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Title: This message was too old and has been purged Post by: Evil-Knievel on January 28, 2015, 07:00:23 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: coinsocieties on January 28, 2015, 07:04:52 PM Excellent!
Will try to Solve it. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: redsn0w on January 28, 2015, 07:12:44 PM Can you sign a message from the bitcoin address (18b2no9rBkovhv5gf3vkd5VQ9MKxHvqSzu) ?
Title: This message was too old and has been purged Post by: Evil-Knievel on January 28, 2015, 07:14:15 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: redsn0w on January 28, 2015, 07:15:34 PM Can you sign a message from the bitcoin address (18b2no9rBkovhv5gf3vkd5VQ9MKxHvqSzu) ? If you tell me how I can do that in Amory, I will. I am trying hard for the last 15 minutes ;) I've find this thread : https://bitcointalk.org/index.php?topic=252848.0 maybe it will be helpful for you ( I don't use armory , I prefer electrum). Title: This message was too old and has been purged Post by: Evil-Knievel on January 28, 2015, 07:28:48 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: redsn0w on January 28, 2015, 07:33:19 PM No idea if this helps, buts that is what I got when I followed the instructions in the referenced thread :-D Code: -----BEGIN BITCOIN SIGNED MESSAGE----- Yes , I've verified on https://brainwallet.github.io/#verify : Code: -----BEGIN BITCOIN SIGNED MESSAGE----- PS: I removed the =oRUP , I don't know why the sign process gives you that. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: coinsocieties on January 28, 2015, 07:35:26 PM No idea if this helps, buts that is what I got when I followed the instructions in the referenced thread :-D Code: -----BEGIN BITCOIN SIGNED MESSAGE----- Yes , I've verified on https://brainwallet.github.io/#verify : Code: -----BEGIN BITCOIN SIGNED MESSAGE----- PS: I removed the =oRUP , I don't know why the sign process gives you that. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: haploid23 on January 28, 2015, 07:49:34 PM Everything there is gibberish to me, but it does reminds me of this riddle below. Quite entertaining to follow even if you understood none of it.
https://bitcointalk.org/index.php?topic=661781.0 Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: david123 on January 28, 2015, 07:53:46 PM Quote Being a some constant, further assume that we What do you mean with “a factor ring“? Any ring is a factor ring.are in a factor ring (basically all operations modulo some sumber p). I assume you mean the ring Z/pZ for some nat. number p? If so, is this p supposed to be prime (as the letter suggests)? You always have to start with x=9. Consider the following recursive formula: Code: new_x = (x²-1)² / (4*x*(x²+a*x+1)) How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)? Let f:Z/pZ -> Z/pZ be the map given by your assignment x |-> new_x. Then you basically ask for a map g:Z/pZ -> N s.t. f^(g(y))(9) = y for all y in Z/pZ, right? Note: You can start multiple such chains beginning at x=9, and add the resulting x values using the addition algorithm from http://en.wikipedia.org/wiki/Montgomery_curve (Montgomery arithmetic section). Note, that the x value, is the value you get at the end of such calculation-chain, and the z value is always 1. I don't know what you mean with all of this.. Could you put it in more mathematical terms? Be also advised that the referenced addition “algorithm“ is not specific to Montgomery curves, so it would be better to link to the wikipedia article for elliptic curves where it is also described. Do you try to consider elliptic curves over F_p? I have the impression, but you should reformulate your question.. Title: This message was too old and has been purged Post by: Evil-Knievel on January 28, 2015, 07:59:09 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: david123 on January 28, 2015, 08:05:43 PM I still missed the part where the elliptic curve comes in. You need one
if you want to apply this addition method. If you can describe your problem more formally, I might be able to help. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 02:40:59 AM 14DFu1bW6DSPPuJYnZLn9EfgKeFYcLaFAN
14DFu1bW6DSPPuJYnZLn9EfgKeFYcLaFAN 14DFu1bW6DSPPuJYnZLn9EfgKeFYcLaFAN i just sent you a pm with the appropriate script on how to compute and find your solution please send my bounty the addy above thanks you! Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: izanagi narukami on January 29, 2015, 02:48:12 AM I have a friend that might interest for this Bounty.
Will let you no when I got respond from him Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 02:48:29 AM 14DFu1bW6DSPPuJYnZLn9EfgKeFYcLaFAN 14DFu1bW6DSPPuJYnZLn9EfgKeFYcLaFAN 14DFu1bW6DSPPuJYnZLn9EfgKeFYcLaFAN i just sent you a pm with the appropriate script on how to compute and find your solution please send my bounty the addy above thanks you! @OP:You can run it yourself in a .html file just copy and paste it into notepad. Of course over 100000 is kinda slow on my computer so there are some limitations to it. If I was to have it calculated I would run the above script as php and then use that to generate the javascript code to give me an answer. there your problem is solved in your pm please send me the bounty and close this thread Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: shluher on January 29, 2015, 02:52:01 AM Problem Description: Being a some constant, further assume that we are in a factor ring (basically all operations modulo some sumber p). Note, that the division below is a multiplication by the modular inverse. You always have to start with x=9. Consider the following recursive formula: Code: new_x = (x²-1)² / (4*x*(x²+a*x+1)) How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)? Note: You can start multiple such chains beginning at x=9, and add the resulting x values using the addition algorithm from http://en.wikipedia.org/wiki/Montgomery_curve (Montgomery arithmetic section). Note, that the x value, is the value you get at the end of such calculation-chain, and the z value is always 1. Is this really solvable at all? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 02:55:50 AM yes i just sent him how to solve it in pm
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 03:29:54 AM so the bounty is @ 34 for me now? ;) please check your messages form me ive finished this bounty thanks!
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: GLBrim on January 29, 2015, 03:32:44 AM so the bounty is @ 34 for me now? ;) please check your messages form me ive finished this bounty thanks! so you mean you already got the answer? ??? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 03:39:55 AM yeah ive given him the instructions to find his answer and how to do it in which languages thank you!
