brute-forcing public keys at amazing speed 2.2 PH/s on CPU [malware warning] - page 2.

MrFreeDragon

sr. member

Activity: 443

Merit: 350

Quote from: arulbero on April 29, 2020, 03:02:09 PM

-snip-
If we suppose that W_100 is = (2^37)*G and T_100 is (2^38)*G, than between T_101, T_102, .... , T_2**32 it is no longer possible to find a single distinguished point with the same coordinate of any distinguished point that lies in W_0, W_1, W_2, ....., W_100. For sure.
-snip-

I am not sure if I understand you correct. But T_101, T_102, ... etc are not the distinguished points, these are jump points. At the start only the jump point table is prepared.
It is not possible to know all the distinguished points within the working range. Distinguished point is a property of point. As soon as the point meets this property, it goes to the hash table:

if tamePosi is distinguished
add (TAME,tamePosi,tamei) to hashTable
if wildPosi is distinguished
add (WILD,wildPosi,wildi) to hashTable

The kangaroo (as wild so tame) will jump permanently by pseudorandom steps from the jump table while reach the Point with patterned X-coordinate (the distinguished point). As reach the distinguished point, this point just saved in the hashtable (kangaroo type, distance, Point) check for coliddion, and kangaroo continues to jump.

Quote from: arulbero on April 29, 2020, 03:02:09 PM

-snip-
It is impossible to get a collision in the path of the same tame kangaroo too, because the same kangaroo cannot turn back, then this is a pseudorandom sequence very particular ...

The same kangaroo can not go back, but due to symmetry point it so not needed.
P=k*G, you know P and you know that a < k < b. Actually Point P'=k'*G is also suitable for us if k' = b - (k-a) = b + a - k, which is also lies in the range a..b

HardwareCollector

member

Activity: 144

Merit: 10

Quote from: arulbero on April 29, 2020, 03:02:09 PM

Yes, this is clear, but these points seem to me not to be really (pseudo)random. There is a order. You can move only forward (from private key's point of view). Therefor many collisions are just impossible to get (instead in the birthday paradox, each new distinguished point has the chance to produce a collision with any previous distinguished point, for example that happens in BTCCollider, because in that case you can jump in any position, you go back and forth across the entire space)

Example with only 2 sequences:

If we suppose that W_100 is = (2^37)*G and T_100 is (2^38)*G, than between T_101, T_102, .... , T_2**32 it is no longer possible to find a single distinguished point with the same coordinate of any distinguished point that lies in W_0, W_1, W_2, ....., W_100. For sure.

Then how do you apply in this case birthday paradox?

It is impossible to get a collision in the path of the same tame kangaroo too, because the same kangaroo cannot turn back, then this is a pseudorandom sequence very particular ...

Maybe the following links will help with understanding the motivations behind the Kangaroo method:

https://web.northeastern.edu/seigen/11Magic/KruskalsCount/Kruskal'sCount.html

https://web.northeastern.edu/seigen/11Magic/KruskalsCount/Pollard.pdf

Pollard’s Rho method is based on the birthday paradox, but the Kangaroo method on the other hand is not.

Tamarindei

newbie

Activity: 17

Merit: 25

Quote from: arulbero on April 29, 2020, 03:02:09 PM

Quote from: MrFreeDragon on April 29, 2020, 02:23:27 PM

Quote from: arulbero on April 29, 2020, 01:59:34 PM

-snip-
But can you treat these points like if they were random? Can you apply in this case the birthday paradox?

The DP method (distinguished points) with a hashtable is used. That means that every subsequent jump is dependent from the x-coordinate of the current location. That means that pseudorandom walks are used for the kangaroos. No need to store all the visited points for this case.

Yes, this is clear, but these points seem to me not to be really (pseudo)random. There is a order. You can move only forward (from private key's point of view). Therefor many collisions are just impossible to get (instead in the birthday paradox, each new distinguished point has the chance to produce a collision with any previous distinguished point, for example that happens in BTCCollider, because in that case you can jump in any position, you go back and forth across the entire space)

Example with only 2 sequences:

If we suppose that W_100 is = (2^37)*G and T_100 is (2^38)*G, than between T_101, T_102, .... , T_2**32 it is no longer possible to find a single distinguished point with the same coordinate of any distinguished point that lies in W_0, W_1, W_2, ....., W_100. For sure.

