons (the woke version of yes-men), shielded from any negative or unexpected news that might undermine their already shaky grip on reality. This characterizes the current state of the American democracy reasonably well, but leaves some questions yet to be answered.

Such as: Why are these oldsters afraid to retire? Why aren’t younger people allowed to take their place? How distorted is their image of the world and what are the consequences of that? and, finally, How long can this possibly go on and how is it likely to end?Starting from the end and working toward the beginning of this list of questions, we have the wonderful and relatively recent example of the slow decline and sudden fall of the USSR. World War I exposed the rotting hulk of the Russian Empire and its dysfunctional monarchy was replaced with a bourgeois democracy which failed spectacularly within half a year and was replaced by the Bolsheviks, who were Marxist communist revolutionaries. A civil war ensued, which the Bolsheviks won. It then fell upon Stalin to quell the revolutionary fervor of Trotsky and his followers, mostly by simply having them all killed, and to reorient the ideology from world revolution to building socialism in just the one country he ruled. In this he succeeded beyond anyone’s wildest imagination: industrialization, World War II victory, the atomic bomb, the space race and various other stunning Soviet achievements are mostly to his credit. But he certainly wasn’t picky about his methods—he didn’t have that luxury—and after his death this allowed his legacy to be very much tarnished by the likes of the very stupid and incompetent

Nikita Khrushchev and the compulsive liar, eclectic prose stylist and anti-Soviet propagandist Alexander Solzhenitsyn. The Soviet system, although effective for its time, had a congenital defect: it had no ability to renew itself. After Khrushchev was summarily dismissed while on holiday came the overly cautious Brezhnev who opposed even the most necessary reforms. Then came a procession of near-corpses: Andropov with his faulty kidneys and his insane wife; Chernenko who wasn’t quite alive throughout his 13-month term in office. And then came the young, charismatic, popular Gorbachev who destroyed the country in five years and is now the most reviled person in all of Russia, comparing favorably only to Hitler.

I will spare you the thumbnail sketch of American history and simply note that the US went from a post-World-War-II industrial powerhouse with top-notch science and engineering to a country full of ignorant, lazy, slovenly people that just prints money, scares the world with its aircraft carriers into using that money for foreign trade, and imports most of what it needs, including intelligent, educated people. And now the money-printing business is failing too, with the share of the USD in international trade having shrunk from nearly 100% to barely a third. But the crusty old gerontocrats don’t know that the world has changed and the yes-persons who surround them won’t tell them that the money-printing affair is almost over, that the aircraft carriers no longer frighten anyone and that the intelligent, educated people are leaving.Reasoning by analogy, we might think that once Americans manage to get someone young into the White House, it will take five years for the USA to collapse. Supposing Joe Biden croaks tomorrow, how long would it take his VP Kamala Harris to destroy the country? She would have two whole years to do it; would she manage? No wagering, please! Instead, let us answer the other questions.Why are the American gerontocrats so tenacious in clinging to their offices even as they struggle to fight off Death’s cold embrace? Why were the Soviet gerontocrats so loathe to let in new blood by retiring? Perhaps it was because they and their families enjoyed lives of exorbitant privilege, walled off from hoi polloi in special compounds. They had their own special apartment buildings, clinics, hospitals, sanatoria, schools for their children and shops in which they could buy luxury goods, living in a different universe from the citizenry of their land. Perhaps it was because this entire edifice of exorbitant privilege was build on a foundation of lies, corruption and theft that negated the very premise of a just and egalitarian socialist society. Or perhaps it was that the new blood would naturally have to be their own flesh and blood—their own precious children, that is, to whom would go all the cushiest jobs, except that their children weren’t turning out so well. They were unfit to serve in any capacity, being a special-bred race of overprivileged, pampered, psychopathic assholes. And so their only choice was to cling to power until death’s kiss because the alternative was the kiss of death for the entire Soviet institution—as it in fact happened.

It’s not that unusual in countries around the world for the new president to be the son of the old president. In Syria, when old al Assad died, young al Assad took his place; in North Korea, the great leader Kim Il-sung was succeeded by his equally illustrious son Kim Jong-il, who was succeeded by his grandson Kim Jong-un, who isn’t turning out to be too shabby either, what with his nuclear-tipped hypersonic missiles that can hit California (whereas the US ain’t got none). And let’s not even bring up Muḥammad bin Salmān Āl Su’ūd, who is quite a lively character too; he is there because his country is a kingdom in which his daddy is king. But that sort of family succession works well in honor-based polities; in privilege-based polities like the USSR and the USA, that just doesn’t work.