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: GLBrim on January 29, 2015, 03:43:54 AM i tried and came up with this.. hope i can get some xD
=((x-1)^2 (x+1)^2)\/(4 x (a x+x^2+1)) =(x^4-2 x^2+1)\/(4 a x^2+4 x^3+4 x) x = 1, a - 2=/0 x = 1, a + 2=/0 ={x element R : (a<=-2 and x<0) or (a<=-2 and x>0 and sqrt(a^2-4)+a+2 x<0) or (a<=-2 and sqrt(a^2-4)+a+2 x>0 and sqrt(a^2-4)>a+2 x) or (a<=-2 and a+2 x>sqrt(a^2-4)) or (-2<a<2 and x!=0) or (a>=2 and sqrt(a^2-4)>a+2 x and sqrt(a^2-4)+a+2 x>0) or (a>=2 and sqrt(a^2-4)<a+2 x and x<0) or (a>=2 and x>0) or (a>=2 and sqrt(a^2-4)+a+2 x<0)} 1\/(4 x)-a\/4+1\/4 (a^2-3) x+(a-a^3\/4) x^2+1\/4 (a^4-5 a^2+4) x^3+O(x^4)\n(Laurent series) x\/4-a\/4+(a^2-3)\/(4 x)+(a-a^3\/4)\/x^2+O((1\/x)^3)\n (d)\/(dx)((x^2-1)^2\/(4 x (x^2+a x+1))) = ((x^2-1) (2 a (x^3+x)+x^4+6 x^2+1))\/(4 x^2 (a x+x^2+1)^2) integral (-1+x^2)^2\/(4 x (1+a x+x^2)) dx = 1\/8 ((a^2-4) log(a x+x^2+1)+2 a sqrt(4-a^2) tan^(-1)((a+2 x)\/sqrt(4-a^2))-2 a x+x^2+2 log(x))+constant BTC: 199hWWjMZdZ59dfyKpi7AG7wKv9LnqJSij Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 03:46:59 AM i tried and came up with this.. hope i can get some xD =((x-1)^2 (x+1)^2)\/(4 x (a x+x^2+1)) =(x^4-2 x^2+1)\/(4 a x^2+4 x^3+4 x) x = 1, a - 2=/0 x = 1, a + 2=/0 ={x element R : (a<=-2 and x<0) or (a<=-2 and x>0 and sqrt(a^2-4)+a+2 x<0) or (a<=-2 and sqrt(a^2-4)+a+2 x>0 and sqrt(a^2-4)>a+2 x) or (a<=-2 and a+2 x>sqrt(a^2-4)) or (-2<a<2 and x!=0) or (a>=2 and sqrt(a^2-4)>a+2 x and sqrt(a^2-4)+a+2 x>0) or (a>=2 and sqrt(a^2-4)<a+2 x and x<0) or (a>=2 and x>0) or (a>=2 and sqrt(a^2-4)+a+2 x<0)} 1\/(4 x)-a\/4+1\/4 (a^2-3) x+(a-a^3\/4) x^2+1\/4 (a^4-5 a^2+4) x^3+O(x^4)\n(Laurent series) x\/4-a\/4+(a^2-3)\/(4 x)+(a-a^3\/4)\/x^2+O((1\/x)^3)\n (d)\/(dx)((x^2-1)^2\/(4 x (x^2+a x+1))) = ((x^2-1) (2 a (x^3+x)+x^4+6 x^2+1))\/(4 x^2 (a x+x^2+1)^2) integral (-1+x^2)^2\/(4 x (1+a x+x^2)) dx = 1\/8 ((a^2-4) log(a x+x^2+1)+2 a sqrt(4-a^2) tan^(-1)((a+2 x)\/sqrt(4-a^2))-2 a x+x^2+2 log(x))+constant BTC: 199hWWjMZdZ59dfyKpi7AG7wKv9LnqJSij i tried and came up with this.. hope i can get some xD =((x-1)^2 (x+1)^2)\/(4 x (a x+x^2+1)) =(x^4-2 x^2+1)\/(4 a x^2+4 x^3+4 x) x = 1, a - 2=/0 x = 1, a + 2=/0 ={x element R : (a<=-2 and x<0) or (a<=-2 and x>0 and sqrt(a^2-4)+a+2 x<0) or (a<=-2 and sqrt(a^2-4)+a+2 x>0 and sqrt(a^2-4)>a+2 x) or (a<=-2 and a+2 x>sqrt(a^2-4)) or (-2<a<2 and x!=0) or (a>=2 and sqrt(a^2-4)>a+2 x and sqrt(a^2-4)+a+2 x>0) or (a>=2 and sqrt(a^2-4)<a+2 x and x<0) or (a>=2 and x>0) or (a>=2 and sqrt(a^2-4)+a+2 x<0)} 1\/(4 x)-a\/4+1\/4 (a^2-3) x+(a-a^3\/4) x^2+1\/4 (a^4-5 a^2+4) x^3+O(x^4)\n(Laurent series) x\/4-a\/4+(a^2-3)\/(4 x)+(a-a^3\/4)\/x^2+O((1\/x)^3)\n (d)\/(dx)((x^2-1)^2\/(4 x (x^2+a x+1))) = ((x^2-1) (2 a (x^3+x)+x^4+6 x^2+1))\/(4 x^2 (a x+x^2+1)^2) integral (-1+x^2)^2\/(4 x (1+a x+x^2)) dx = 1\/8 ((a^2-4) log(a x+x^2+1)+2 a sqrt(4-a^2) tan^(-1)((a+2 x)\/sqrt(4-a^2))-2 a x+x^2+2 log(x))+constant BTC: 199hWWjMZdZ59dfyKpi7AG7wKv9LnqJSij can check the times of his post my posts on the forums and messages in your inbox i messaged you first money please and thank you Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 04:15:47 AM anyone know where the original poster is at?!
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ticoti on January 29, 2015, 04:19:45 AM anyone know where the original poster is at?! relax sir, he must be sleeping he won't answer until tomorrowTitle: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ncsupanda on January 29, 2015, 06:24:52 AM I've written a script to solve the iterations and print outputs for them.