Then how do you apply in this case birthday paradox?

It is impossible to get a collision in the path of the same tame kangaroo too, because the same kangaroo cannot turn back, then this is a pseudorandom sequence very particular ...

I think that's why the papers you find don't use the birthday paradox to analyze pollard kangaroo. Birthday paradox is used for the very similar gaudry schost algorithm. Gaudry schost algorithm sets the point to a new random location in the interval as soon as a distinguished point is found and saved.

arulbero

legendary

Activity: 1948

Merit: 2097

Quote from: MrFreeDragon on April 29, 2020, 02:23:27 PM

Quote from: arulbero on April 29, 2020, 01:59:34 PM

-snip-
But can you treat these points like if they were random? Can you apply in this case the birthday paradox?

The DP method (distinguished points) with a hashtable is used. That means that every subsequent jump is dependent from the x-coordinate of the current location. That means that pseudorandom walks are used for the kangaroos. No need to store all the visited points for this case.

Yes, this is clear, but these points seem to me not to be really (pseudo)random. There is a order. You can move only forward (from private key's point of view). Therefor many collisions are just impossible to get (instead in the birthday paradox, each new distinguished point has the chance to produce a collision with any previous distinguished point, for example that happens in BTCCollider, because in that case you can jump in any position, you go back and forth across the entire space)

Example with only 2 sequences:

If we suppose that W_100 is = (2^37)*G and T_100 is (2^38)*G, than between T_101, T_102, .... , T_2**32 it is no longer possible to find a single distinguished point with the same coordinate of any distinguished point that lies in W_0, W_1, W_2, ....., W_100. For sure.

Then how do you apply in this case birthday paradox?

It is impossible to get a collision in the path of the same tame kangaroo too, because the same kangaroo cannot turn back, then this is a pseudorandom sequence very particular ...

MrFreeDragon

sr. member

Activity: 443

Merit: 350

Quote from: arulbero on April 29, 2020, 01:59:34 PM

-snip-
But can you treat these points like if they were random? Can you apply in this case the birthday paradox?

The DP method (distinguished points) with a hashtable is used. That means that every subsequent jump is dependent from the x-coordinate of the current location. That means that pseudorandom walks are used for the kangaroos. No need to store all the visited points for this case.

From here the definition (page 4, 1st par): https://eprint.iacr.org/2014/565.pdf

a point is a distinguished point - if its representation exhibits a certain bit pattern, e.g., has the top 20 bits equal
to zero. Whenever one of the parallel random walks reaches such a point it is stored on a central processor

arulbero

legendary

Activity: 1948

Merit: 2097

Quote from: Jean_Luc on April 27, 2020, 02:26:14 AM

I did a test, wanting to know the average time of the birthday paradox when searching collision between 2 tables (like the kangaroo problem).

The kangaroo method is announced to be 2.sqrt(n) but this is for a simple 2 stages algorithm where:
- you first travel a single tame kangaroo sqrt(n) steps to setup a trap
- then you make steps with the wild until a collision occurs (it falls in the trap), this second stage is expected to end in sqrt(n) steps.
The factor 2 comes from that. There no need of a hashtable there.

Hi,

let's see if I have understood this Kangaroo algorithm:

P=k*G, you know P and you know that a < k < b, for semplicity : 0 < k < a, for example: 0 < k < 2^64 (starting interval)

you generate many sequence of 2 type of points:

1) tame: each sequence starts from a random point T0 that lies in the starting interval, then

T0, T1, T2, …. the difference between 2 consecutive points is: G, or 2*G, or 4*G, or 8*G, …, or 2^32*G

2) wild: each sequence starts from P + r*G, where r*G is a random point with a random r private key between 0 < k < 2^31), then:

W0, W1, W2, ….. the difference between 2 consecutive points is: G, or 2*G, or 4*G, …, or 2^32*G

each jump towards the next point depends on the x coordinate (mod 33) of the current point; in this way if a tame kangaroo reach a points already reached from a wild kangaroo (or viceversa), you have a collision and then same path from there.

In that case T = W -> t*G = w*G -> t*G = P + w*G -> t*G = k*G + w*G -> k = (t-w) mod n

Besides you use distinguished points to detect this collision.