Imagine Hunter Biden strolling into the Oval Office, crack pipe in his teeth and a couple of underage Ukrainian prostitutes in tow, ready to accept lavish presents from foreign officials in exchange for huge chunks of the American pie. Imagine his crackhead buddies infesting the halls of Congress and enriching themselves through insider trading by buying defense company stocks the day before they sign huge defense contracts, then selling them the day after and pocketing the difference, then getting massive kickbacks from the defense contractors via their employees’ political campaign contributions—all perfectly legally, by the way! Imagine the State Department and the Treasury being restocked with cousins and uncles of the Ukrainian prostitutes in exchange for some very special, extra-kinky bedtime favors.

Mind you, all of these things are happening even with the old guard still in office—the giveaways of huge chunks of the American pie, the insider trading, the kickbacks, Ukrainians all over the place and all the rest—but with the difference that the old guard knows how to be secretive and cautious and how to hush things up when there are leaks, which are traits that develop with age and experience, whereas the young guard won’t know better than to flaunt their wealth and privilege, party like there is no tomorrow (which for them there probably won’t be) and very quickly burn down the house.And that’s the optimistic scenario. The pessimistic scenario, which is similar to what Gorbachev put into motion in the creaky old USSR, is a plague of reformers. The environmentalists would ban all internal combustion vehicles, all power plants and all cows (because they fart). The sound money maniacs would reintroduce the gold standard (only to discover that the Chinese and the Russians now own most of the gold). The libertarians would get rid of fire departments and just let everyone buy their own fire hoses and fire extinguishers. And the wokesters would fire all men who aren’t gay and green-light the careers of handicapped obese black trans lesbians.Now let’s combine the two: the degenerate, sociopathic scions of the old guard usher in the barking-mad reformers as a cover for their crimes. Now they’ll be burning down the house from the top even as the reformers undermine the foundation.

Gerontocracy is bad; but what’s worse is when the gerontocrats start joining the crowd invisible and are replaced by troglodytes of every stripe. The American gerontocrats are all of a single very numerous generation—the Baby Boomers—and they fit quite neatly under a bell curve. If we wish to test this hypothesis, then timing the collapse of the USA is mostly an exercise for an actuary. Perhaps Gail Tveberg the actuary would like to take a stab at it? Let’s ask her.

Sometimes we come across a great paper and we want to share it.

PDF Embedder requires a url attribute music

As you all know, there’s been a problem with disinformation recently. Governments and advertisers are working to protect us from this threat, but none the less the threat exists and we should be aware that dangerous and wrong information exists and can fool us, hurt us, hurt our families, and hurt our countries and the businesses that our country’s leaders have invested in. Hopefully a solution will be found soon that can protect us once and for all from these threats, but for now we have to be on our toes. In that spirit I would like to share a particularly pernicious bit of disinformation, so that you can be aware it exists and be prepared to ban people from your platforms who might parrot it.

Without further ado, here is the pernicious disinformation. It concerns the topic of disinformation.

WARNING: THE FOLLOWING HAS BEEN DETERMINED BY AUTHORITIES TO BE DISINFORMATION ABOUT DISINFORMATION

The idea is simple, it is that learning new things can sometimes be good. It could even save your life. Once we accept that learning new things might be OK, we can then realize that these new things once were not yet learned, which means these things were not already in our belief system. These things were disinformation, in the context of what we knew at that point. Every major advance in any scientific field began its life as disinformation. For example, Boltzmann went to his grave with his atomic theory of gases still mostly banned and considered as disinformation. After all, “everyone knows” that the ideal gas law and the attributes of a gas such as pressure and temperature are the final story, as science confirmed, according to authorities at the time. Today Boltzmann’s atomic theory is considered correct, because it got by some of the filters and fact checkers **, which weren’t very advanced at the time.

Anyone who hopes to survive, as an individual, as a family, as a company, as a country, as Gaia (life on Earth), must be sure to often expose themselves to disinformation. Disinformation is the only hope to adapt, to be aware of new threats, and to remain competitive with others who are learning and adapting. It also can teach us what kidn of nonsense people are up to so we can safely ignore it. To eliminate all disinformation would be to set ourselves permanently in whatever existing paradigm we have at the moment, which probably isn’t 100% perfect in its extrapolations and interpolations of the infinite world based on a limited past set of finite observations. Sure, disinformation is likely to often be wrong, or worse (like trolling) but it also has the potential to very occasionally contain an important lesson. We have especially learned this in the last few years, as some censored information wound up a year later as square in the middle of overwhelming scientific consensus.

If we are intellectuals, we need to recognize that intellectual activity must stand on a foundation of humility, of recognition that our own understanding isn’t perfect and so we are willing to wade through the sewer of disinformation and hope we can find some new viewpoint worth seeing. Disinformation might not have a place everywhere but it is absolutely essential to learning and survival. Seek it out and revel in it!