You can view the current values, including the previous x value and the new_x value here: http://www4.ncsu.edu/~ltwalz/bounty.txt And a graph of the comparison of the x value calculated compared to the previous value: http://www4.ncsu.edu/~ltwalz/Algorithm.png I'm happy to do more on request - usually seeing the numbers help people to visualize the problem they are approaching. Let me know if the links cause any problems (I'm hosting them through my university). Also, I did my modeling and calculations in MATLAB, so if anyone would like that as well, feel free to PM me. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 06:28:27 AM its funny cause the script ive written and sent him like 5 hours ago wil display the correct answer using the algorithm that i used i like how everyone is trying to step on my fucking toes cause i KNOW the one i sent him is correct. OP please make the right decision here as to who gets the bounty cause ive sent multiple pm's thanks again
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ncsupanda on January 29, 2015, 06:32:30 AM its funny cause the script ive written and sent him like 5 hours ago wil display the correct answer using the algorithm that i used i like how everyone is trying to step on my fucking toes cause i KNOW the one i sent him is correct. OP please make the right decision here as to who gets the bounty cause ive sent multiple pm's thanks again The guy is likely sleeping. Nobody is trying to "step on your toes" and you ought to relax. In fact, if you looked at what I provided, it was not an answer as much as it was a simulation. He'll choose based on the effort placed on the solution and how correct/helpful that solution is. You could send first and be completely correct, but it is his discrepancy and that's just how it is. Thanks. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Vortex20000 on January 29, 2015, 06:39:32 AM Silence in this thread...
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 06:42:20 AM ""The winner is the first person to post such formula in private. The formula must work in all cases, and be computationally feasible (let us say calculatable in less than 24 hours)""
Well simply put, i did this, but with php and html lol the formula is written in a script in a private message in his inbox. i hope he gets on son cause the anticipation is killing me Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: redsn0w on January 29, 2015, 06:45:28 AM ""The winner is the first person to post such formula in private. The formula must work in all cases, and be computationally feasible (let us say calculatable in less than 24 hours)"" Well simply put, i did this, but with php and html lol the formula is written in a script in a private message in his inbox. i hope he gets on son cause the anticipation is killing me Keep calm and wait him , if you have sent the solution (and it is valid) for first to him, you will be the winner. Title: This message was too old and has been purged Post by: Evil-Knievel on January 29, 2015, 07:53:24 AM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: david123 on January 29, 2015, 08:31:49 AM Don't expect a reasonable answer in the question is still unclear.
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: izanagi narukami on January 29, 2015, 08:44:59 AM Don't expect a reasonable answer in the question is still unclear. My friend said that it still connect on ECDSA scheme ? Is it true ? Also, additionally to that, the division must me a multiplication with the modular inverse modulo p (just as a hint for future tries). Thanks hope this help Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: gbianchi on January 29, 2015, 02:19:36 PM The winner: The winner is the first person to post such formula in private. The formula must work in all cases, and be comutationally feasible (let us say calculatable in less than 24 hours). If there are any wrong descriptions in this post at this time, they may be corrected or adjusted later on. Bounty ends on 02/15/2015. calculate in less than 24 hours ... what is the magnitude of a, given x and p ? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Watoshi-Dimobuto on January 29, 2015, 04:33:26 PM Can someone simplify the question?
Quote Problem Description: Being a some constant, further assume that we are in a factor ring (basically all operations modulo some sumber p). Note, that the division below is a multiplication by the modular inverse. You always have to start with x=9. Consider the following recursive formula: Code: new_x = (x²-1)² / (4*x*(x²+a*x+1)) How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)? Note: You can start multiple such chains beginning at x=9, and add the resulting x values using the addition algorithm from http://en.wikipedia.org/wiki/Montgomery_curve (Montgomery arithmetic section). Note, that the x value, is the value you get at the end of such calculation-chain, and the z value is always 1. I have to start with x = 9 and get new x(s) using the formula? and I have to find how often to do this to get a specific x? Is this right? What is a? What is z? Is both user defined? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: izanagi narukami on January 29, 2015, 04:54:10 PM What is a? What is z? Is both user defined? a and z are constant of the Montgomery curve algorithm (http://en.wikipedia.org/wiki/Montgomery_curve) the z value is always 1. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on January 29, 2015, 06:27:07 PM THE FORMULA YOU REQUIRE IS CALLED pemdas
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ncsupanda on January 29, 2015, 07:07:36 PM I've done more calculations, and replaced the previous calculations with them.
http://www4.ncsu.edu/~ltwalz/bounty.txt And the graphic visualization: http://www4.ncsu.edu/~ltwalz/Algorithm.png Still haven't been able to get the next x value to match the current (x=9). I could let it run for a lot longer, but the number drops off exponentially after the first few iterations. Maybe I'm approaching this incorrectly, but just throwing it out there. Title: This message was too old and has been purged Post by: Evil-Knievel on January 29, 2015, 10:16:00 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Josepht on January 29, 2015, 10:32:37 PM Hey,
I am not much of a mathematician, but I'll give it a try. I have two questions: 1. The a in the formula. Does it mean it can be any number? 2. You said the z value is always 1. What does that mean? I can't find a value z. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ncsupanda on January 29, 2015, 10:42:31 PM Hey, I am not much of a mathematician, but I'll give it a try. I have two questions: 1. The a in the formula. Does it mean it can be any number? 2. You said the z value is always 1. What does that mean? I can't find a value z. With z I believe he is referring to the standard deviation. http://en.wikipedia.org/wiki/Standard_score Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: jsmit332 on January 29, 2015, 10:53:01 PM I love all these bounties that Evil-Knievel puts up. Why do you put up all these bounties?
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: NeuroticFish on January 30, 2015, 09:29:28 AM I love all these bounties that Evil-Knievel puts up. Why do you put up all these bounties? If you want to make money, you have to invest money or knowledge. I can bet that he has some interesting idea to get some coins in a way we cannot think of. And I am almost sure that he will not actually share with us, especially seeing this big bounty. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Reynaldo on January 30, 2015, 01:36:26 PM Seems like someone found a solution, https://blockchain.info/address/18b2no9rBkovhv5gf3vkd5VQ9MKxHvqSzu
the money is not there anymore. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: lili song on January 30, 2015, 03:01:12 PM Seems like someone found a solution, https://blockchain.info/address/18b2no9rBkovhv5gf3vkd5VQ9MKxHvqSzu the money is not there anymore. But OP still doesn't post anything here I want to ask : Are we looking for simplify the formula or looking x value ? Why x must be start from 9 ? If we are looking for x value, How "a" value (coefficient from x variable ) on denominator ? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 09:09:31 AM Seems like someone found a solution, https://blockchain.info/address/18b2no9rBkovhv5gf3vkd5VQ9MKxHvqSzu the money is not there anymore. The funds from that address got used to fund another of his projects it seems, he likely just used Armory and it chose those coins to send because they are all in his wallet. I'd be willing to bet this bounty is still open as Evil-Knievel has much more in his wallet than just that. 1PayC5RCF2aXZ6Rjg2DpVM73gaQbndiZVX is the payout address for his "nxt-miner" https://bitcointalk.org/index.php?topic=929196.0 Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: josef2000 on January 31, 2015, 10:43:46 AM So may OP share the winner?