In this example you generate about 2^32 points (T points) in the interval [1*G, (2^64+(2^32)(2^32))*G]
and about 2^32 points (W points) in the interval [P+r*G, ((k+r)+(2^32*2^32))*G]

let's say that both type of points have for sure their private keys in [1, 2^65] interval

But can you treat these points like if they were random? Can you apply in this case the birthday paradox?

NotATether

legendary

Activity: 1568

Merit: 6660

bitcoincleanup.com / bitmixlist.org

Quote from: Jean_Luc on April 29, 2020, 07:04:04 AM

Yes I agree to open an other topic, I'm still fighting to get the average running time in function of dp and nbKangaroo, this is quite complex and I got unexpected results but interesting Wink

I'll open the new thread when I ends my statistics.

It's been very interesting seeing the results from doing kangaroo hops, so I support this decision. And then this thread should be locked since we seem to be getting derailed.

Jean_Luc

sr. member

Activity: 462

Merit: 701

Yes I agree to open an other topic, I'm still fighting to get the average running time in function of dp and nbKangaroo, this is quite complex and I got unexpected results but interesting Wink

I'll open the new thread when I ends my statistics.

MrFreeDragon

sr. member

Activity: 443

Merit: 350

The topic started from one things, and continued with others. TC was wrong in some things, however he understood it. However he created a "marketing" name attracted JeanLuc developer and motivated him (i beleive) to continue his job with BSGS annd Kanagroo codes.

Here the message their Jean_Luc promissed to develop ECDLP solver: https://github.com/JeanLucPons/BTCCollider/issues/3

This topic helped to force that work, and JeanLuc finished his BSGS:
https://github.com/JeanLucPons/BSGS

and later Kangaroo on GPU:
https://github.com/JeanLucPons/Kangaroo

The last one (Kangaroo) is amazing. Many thanks to Jean_Luc!

Jean_Luc, i suggest you to create a separate topic about your Kangaroo program and continue discussions there. We can collect some main things (method, tests, benchmarks, etc) and post them in the 1st message of new topic. What do you think about this?

nullius

copper member

Activity: 630

Merit: 2614

If you don’t do PGP, you don’t do crypto!

Quote from: odolvlobo on April 29, 2020, 04:37:49 AM

Quote from: nullius on April 29, 2020, 02:09:46 AM

I did not bother to read the whole thread, which is now nearly 10 pages. Did I miss anything?

Yes, you did. The thread is 10 pages because there is stuff going on here, despite the ridiculous title.

Quote from: Etar on April 29, 2020, 04:25:50 AM

If you have not read the whole topic, or at least a few pages, then you should not write here.

University professors of the sciences regularly receive e-mails from cranks claiming to have invented perpetual motion machines, free energy devices, simple cures for cancer, etc., etc. (I know this, because I used to have someone forwarding those to me for my amusement.) Would you blame them for not wasting their time reading things that are facially incredible and, moreover, presented in the manner of arrogant ignorance?

The topic title, “brute-forcing public keys at amazing speed 2.2 PH/s on CPU”, is not only ridiculous because of the “2.2 PH/s” claim that I parodied: Nobody who knows anything whatsoever about elliptic curve cryptography would ever talk about “brute-forcing public keys”. It is stunningly ignorant. I say that, having some history here of pointing out that Bitcoin’s secp256k1 has a 128-bit security level. I made that thread because I was sick and tired of people yammering about how long it would take to bruteforce a 2²⁵⁶ keyspace.

Quote from: nullius on January 31, 2018, 05:29:46 PM

If an attacker were to use a bruteforce attack, trying keys one by one, that would require on the order of 2²⁵⁶ work. (I here ignore the restrictions on valid secp256k1 keys, which reduces that to about 2^255.5; the difference would be negligible in practical terms, and it’s anyway not here relevant.)

However, no serious attacker would ever try to bruteforce elliptic-curve crypto. Rather, it is estimated that breaking Bitcoin’s 256-bit keys with the best known attacks should require around 2¹²⁸ work [...]

Although I didn’t read this whole thread, I skimmed Etar’s posts from his post history page. It is easy, because he has been exclusively posting in this thread since 2020-04-07. Before that, his last post was in a shitcoin thread on 2019-02-06.