END DISINFORMATION

Wow, what a load of garbage eh? Imagine being so intellectually weak that we would openly admit to maybe not understanding something completely. That is simply not an option in today’s competitive world in which we have to move at the pace of science to understand what is taking place in the market.

We must show strength and not allow anything at all to get past our defenses for our carefully constructed and perfect standard model ™, which after all is what our scientific history, all the work of our ancestors, has produced! Defend it to the death! Don’t waste your time looking at anything other than material declared to be in perfect agreement with what authorities have determined to be true! You could be corrupted or worse, sent to the camps. Epstein killed himself! All medical products are safe and effective! War is good for the economy!

Alert! The ministry of disinformation has determined that this entire blog post is now considered misinformation, and we are not talking about a beauty pageant for the IT industry. We are talking about misinformation on the topic of what is disinformation about disinformation. This domain has been seized. Be aware that as someone who has read the material herein, your assets are subject to confiscation by agents of the disinformation protection board.

**

As a bonus this week we are going to provide a FactCheck ™ free of charge! We are going to check a statement from Paul Craig Roberts:

” In my opinion, “fact checkers” are unintelligent people devoid of integrity who are hired to support official narratives by stamping out truth and dissenting opinion. Who checks the “fact checkers?” There is no reason to trust a “fact checker.” Anyone can set up a “fact check” site to protect any material or ideological interest from examination. Note that “fact checkers” appeared only after the official narratives became so blatantly false that they had to be protected from examination. Never before did we have an industry of censors employed to protect official narratives. “Fact checkers” are the true enemies of truth.”

Our fact checkers at SaulTheory have checked this statement carefully and determined it to be: False.

(A naive introduction to reversing ECDSA)

We are of course familiar with the millennium problems from the Clay Mathematics Institute. Seven math problems were given, for which a suitable solution of any problem would yield a one million dollar prize. This was by most accounts a lot of money back at the turn of the century.

Great math problems, and there’s lots we could say about each of them here. However we aren’t going to talk about these now, instead focusing on a problem for which the solution looks even more lucrative. A solution to this other problem we focus on now would open up the public ledgers of cryptocurrency to immediate compromise, allowing an attacker to slowly drain the accounts which have a current value of somewhere around a trillion dollars. That’s a million times larger than the Clay Math prize, and hey six orders of magnitude is a lot even among friends so maybe we should take a look, what do you think?

Obviously it can’t be as easy as it looks, as millions of people wouldn’t all be using this system as a safe store of value if breaking it were easy to do. Also the notation is deceptive, as it isn’t a standard multiplication which gives us the public key, but an elliptic curve operation more akin to modular exponentiation, making the goal of our problem more of a discrete logarithm.

The public key Q is determined by Q = d X G, where d is the private key (which is chosen a random number) and G is the generator point. The trillion dollar problem is: can we invert this and determine the private key d by solving d = Q / G ?

To see exactly what’s going on here, lets look at some python code.  

Pcurve = 2**256 - 2**32 - 2**9 - 2**8 - 2**7 - 2**6 - 2**4 -1 
# The proven prime

N=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 
# Number of points in the field

Acurve = 0; Bcurve = 7 
# These two defines the elliptic curve. y^2 = x^3 + Acurve * x + Bcurve

Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424
GPoint = (Gx,Gy) 
# This is our generator point. 

privKey = 0xA0DC65FFCA799873CBEA0AC274015B9526505DAAAED385155425F7337704883E #replace with any private key

def modinv(a,n=Pcurve): 
    lm, hm = 1,0
    low, high = a%n,n
    while low > 1:
        ratio = high/low
        nm, new = hm-lm*ratio, high-low*ratio
        lm, low, hm, high = nm, new, lm, low
    return lm % n

def ECadd(a,b): 
    LamAdd = ((b[1]-a[1]) * modinv(b[0]-a[0],Pcurve)) % Pcurve
    x = (LamAdd*LamAdd-a[0]-b[0]) % Pcurve
    y = (LamAdd*(a[0]-x)-a[1]) % Pcurve
    return (x,y)

def ECdouble(a): 
    Lam = ((3*a[0]*a[0]+Acurve) * modinv((2*a[1]),Pcurve)) % Pcurve
    x = (Lam*Lam-2*a[0]) % Pcurve
    y = (Lam*(a[0]-x)-a[1]) % Pcurve
    return (x,y)

def EccMultiply(GenPoint,ScalarHex): 
    ScalarBin = str(bin(ScalarHex))[2:]
    Q=GenPoint
    for i in range (1, len(ScalarBin)): 
        Q=ECdouble(Q); 
        if ScalarBin[i] == "1":
            Q=ECadd(Q,GenPoint); 
    return (Q)


PublicKey = EccMultiply(GPoint,privKey)
print "the private key:"; 
print privKey; print
print "the uncompressed public key (not address):"; 
print PublicKey; 

The first few lines here are just defining the elliptic curve parameters (in this case the ones used by bitcoin often referred to with the cute natural name of “secp256k1”, k for Koblitz), and declaring a private key which we will use to create the public key.