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 10:45:11 AM So may OP share the winner? There isn't a winner. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 11:04:50 AM 1,000 results in tiny text [Code ] box will get a scroll bar rather than a blob of tiny text Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on January 31, 2015, 11:11:39 AM thanks^ :)
What is a? I got this one: (I am assuming a=1, since idk what it is) Code: 9 Can somone tell me I am in the right path or what? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 11:27:06 AM What is a? What is a? What is z? Is both user defined? a and z are constant of the Montgomery curve algorithm (http://en.wikipedia.org/wiki/Montgomery_curve) the z value is always 1. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: mailmansDOGE on January 31, 2015, 11:42:39 AM Seems like someone found a solution, https://blockchain.info/address/18b2no9rBkovhv5gf3vkd5VQ9MKxHvqSzu Has the winner been found or you are still looking for an answer?the money is not there anymore. Please update the OP. And if the bounty is still on then where are the coins? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 11:46:33 AM Seems like someone found a solution, https://blockchain.info/address/18b2no9rBkovhv5gf3vkd5VQ9MKxHvqSzu Has the winner been found or you are still looking for an answer?the money is not there anymore. Please update the OP. And if the bounty is still on then where are the coins? 2 posts below that I offer insight into how that happened: https://bitcointalk.org/index.php?topic=939215.msg10317539#msg10317539 Also, that transaction happened less than 24 hours ago during which time OP hasn't even logged into the forums yet. Spam your signature somewhere else. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on January 31, 2015, 11:57:43 AM What is a? What is a? What is z? Is both user defined? a and z are constant of the Montgomery curve algorithm (http://en.wikipedia.org/wiki/Montgomery_curve) the z value is always 1. I read that, but what is 'a' exactly? If it is an unknown constant, then how will I find when the said result will occur. Is it 1? Or does the value of a has no impact on the result (but it certainly does)? Or on calculation the value of 'a' will be given? I think I did not understand the question properly. ??? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 12:01:00 PM Evil-Knievel is this algorithm related to your project over at https://bitcointalk.org/index.php?topic=929196.0 ?
I was looking at curve25519 and notice that it's starting parameter is x=9 I read that, but what is 'a' exactly? If it is an unknown constant, then how will I find when the said result will occur. Is it 1? Or does the value of a has no impact on the result (but it certainly does)? Or on calculation the value of 'a' will be given? I think I did not understand the question properly. ??? That I cannot answer. I'm currently doing some reading on the curves and trying to see what I can get out of it. (so far not much ;)) Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on January 31, 2015, 12:13:43 PM Evil-Knievel is this algorithm related to your project over at https://bitcointalk.org/index.php?topic=929196.0 ? I was looking at curve25519 and notice that it's starting parameter is x=9 I read that, but what is 'a' exactly? If it is an unknown constant, then how will I find when the said result will occur. Is it 1? Or does the value of a has no impact on the result (but it certainly does)? Or on calculation the value of 'a' will be given? I think I did not understand the question properly. ??? That I cannot answer. I'm currently doing some reading on the curves and trying to see what I can get out of it. (so far not much ;)) But I know nothing about coding. I am trying kind of mathematically. It is okay, right? Quote Hereby I am offering a bounty of 30 BTC to the first one solving the following mathematical problem either mathematically or using an algorithm: I just need OP to tell me whether the results I got are correct or not to proceed any further. I want to be sure whether I am in the correct understanding of it or not. Thanks for the link. Now i think 'a' is a value input by the user. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ncsupanda on January 31, 2015, 01:59:51 PM Evil-Knievel is this algorithm related to your project over at https://bitcointalk.org/index.php?topic=929196.0 ? I was looking at curve25519 and notice that it's starting parameter is x=9 I read that, but what is 'a' exactly? If it is an unknown constant, then how will I find when the said result will occur. Is it 1? Or does the value of a has no impact on the result (but it certainly does)? Or on calculation the value of 'a' will be given? I think I did not understand the question properly. ??? That I cannot answer. I'm currently doing some reading on the curves and trying to see what I can get out of it. (so far not much ;)) But I know nothing about coding. I am trying kind of mathematically. It is okay, right? Quote Hereby I am offering a bounty of 30 BTC to the first one solving the following mathematical problem either mathematically or using an algorithm: I just need OP to tell me whether the results I got are correct or not to proceed any further. I want to be sure whether I am in the correct understanding of it or not. Thanks for the link. Now i think 'a' is a value input by the user. Mathematically as long as the "a" value remains constant during each new iteration then the effect it has is constant - it's not unnecessary, it just doesn't need to be evaluated for, so it should be fine to set as any integer and leave it alone. As got the results you got, I don't think you are substituting the equation back into itself for each new x value, I think you are just increasing x by 1 and then repeating the calculation. What you want to be doing is leaving x constant (in this case 9) and then reevaluating each iteration until your new x value matches the next incremented integer value of x (in this case 10). If I've misunderstood anything, feel free to correct me. That's just how I understand it. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 02:22:23 PM No, I am substituting the equation back into itself. Please check if I was wrong. Are you using standard division where the / is or are you using "multiplication by the modular inverse" http://cs.brown.edu/courses/cs007/modmult/node2.html Should we be knowing what 'p' is or is this another arbitrary number like 'a'? (basically all operations modulo some sumber p) Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on January 31, 2015, 02:27:33 PM No, I am substituting the equation back into itself. Please check if I was wrong. Are you using standard division where the / is or are you using "multiplication by the modular inverse" http://cs.brown.edu/courses/cs007/modmult/node2.html Should we be knowing what 'p' is or is this another arbitrary number like 'a'? (basically all operations modulo some sumber p) lol, sorry, I did a mistake. I simply substituted the equation back in after each process. I skipped adding it. understood the question better now. But still have things unclear. Quote You can start multiple such chains beginning at x=9, and add the resulting x values using the addition algorithm from http://en.wikipedia.org/wiki/Montgomery_curve (Montgomery arithmetic section). Note, that the x value, is the value you get at the end of such calculation-chain, and the z value is always 1. what is meant by multiple chains? aand where is this 'z'? and is this the reqd formula?http://i.gyazo.com/44c0566495e87ced1a180840c2fb9555.png Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 02:37:53 PM Quote You can start multiple such chains beginning at x=9, and add the resulting x values using the addition algorithm from http://en.wikipedia.org/wiki/Montgomery_curve (Montgomery arithmetic section). Note, that the x value, is the value you get at the end of such calculation-chain, and the z value is always 1. wHat is meant by multiple chains? aand where is this 'z'? I don't know what he is referring to by 'multiple chains' Another user suggested 'z' might be Standard_Score/Standard_Deviation although I don't think that is correct Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 02:43:47 PM Was just reading more on the Montgomery curve under the arithmetic section, I think we are safe to "ignore" z, him saying z=1 allows us to say X=x and that's all we need the z for.