I also noticed what others here seem not to, at least not in the first few pages which I did read: Etar appears to have no history of posting in D&T, at least not that I could find on a cursory check. He used to post prolifically in shitcoin threads. In 2017–19, the account had several large posting gaps; then it was dormant for over a year. It seems to have the same style as before; but that is easy, when the style is basically gibberish. Anyway, the account suddenly woke up and immediately, exclusively started pushing this thread in a know-it-all belligerent manner.

Quote from: nullius on April 29, 2020, 02:09:46 AM

Let me get this straight: OP, who has a past history of prolific posting in shitcoin threads before some long post history gaps, suddenly “woke up” and started posting in Development & Technology with wild claims backed only by semantic games and insulting the intelligence of people who know far more than he does.

Quote from: Etar on April 29, 2020, 04:25:50 AM

@lauda, @ nullius
You are just bored and you decided to flood here?

Back at you.

Post history is the kind of thing that Lauda would notice...

Quote from: Lauda on April 29, 2020, 04:41:55 AM

Don't try to teach me how to use the trust system, you have no idea what you are talking about in that aspect.

...indeed.

Quote from: odolvlobo on April 29, 2020, 04:37:49 AM

The fact that I challenged him to find 16 specific private keys in a 2⁶⁴ range and he succeeded clearly demonstrates that he has accomplished something. If you want to know the details, you'll have to read the thread.

Eh...

Quote from: Jean_Luc on April 09, 2020, 02:42:23 AM

This is well know since the beginning of elliptic curve usage in crypto.
But we count the number of group operation really performed (not the size of the range divided by time).

For instance in my BTCollider which use the DP method (also in O(sqrt(n))), I get 27.9 Mips (GeForce GTX 1050 Ti) for 80bit collision search. That means that I really compute 27.9M group operation and hash per second. It solves 80bit collision in 14h30 (in average). Note that in that case, it have to compute an EC mult for each group operation.

https://github.com/JeanLucPons/BTCCollider

Quote from: Etar on April 09, 2020, 12:39:43 PM

Quote from: MrFreeDragon on April 09, 2020, 11:02:30 AM

Most famous Square root methods:
- Baby-step Gian-step
- Pollard's Rho algorithm
- Pollard's kangaroo algorithm

Have a look this link as well: https://www.embeddedrelated.com/showarticle/1093.php

You guys are so smart here, I even feel awkward.

[...discussion continued right up to the top of this page.]

So... after others drew him an introductory map of methods better than brute-force, Etar managed to find your challenge keys in a 2⁶⁴ range? It is manifestly unimpressive for someone with this attitude:

Quote from: Etar on April 08, 2020, 01:09:52 AM

Quote from: gmaxwell on April 07, 2020, 06:29:52 PM

~

if you do not know how, this does not mean that it is impossible.
I'm not going to post programs, source codes or algorithms. It's just a fact.

Quote from: Etar on April 08, 2020, 06:20:59 AM

Quote from: gmaxwell on April 08, 2020, 06:01:57 AM

~

I think yo do not understand what are you talking...
And if you do not understand the topic,

Quote from: Etar on April 29, 2020, 04:25:50 AM

But it seems like some people just don’t have enough manners in communication.

You are not one to be lecturing others on “manners in communication”. Your rudeness is as bad as your conceited ignorance.

Lauda

legendary

Activity: 2674

Merit: 2970

Terminated.

Quote from: odolvlobo on April 29, 2020, 04:37:49 AM

He claimed rates that are clearly impossible, but that is because his measurement methodology is flawed. He was not lying or trying to misrepresent anything. He was just wrong.

Insisting that you are right or that you are providing knowledge when you have been proven wrong is malicious, therefore the rating.

Quote from: odolvlobo on April 29, 2020, 04:37:49 AM

The fact that I challenged him to find 16 specific private keys in a 2⁶⁴ range and he succeeded clearly demonstrates that he has accomplished something.

Yes, and I am Santa Claus.

Don't try to teach me how to use the trust system, you have no idea what you are talking about in that aspect.

odolvlobo

legendary

Activity: 4508

Merit: 3425

Quote from: nullius on April 29, 2020, 02:09:46 AM

I did not bother to read the whole thread, which is now nearly 10 pages. Did I miss anything?

Yes, you did. The thread is 10 pages because there is stuff going on here, despite the ridiculous title.