The function EccMultiply is the one which we need to reverse to qualify for the prize. The first thing we notice there is that it uses the “double and add” algorithm to compute the multiplication. This EC multiplication is nothing other than the repeated “adding” of GPoint to itself privKey times, as we would expect from the word “multiply”. However, privKey is a large number and so it’s better to use an algorithm that runs with fewer steps, just as we do when multiplying numbers with paper and pencil. For reversing this, we’d also better not have to do anything privKey times. It could be that another multiplication algorithm could be taken as a basis for our analysis to solve the problem, so it’s worth noting that there is no “best algo” known for mulitiplication in general. For now lets just look at reversing the double-and-add algo.

Another observation is that as we step backwards through EccMultiply we are going to need an EccHalf and an EccSubtract function. Lets just assume we have these in hand, and ignore for now the fact that these are not going to be unique (as EccDouble and EccAdd both have modular operations, their inverses are likely to be multi-valued functions). We can proceed then with our “half and subtract” approach for creating our trillion dollar EccDivide function.

The goal in the half-and-subract algo is to wind up at the end, after carefully choosing each binary digit of our reconstructed privkey, and halving or subtracting at each step accordingly, with exactly the generator point G. The trouble is that we don’t know until the end if we have chosen any digit correctly, and so it looks like we will need to perform this algo roughly privKey times which is of course untenable.

Some hope can be gained by considering that we can work from both sides of the digits of privKey at once, with a “meet in the middle” approach. We can e.g. first do half-and-subract 2^128 times, building a tree database of the results, and then work from the generator point doing double-and-add until we (hopefully) reach a match in the center as we compare our double-and-add result at depth 128 to our database of half-and-subtract results at depth 128. This is an absolutely enormous reduction in run time, however it leaves us still requiring on the order of 2^128 long memory addresses, 2*2^128 ecc operations a similar number of hashtable lookups. Still untenable with today’s hardware, even on a global collaborative scale. We are talking something like quadrillions of petabytes here.

If we step back from this problem, we see another potentially useful observation, that there is a potential mismatch in the keysize from the private key to the public key. It is entirely possible for a “key collision” to occur where more than one private key yields the same public key. This is especially true because the public key need not be the verifying item but rather the hash of the public key (as in the bitcoin address) must be matched. This potentially opens up a window for our algorithm, IF we could choose the eccHalf and eccSubtract results carefully to construct a lucky collision. Unfortunately hash functions are even more difficult to reverse or gain information from than ECDSA operations, and so it looks like we are again stuck with what amounts to a brute force method.

With that extremely naive introduction to the problem of reversing ECDSA, lets take a look at how the signatures are verified to see what insight we can gain:

print; print "******* Signature Generation *********"
xRandSignPoint, yRandSignPoint = EccMultiply(Gx,Gy,RandNum)
r = xRandSignPoint % N; print "r =", r
s = ((HashOfThingToSign + r*privKey)*(modinv(RandNum,N))) % N; print "s =", s

print; print "******* Signature Verification *********>>"
w = modinv(s,N)
xu1, yu1 = EccMultiply(Gx,Gy,(HashOfThingToSign * w)%N)
xu2, yu2 = EccMultiply(xPublicKey,yPublicKey,(r*w)%N)
x,y = ECadd(xu1,yu1,xu2,yu2)
print r==x; print

Here the functions have been redefined to accept the points individually rather than as arrays, but they are the same functions otherwise. We see here that we don’t really need to recover privKey completely to obtain our prize, as it is enough to generate a signature s which verifies according to the verification procedure… however it looks like this still requires reversing an EccMultiply.   Back to square 2^128.

We can also see that there may be vulnerabilities here in the choosing of the random numbers, the one which is the privKey and the one which is used in the signature algorithm. If either of these are not random enough, one can greatly limit the search space. However that’s boring and old hat, even if it has netted quite a few folks the contents of someone else’s wallet, it isn’t enough to claim our trillion dollar prize.

It does appear at this stage that simply waiting for the dollar to be worthless, making a trillion dollars easy to obtain, is going to be far quicker than any brute force code breaking ECDSA. However, there’s no proof of this, and so a clever reader might just be the one who does figure this thing out and claim the prize. Stranger things have happened. Good luck!