Code: A point P=(x,y) on the elliptic curve in the Montgomery form By^2 = x^3 + Ax^2 + x can be represented in Montgomery coordinates P=(X:Z), where P=(X:Z) are projective coordinates and x=X/Z for Z!=0 Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on January 31, 2015, 02:46:36 PM Was just reading more on the Montgomery curve under the arithmetic section, I think we are safe to "ignore" z, him saying z=1 allows us to say X=x and that's all we need the z for. Code: A point P=(x,y) on the elliptic curve in the Montgomery form By^2 = x^3 + Ax^2 + x can be represented in Montgomery coordinates P=(X:Z), where P=(X:Z) are projective coordinates and x=X/Z for Z!=0 yes, that seems a reasonable interpretation. Should i ignore a as given by ncsupanda. I don't think that ignoring 'a' is right. Mathematically as long as the "a" value remains constant during each new iteration then the effect it has is constant - it's not unnecessary, it just doesn't need to be evaluated for, so it should be fine to set as any integer and leave it alone. As got the results you got, I don't think you are substituting the equation back into itself for each new x value, I think you are just increasing x by 1 and then repeating the calculation. What you want to be doing is leaving x constant (in this case 9) and then reevaluating each iteration until your new x value matches the next incremented integer value of x (in this case 10). If I've misunderstood anything, feel free to correct me. That's just how I understand it. Also, is this http://i.gyazo.com/44c0566495e87ced1a180840c2fb9555.png the right formula? If so, A=a? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on January 31, 2015, 02:51:39 PM Quote How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)? that is the exact operation I did. So I was not wrong? I also get an impression that, each one has multiple solutions? which probably explains Quote You can start multiple such chains beginning at x=9, and add the resulting x values ? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 03:19:40 PM Should i ignore a as given by ncsupanda. I don't think that ignoring 'a' is right. Mathematically as long as the "a" value remains constant during each new iteration then the effect it has is constant - it's not unnecessary, it just doesn't need to be evaluated for, so it should be fine to set as any integer and leave it alone. Also, is this http://i.gyazo.com/44c0566495e87ced1a180840c2fb9555.png the right formula? If so, A=a? I think 'a' is an arbitrary constant provided by Evil-Knievel From the problem description "Being a some constant," I think is meant to be interpreted as Code: 'a' being some constant Quote How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)? that is the exact operation I did. So I was not wrong? Here's my thinking on the question... https://i.imgur.com/E4WgWN0.png x_0 is always 9 a is an arbitrary constant G is the end goal, also an arbitrary number chosen by Evil-Knievel _i is the number of steps through the recursive function you must take to reach G Evil-Knievel is looking for a way to solve '_i' provided any 'a' and any 'G' EDIT: That's not just standard division, it's as he mentioned using inverse modular multiplication, but visually it's depicted as division. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: crazykiddo on January 31, 2015, 03:38:06 PM Did someone solve the problem and get the bounty? What was that mathematical formula for? I heard evil wants to crack bitcoin. This formula is useful for cracking bitcoin?
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on January 31, 2015, 03:40:19 PM Did someone solve the problem and get the bounty? What was that mathematical formula for? I heard evil wants to crack bitcoin. This formula is useful for cracking bitcoin? http://img2.wikia.nocookie.net/__cb20140808184223/bloodbrothersgame/images/c/c7/Implied_facepalm.jpg Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on January 31, 2015, 04:38:54 PM Should i ignore a as given by ncsupanda. I don't think that ignoring 'a' is right. Mathematically as long as the "a" value remains constant during each new iteration then the effect it has is constant - it's not unnecessary, it just doesn't need to be evaluated for, so it should be fine to set as any integer and leave it alone. Also, is this http://i.gyazo.com/44c0566495e87ced1a180840c2fb9555.png the right formula? If so, A=a? I think 'a' is an arbitrary constant provided by Evil-Knievel From the problem description "Being a some constant," I think is meant to be interpreted as Code: 'a' being some constant Quote How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)? that is the exact operation I did. So I was not wrong? Here's my thinking on the question... https://i.imgur.com/E4WgWN0.png x_0 is always 9 a is an arbitrary constant G is the end goal, also an arbitrary number chosen by Evil-Knievel _i is the number of steps through the recursive function you must take to reach G Evil-Knievel is looking for a way to solve '_i' provided any 'a' and any 'G' EDIT: That's not just standard division, it's as he mentioned using inverse modular multiplication, but visually it's depicted as division. I think you are right. thanks for clarifying it. :) Did someone solve the problem and get the bounty? What was that mathematical formula for? I heard evil wants to crack bitcoin. This formula is useful for cracking bitcoin? http://img2.wikia.nocookie.net/__cb20140808184223/bloodbrothersgame/images/c/c7/Implied_facepalm.jpglol. :) Been seeing a lot of people asking the same thing. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: koelen3 on January 31, 2015, 08:16:52 PM Maths always seemed to hard for me :(
But i'll try it Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: redsn0w on February 01, 2015, 08:21:09 PM So what is the winner of this contest ? I've seen he moved the funds to other bitcoin addresses :
- https://blockchain.info/it/tx/ce4473df59f34aedfca5e5ead092f2c864292eb4cb7cffb91461f814c994ebc8 - https://blockchain.info/it/tx/2fa9040b611069fa97779ee7db0d3ff1088095d3c0e1131973946f904d429f22 Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: jsmit332 on February 01, 2015, 08:24:44 PM I would like to know what the winning solution was.