Quote from: Lauda on April 29, 2020, 02:51:23 AM

Tagged this user named Etar for intellectual dishonesty/trying to fool newbies. Do not forget this:

You are wrong. You didn't bother to read the thread and you just copy-pasted gmaxwell's undeserved negative trust.

Etar doesn't deserve the negative trust.

He claimed rates that are clearly impossible, but that is because his measurement methodology is flawed. He was not lying or trying to misrepresent anything. He was just wrong.

The fact that I challenged him to find 16 specific private keys in a 2⁶⁴ range and he succeeded clearly demonstrates that he has accomplished something. If you want to know the details, you'll have to read the thread.

BitBanksy

sr. member

Activity: 350

Merit: 250

Participate directly & privately to the most anticipated Celo Gold Auction with our OTC Proxy Service!

Bonus: For every 2 cGLD purchased, you get 1 free cGLD!

Early Bidding Begins: 7 PM UTC April 29, 2020

Live Auction: 5 AM UTC May 7, 2020

PM me now for more info

Celo Auction FAQs

Celo White Paper

Celo in the Press

Lauda

legendary

Activity: 2674

Merit: 2970

Terminated.

Quote from: Etar on April 29, 2020, 04:25:50 AM

In fact, I just shared information and nothing more, and adequate people explained to me that this is not new, but long known.

I will rather consult monkeys from the local zoo before I consult you. Please do not post any more of your "information".

brainless

member

Activity: 348

Merit: 34

Quote from: COBRAS on April 27, 2020, 05:06:03 PM

Quote from: brainless on April 27, 2020, 04:42:48 PM

Quote from: COBRAS on April 27, 2020, 03:59:17 PM

arulbero you giant-step code down then not enoth memory to ?

::00::38::83::88

Not understand this. Sorry.Will try tomorrow.I think code faster then memory more, but not nown calculation.

And yes, I understand how to add pubkey to code.

above is generic EYE test, and come to know your brain is damage, damaged brain only can test baby step not Gaint step

Etar

sr. member

Activity: 642

Merit: 316

@lauda, @ nullius
You are just bored and you decided to flood here?
If you have not read the whole topic, or at least a few pages, then you should not write here.
For people who have problems with trust in people and who see scam in any person, I will repeat
I created the topic because I didn’t know that algorithms such as bsgs or kangaroos had existed for a long time.
In fact, I just shared information and nothing more, and adequate people explained to me that this is not new, but long known.
I did not publish codes, I did not upload releases, so that I could be accused of something.
But it seems like some people just don’t have enough manners in communication.
One reason why i still look here is to find out how things are going Jean_luc with his kangaroo algorithm.

COBRAS

member

Activity: 873

Merit: 22

$$P2P BTC BRUTE.JOIN NOW ! https://uclck.me/SQPJk

Quote from: brainless on April 27, 2020, 04:42:48 PM

Quote from: COBRAS on April 27, 2020, 03:59:17 PM

arulbero you giant-step code down then not enoth memory to ?

::00::38::83::88

Not understand this. Sorry.Will try tomorrow.I think code faster then memory more, but not nown calculation.

And yes, I understand how to add pubkey to code.

Lauda

legendary

Activity: 2674

Merit: 2970

Terminated.

Tagged this user named Etar for intellectual dishonesty/trying to fool newbies. Do not forget this:

Quote from: gmaxwell on April 08, 2020, 06:38:56 AM

Quote from: Etar on April 08, 2020, 06:20:59 AM

I think yo do not understand what are you talking...

Clearly you're looking to fool people who don't, sadly for you I'm not one of them. Though the fact that you don't recognize that I do is odd...

brainless

member

Activity: 348

Merit: 34

Quote from: COBRAS on April 27, 2020, 03:59:17 PM

arulbero you giant-step code down then not enoth memory to ?

::00::38::83::88

nullius

copper member

Activity: 630

Merit: 2614

If you don’t do PGP, you don’t do crypto!

Quote from: MrFreeDragon on April 08, 2020, 09:41:52 AM

Etar, you are funny person.

Yes, you just overestimate the rate. It is known that due to pollard kanagaroo method it is possible to perform less bruteforce operations. And roughly it is square root from the total length.

You just count the operations which are not actually performed. You use the method which is good due to birthday paradox. However, due to this methond you just need less operations.

So, your actual speed is not 2.2Ph/s but the square root from this amount, i.e. approx. 47 Mh/s in total.

Quote from: Jean_Luc on April 17, 2020, 12:52:02 PM

I did few optimizations (commited to github), I reached 13.6M giant steps of 2^30 per second on my Xeon X5647 2.93GHz with 12GB of RAM.
It solves the 16 keys of the odolvlobo's set in 3:35:53 from scratch, I mean without any precomputation.
If I convert to the Etar's unit: It does 14.6 PKey/s.

Newsflash: I, nullius, have written a very small shell script that can do over 100 trillion operations per second on a single core of an ancient 3.3 GHz CPU! Here is the source code, including a benchmark, on a Linux system (FreeBSD will be a bit different):

Code:

$ echo '1048576^1024' | time -p bc -sql
12425423456181365279925387080786307311597595610838347638850287747623\
60861068891428772905674656322752135427515054673539621055134262585183\
19758974258574370940046385769635382008544820357548872424501984530330\
07298954744930507666995488232800628320702554659038871038462856168892\
86081195063491219050898500215483033932486747164814339647481138414482\
46888917028564677545436961362035603246262743087461966109644786182741\
43113267232859737251775529839066894535312855298925318702786023730327\
19869958099828161372489304583433717069182227464187121063444543113687\
08508016817415834539561007557262362984166823937246086587688258356477\
00836976266833112093887575424667085600301886904838933510219463816130\
80902598605780629569631487856056084824428655665090823522085781848136\
90257281434662352060481338229879814647807435854905171792202651978347\
81576216598469678835525935558383051575769346443249751553902761298124\
16603376553195639027589983660665862094399483358459126504039467900670\
57848445654106692228540961696646160891611201176550731263658980952921\
79661180975723679821903326940014763241580326424148011608373928415839\
89799573086647874776450926010315260838864367653687522517200666183052\
78046681072569421716140184999814186049906737726847623187904023921869\
96493297393422826404482175417711937716534206615666157396727516750219\
91851182241223465341934177526160075853973517749105067707179469601845\
88330671948952814804211541112010786462301589154313085414717834325712\
13484577645520690543228926603184248994369361889663953324943538057692\
09142925292218241559518002462550357529467477707118089331738992523144\
12851389177004142395041260697284263133880780366217511217984043484829\
53325405978696911189665650780516493277780136150107415182697715538908\
88939125791581583722002310729942726531722583550670593647217988951143\
92521808675257335863861193806735924700446683310178995467034389623843\
34637501209612847511049916048620985432493518099051493506017025211609\
28445644828520351429402092953664848212010413254950535181316532179730\
47923723479492788069287202544924191902788739261046871261774192771595\
98592964369820978291410445759190143932392603554581408191522473988300\
78968537639501149013877800816286561791691358636572217216223056875928\
17092366529353468311118760692178408198029055674402652184529251245244\
02444158263061794917079395096000934259933755433146079126284408690042\
38324933687603968469583639260051178509345170832212772332066117998429\
78113094510577400457305062492992418480494715522786170957895839161090\
90679234697955146377040610964269301216587823655778069747692220154167\
70472400404041730870427533141385209154167773633401949758275582595580\
27019512304014991243449078715269261165419536452307568016928400885256\
23776177665575668603825365845156272635985606083707288176434594230550\
63821924320631190657490067933585520675018760684824866176435920685678\
63296909178438390152244400222647826063647022042540400075485011545999\
00189922038235751253299117681279273929701919536924732136567627766777\
04272072134504254916928323201471851352779331900325117027741482200181\
92390633227909351864687090818155037147671652619953709590048531015638\
67766944930820904022173238020823903767522872288256850258417608533098\
55710889239543384650225162736547201843957566299847464495309572962950\
42100547721511026509080617441578235291230797585596956723791898048054\
94393551619189003705862052625203047394451564786087506671990059650588\
42311700375195922932824912529284060788340967215716848525338227678858\
31002874066317264714873448648393414928386389626018123213950936837951\
21684530567458009683534343813278777818354930730330893607406282866925\
70103938566958665744906496118155917745662805567050399327736908498724\
43501504905974334406632067569317805770368874333462501444598418238980\
06216784554109955223039089466808238818647459407144324415209786295284\
85351735941250780778945454134699359309040121089264637439201843749119\
15314754026062773120219884614094334344501797490773975165855473939626\
21196092140724536492766178184954443337984925556703373475742985168021\
17883078934435817288096762052976538997318141223726183848768580350589\
51200814398904661260693065337549329110975358618511651893597017063680\
49524900823342544481257688601563369725945461590068162007616574017948\
20914771999143977962015245639168441997258587765506763767166710832557\
71563537685088458448130330050803042730162103745712401339034512242847\
09907124547717119635576597246015627200917541559241502943454956637305\
93422940574002248679572906693549431041616952024928826004627897641216\
24770138766738991174439422719554351731082128344265526579459209824096\
26455027947494463143520489497270848150431960954940852601300917188450\
83650067617931857392960118807817462708184256574641193504040258930891\
99839012206942405624559164212070339133396667428983146045638492533064\
03158572693118328234068512101574762869748178279573282408346844832649\
81933372857871230260859650454635805876968974210471318739872847006616\
00804924005284963470674464976828185259204561264958120568094640836916\
06837889924231208724461928878298859310406116888954935403060987516114\
18405904888301595242442948380076830270819668592368944902754888707385\
35204279102855717837455807640171757260262847344547505722807775030875\
94359812363435941904987045950244172865748098743633724075503552976884\
62784080317728680909109997117711330509573013343458585365228551129794\
81049484143528284230564635011417106533259692707337253646177547883252\
44686207799941805384827372103287633228795533147652926838400042889746\
45173471725823456319919737251506683847696994908372466903589572209409\
39398547770207563852186420979082694689548292795391486301958732319406\
71045025668526409833244577121221967764239502649649279354614518521237\
21869340311444598473461599506348960422697831023422091976250909540756\
61895743811394436416668441435649266854835929322540019881764717021766\
29212632259442546037609341731335269657620305531233672864805604650871\
85427651321373449080020221012906959833983342655018947268462816668916\
24294703168898855422382676912113909067081031599264999514935027284486\
39503819472854481747533388916773509467027133785685914059820113289324\
61413428025585667367075371092228092827478558233432174901584085487469\
46201737657601518077611371103354312093969464251033488916198666142138\
7618179306677175709500343297535791418285490176
real 0.01
user 0.01
sys 0.00