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: brituspol on February 01, 2015, 08:42:23 PM I'm totally confused.
Where is x and y? Edit: The winners? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 01, 2015, 08:47:38 PM There is no winner yet.
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: jsmit332 on February 01, 2015, 08:48:05 PM There is no winner yet. Where have the funds gone then? Why has Evil-Kinevel moved the BTC? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: brituspol on February 01, 2015, 08:49:15 PM There is no winner yet. Where have the funds gone then? Why has Evil-Kinevel moved the BTC? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 01, 2015, 08:53:53 PM There is no winner yet. Where have the funds gone then? Why has Evil-Kinevel moved the BTC? Look at replies 45, 46, 65, 66 and a few others. The balance was selected by his wallet to pay one of his other bounties Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: caga on February 01, 2015, 09:38:00 PM I emember op requested for the solution to be messaged to him in private. He might have got the solution, and might now share. But I was hoping to see a confirmation if there was a winner.
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Watoshi-Dimobuto on February 02, 2015, 05:18:22 AM There is no winner yet. Where have the funds gone then? Why has Evil-Kinevel moved the BTC? Look at replies 45, 46, 65, 66 and a few others. The balance was selected by his wallet to pay one of his other bounties Put that in a large font size. Too many people asking the same question. Don't bother answering them all. Solution not yet found. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: chronicsky on February 04, 2015, 10:28:06 AM Can the OP confirm if the solution has still not been found?
Title: This message was too old and has been purged Post by: Evil-Knievel on February 04, 2015, 10:32:40 AM This message was too old and has been purged
Title: This message was too old and has been purged Post by: Evil-Knievel on February 04, 2015, 10:33:04 AM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: david123 on February 04, 2015, 12:42:31 PM If you want a solution, don't raise the bounty but get your question right.
At the moment, this is not at all about finding a solution, but about guessing what exactly you're asking for. You will only attract php-kiddies in this way. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 04, 2015, 01:05:47 PM If you want a solution, don't raise the bounty but get your question right. At the moment, this is not at all about finding a solution, but about guessing what exactly you're asking for. You will only attract php-kiddies in this way. When he posts test vectors we can infer the proper question. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: david123 on February 04, 2015, 01:12:05 PM yeah, guessing will get a bit easier then, but I don't get why he doesnt spend the time
to make the question meaningful.. ??? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on February 04, 2015, 01:17:11 PM If you want a solution, don't raise the bounty but get your question right. At the moment, this is not at all about finding a solution, but about guessing what exactly you're asking for. You will only attract php-kiddies in this way. Yeah, I agree with this. My problem is I don't know exactly what the question is. I got the average idea but it is not enough. I also have to be sure it is under my capability to solve before attempting harder on it. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Supercomputing on February 04, 2015, 08:25:58 PM Problem Description: Being a some constant, further assume that we are in a factor ring (basically all operations modulo some sumber p). Note, that the division below is a multiplication by the modular inverse. You always have to start with x=9. Consider the following recursive formula: Code: new_x = (x²-1)² / (4*x*(x²+a*x+1)) How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)? Note: You can start multiple such chains beginning at x=9, and add the resulting x values using the addition algorithm from http://en.wikipedia.org/wiki/Montgomery_curve (Montgomery arithmetic section). Note, that the x value, is the value you get at the end of such calculation-chain, and the z value is always 1. The winner: The winner is the first person to post such formula in private. The formula must work in all cases, and be comutationally feasible (let us say calculatable in less than 24 hours). If there are any wrong descriptions in this post at this time, they may be corrected or adjusted later on. Bounty ends on 02/15/2015. The bounty is invalid because the problem description is ambiguous. However, it may be an attempt to solve the ECDLP based on Curve25519 for all instances: http://en.wikipedia.org/wiki/Curve25519 Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Jesse James on February 04, 2015, 08:42:55 PM The bounty is invalid because the problem description is ambiguous. However, it may be an attempt to solve the ECDLP based on Curve25519 for all instances: http://en.wikipedia.org/wiki/Curve25519 My thoughts exactly. Is the organizer willing to offer a consolation prize to anyone who can produce a proof that the original problem is impossible given the Elliptic Curve Discrete Logarithm assumption? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Jesse James on February 04, 2015, 09:45:31 PM Here's my attempt to restate the original problem in a way that is less ambiguous and hopefully reveal more clearly the OP's intent.
Challenge: Optimize the 'find' function in the code below so that on average it can be computed for less than 1M USD in EC2 compute cost. Code: (python) # http://en.wikipedia.org/wiki/Curve25519 parameters Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: LiQio on February 05, 2015, 05:36:34 AM ^ Jesse James/doctorevil this is so over my head.