Well, you see, I realized that an exponentiation is just a bunch of multiplications. In this case, 1024 multiplications—and each of those multiplications is 1,047,576 additions. Thus, I have done 1,073,741,824 additions in 0.01 seconds. But wait! If expressed in tally-style unary units, each operand of each of those additions is 1,048,576 additions of the number 1. Thus, in my units, this counts as 1,125,899,906,842,624 operations in 0.01 seconds. Ergo, >100 trillion operations per second on a CPU that is almost nine years old.

A genius, am I.

Sadly, I am still only in the “tera” range; but surely, if I were to play semantic games a bit more, I could boost myself into the “peta” range as OP did—or even beyond him, into the “exa” range.

Quote from: Jean_Luc on April 09, 2020, 02:42:23 AM

This is well know since the beginning of elliptic curve usage in crypto.
But we count the number of group operation really performed (not the size of the range divided by time).

Soooo... Let me get this straight: OP, who has a past history of prolific posting in shitcoin threads before some long post history gaps, suddenly “woke up” and started posting in Development & Technology with wild claims backed only by semantic games and insulting the intelligence of people who know far more than he does.

I did not bother to read the whole thread, which is now nearly 10 pages. Did I miss anything?

Quote from: Etar on April 08, 2020, 09:13:18 AM

I will give a final explanation of how this works.
***************************************

Extraordinary claims backed by poorly-written explanations riddled with semantic games are the mark of either a crackpot or a scammer. Take your pick.

Quote from: gmaxwell on April 08, 2020, 06:38:56 AM

Quote from: Etar on April 08, 2020, 06:20:59 AM

I think yo do not understand what are you talking...

Clearly you're looking to fool people who don't, sadly for you I'm not one of them. Though the fact that you don't recognize that I do is odd...

Topic: brute-forcing public keys at amazing speed 2.2 PH/s on CPU [malware warning] - page 2. (Read 3490 times)