All I can say is, you're such a cool guy :) *slightly blushes and continues to watch the thread* Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on February 05, 2015, 06:27:28 AM Here's my attempt to restate the original problem in a way that is less ambiguous and hopefully reveal more clearly the OP's intent. Challenge: Optimize the 'find' function in the code below so that on average it can be computed for less than 1M USD in EC2 compute cost. Code: (python) # http://en.wikipedia.org/wiki/Curve25519 parameters Dang! I don't know Python or any programming language. :( But I think I can get a better idea of the question. Thanks for posting this. :) Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 05, 2015, 07:40:43 AM Here's my C++ implementation: https://github.com/bitspill/CurveBounty
The version I PM'd you the other day was ATROCIOUS that was my mind at 4am and it suffered as such, here is a revamped version. If I'm on the right path I can make some adjustments but I don't want to pursue this if I'm running in the wrong direction. Title: This message was too old and has been purged Post by: Evil-Knievel on February 05, 2015, 08:21:19 AM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 05, 2015, 08:26:36 AM Here's my C++ implementation: https://github.com/bitspill/CurveBounty The version I PM'd you the other day was ATROCIOUS that was my mind at 4am and it suffered as such, here is a revamped version. If I'm on the right path I can make some adjustments but I don't want to pursue this if I'm running in the wrong direction. It is the right direction, but it looks like a brute force approach. If it works good (and fast) for all search x, this should be fine, but at this moment an x which is not a power of two would not be found. ;) Yes it is brute forcing it. ;) I'm not sure as to what you mean by an x can't be found if it's not a power of two, the following x is not a power of 2: Code: x=83402281777707715381485212681368749158073214888176003645002923212220704930560 If you are referencing the _i's those are only printed every 256 so as to not bog down performance with constant console writes but yet often enough to know it hasn't stalled. Title: This message was too old and has been purged Post by: Evil-Knievel on February 05, 2015, 08:45:22 AM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on February 05, 2015, 08:47:07 AM Here's my C++ implementation: https://github.com/bitspill/CurveBounty The version I PM'd you the other day was ATROCIOUS that was my mind at 4am and it suffered as such, here is a revamped version. If I'm on the right path I can make some adjustments but I don't want to pursue this if I'm running in the wrong direction. It is the right direction, but it looks like a brute force approach. If it works good (and fast) for all search x, this should be fine, but at this moment an x which is not a power of two would not be found. ;) Yes it is brute forcing it. ;) I'm not sure as to what you mean by an x can't be found if it's not a power of two, the following x is not a power of 2: Code: x=83402281777707715381485212681368749158073214888176003645002923212220704930560 If you are referencing the _i's those are only printed every 256 so as to not bog down performance with constant console writes but yet often enough to know it hasn't stalled. it is not a power of two, because it was calculated modulo, but the exponent is a power of two. So you have doubled "x=9" 10240 times, so basically it is 2^10240 * (x=9) where the multiplication is the montgomery curve scalar multiplication. You could say, that 83402281777707715381485212681368749158073214888176003645002923212220704930560 is easily found, but 83402281777707715381485212681368749158073214888176003645002923212220704930559 not. And this is the tough case, because: - the loop iteration can either grow arbitrary large - or: you need to create multiple such iterations with different "i" values, and add them according to the montgomery curve addition rules. I think this ^ is right. and also brute forcing it many not be feasible if the above points are taken? But now you know what we are searching for. :) Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: SargeR33 on February 05, 2015, 10:02:52 AM I am a programmer/developer, pretty good with maths but this thread blew my brain multiple times.
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 05, 2015, 10:24:39 AM I am a programmer/developer, pretty good with maths but this thread blew my brain multiple times. The wonders of cryptography. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: david123 on February 05, 2015, 10:42:43 AM I am a programmer/developer, pretty good with maths but this thread blew my brain multiple times. The wonders of cryptography. Rather the incompetence of the op. So, did someone get what he is asking for and could kindly repeat it in a clear, concise way without abusing mathematical terms too much? That would be great. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 05, 2015, 10:45:22 AM I am a programmer/developer, pretty good with maths but this thread blew my brain multiple times. The wonders of cryptography. Rather the incompetence of the op. So, did someone get what he is asking for and could kindly repeat it in a clear, concise way without abusing mathematical terms too much? That would be great. It's basically what Jesse James and I were doing but we are only doubling, you must also check addition in order to satisfy his request Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: david123 on February 05, 2015, 10:50:20 AM yeuh but what are you doing? are you performing calculations on an
elliptic curve? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 05, 2015, 11:12:39 AM yeuh but what are you doing? are you performing calculations on an elliptic curve? From what I gather we are Title: This message was too old and has been purged Post by: Evil-Knievel on February 05, 2015, 11:18:18 AM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: david123 on February 05, 2015, 11:36:16 AM yeuh but what are you doing? are you performing calculations on an elliptic curve? From what I gather we are So with searching you mean finding a logarithm? This is a well studied problem believed to be hard in general, and there are software packages doing this as good as possible (which is not very good. this is the whole point of using elliptic curves for cryptography^^) I really don't get the point of this thread. 30 BTC bounty for cracking ECC?? I offer 100 BTC for cracking SHA! (But maybe I have to obsure the problem and rephrase it into semi-mathematical terms for it to be taken seriously..) Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 05, 2015, 11:43:14 AM Maybe each addition can be replaced by an arbitrary number of doubles? Not sure about that, but possible. Example: modulo 11 four doubles: 1*2*2*2*2 = 5 two doubled one add: 1*2*2 + 1 = 5 mod: 11 Goal: 6 9 doubles: Code: 1 *2 *2 *2 *2 *2 *2 *2 *2 *2 = 6 Code: 1 *2 *2 *2 *2 +1 = 6 Code: 1 *2 *2 +1 +1 = 6 Title: This message was too old and has been purged Post by: Evil-Knievel on February 05, 2015, 11:55:16 AM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 05, 2015, 12:30:40 PM @bitspill: This is the point ... maybe each combinations of adds and doubles can be represented by a (way higher) number of doubles only. That does not appear to be the case from super basic testing http://pastebin.com/raw.php?i=C9KhyFry https://github.com/bitspill/Doubling/blob/master/main.cpp A value of -999 means it attempted doubling 100 million times and did not find the goal, so I'm treating that as if it wont ever find it. It's likely possible to add checks such that when all possibilities have been exhausted it quits rather than an arbitrary 100 million but I have not So it would seem in some cases you can't simply double your way there, an add is required occasionally. Edit: actually it shouldnt be checking for the exhaustion of possibilities but rather the entrance of a loop. Which is possible to implement on tgese small scale test but a loop would be nearly impossible to detect at the scale of 2^256 Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: swapcoiner on February 05, 2015, 06:18:26 PM After fixing my computer,my first job would be to sweep the fund here.
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Jesse James on February 06, 2015, 02:02:56 AM What Evil hints at is correct.
If you have a generator element b of an additive group of order N, and you know it takes x repeated doubling operations (squaring operations in the context of a multiplicative group) on this element in order to reach q then you have effectively solved [multiplicative group notation]: q = b2x for x. What we really want to do is crack the discrete logarithm, which means finding x in the context of: q = bx So the question becomes: if we can solve the first equation can we solve the second? The answer is yes. The reason is that the exponent of b is itself an element of it's own multiplicative group ℤN× of which 2 is a generator since N is prime (at least in the context of Curve25519 or secp256k1). So if you find x that satisfies: q = b2x then you can use your solution to solve the discrete log easy peasy lemon squeezy.: logb(q) = 2x mod N Having at this point successfully solved the discrete log, you can happily collect your 30 BTC which will shortly be worthless since the security of bitcoin relies on the discrete logarithm assumption. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: fox19891989 on February 06, 2015, 03:36:24 AM What a huge bounty, does anyone solve it? I just check your btc address, the balance is 0. I guess it must be solved. What a pity, I am good at math very much.
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 06, 2015, 03:50:33 AM What a huge bounty, does anyone solve it? I just check your btc address, the balance is 0. I guess it must be solved. What a pity, I am good at math very much. It is not solved. Funds were used by the wallet for another bounty but he does have enough to cover it, and actually raised it to 40 BTC Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: LiQio on February 06, 2015, 06:07:27 AM ... Having at this point successfully solved the discrete log, you can happily collect your 30 BTC which will shortly be worthless since the security of bitcoin relies on the discrete logarithm assumption. OP should switch the bounty to fiat (or crypto money not based on discrete logarithm assumption) Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: michietn94 on February 06, 2015, 07:40:00 AM What a huge bounty, does anyone solve it? I just check your btc address, the balance is 0. I guess it must be solved. What a pity, I am good at math very much. It is not solved. Funds were used by the wallet for another bounty but he does have enough to cover it, and actually raised it to 40 BTC I just look OP's receive red feedback because offering this bounty for his research's good. Hope he will paid what he promise or OP can use escrow to hold the fund. Title: This message was too old and has been purged Post by: Evil-Knievel on February 06, 2015, 07:41:22 AM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: mriulian on February 07, 2015, 04:13:32 PM hmm.at school i didn't studied anything like that..i will give my best :)
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on February 07, 2015, 07:20:14 PM I HAVE SOLVED THE ISSUE WITH THE MATHEMATICAL EQUATION! ITS FINALLY CLEAR NOW!!!!
here var equation = equation.replace("x", "(x²-1)² / (4*x*(x²+a*x+1))"); should read var equation = equation.replace(/x/gi, "(x²-1)² / (4*x*(x²+a*x+1))"); which I already tested for you <script> var equation= "(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))"; var a=0;var b=1;var x=9; document.write(equation+"</br>"); while(a<b) { var equation = equation.replace(/x/gi, "(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))"); document.write(equation+"</br>"); a=a+1; } var x2=x*x; var answer=(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1)); document.write(answer+"</br>"); var answer=((x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))*x-1)*(x*x-1) / (4*x*(x*x+a*x+1)); document.write(answer+"</br>"); var x=9; var answer=(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1)); document.write(answer+"</br>"); var x=answer; var answer=(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1)); document.write(answer+"</br>"); var x=9; var answer=((x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))-1)*((x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))-1) / (4*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))*((x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))+a*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))+1)) document.write(answer+"</br>"); </script> I also changed (x²-1)² / (4*x*(x²+a*x+1)) and used (x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1)) instead because javascript can directly evaluate it. Just for demonstation purposes I left var x=9; var answer=(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1)); document.write(answer+"</br>"); var x=answer; var answer=(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1)); document.write(answer+"</br>"); which is evaluation by recursion. Find the answer plug it back into the equation etc. Compared with the created equation var x=9; var answer=((x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))-1)*((x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))-1) / (4*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))*((x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))+a*(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))+1)) document.write(answer+"</br>"); both of which return the same answer so the code in the end is <script> var equation= "(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))";var a=0;var b=6;var x=9;var c=0;document.write(eval(equation)+"</br>"); while(c<b){var equation = equation.replace(/x/gi, "(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))"); document.write(equation+"</br></br>");document.write(eval(equation)+"</br>");c=c+1;} </script> This will give you just the answers minus the equations <script> var equation= "(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))";var a=0;var b=6;var x=9;var c=0;document.write(eval(equation)+"</br>"); while(c<b){var equation = equation.replace(/x/gi, "(x*x-1)*(x*x-1) / (4*x*(x*x+a*x+1))"); document.write(eval(equation)+"</br>");c=c+1;} </script> Please send bounty to THIS BTC adress!!! 14DFu1bW6DSPPuJYnZLn9EfgKeFYcLaFAN 14DFu1bW6DSPPuJYnZLn9EfgKeFYcLaFAN 14DFu1bW6DSPPuJYnZLn9EfgKeFYcLaFAN Title: This message was too old and has been purged Post by: Evil-Knievel on February 07, 2015, 07:36:06 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on February 07, 2015, 08:14:47 PM WHAT IS WRONG WITH WHAT I POSTED?! WHAT IS NOT CORRECT?! YOU POSTED SOMETHING YOU NEEDED AN ANSWER FOR, I DID THE MATH AND THE ALGORITHM, IT IS NOT INCORRECT!!!!
Title: This message was too old and has been purged Post by: Evil-Knievel on February 07, 2015, 08:15:44 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on February 07, 2015, 08:21:42 PM can you please give me exactly what you are looking for in a CLEAR AND PRECISE PRivate Message? cause i mean you were unclear to begin with and every post its all jumping around to different maths and shit. like seriously you want me to solve thois shit you gotta be clear what you are looking for what types of maths are involved and what type of algorithm or mathematical formula you are requesting. i only went off of what your OP stated (which, was still very unclear)
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ncsupanda on February 07, 2015, 09:19:58 PM can you please give me exactly what you are looking for in a CLEAR AND PRECISE PRivate Message? cause i mean you were unclear to begin with and every post its all jumping around to different maths and shit. like seriously you want me to solve thois shit you gotta be clear what you are looking for what types of maths are involved and what type of algorithm or mathematical formula you are requesting. i only went off of what your OP stated (which, was still very unclear) Yes Evil, please give him the answer so that he can earn his 30 BTC by doing mindless calculations and no real math to prove anything. If the question tells you exactly how to get the answer, then it is a tutorial. The answer is to THINK, not just complain. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on February 07, 2015, 11:02:01 PM I'm not entirely sure what you're asking here OP, but a couple of things popped into my mind while RE-reading:
1. Using the formula for new_x i presented, if we have to start with x = 9, then we have (x2 - 1)2 = 6400, which means the formula will never reach 10 for any p where 6400 = 0 (mod p), or for which (64002 - 1)2 = 1677721518080001 = 0 (mod p), etc. 2. Though you possibly qualified it by saying "at least in the context of...", I just thought I'd note that 2 is not necessarily a generator of ℤp× where p is prime. Consider, for example, p = 7. Of course, I may be misunderstanding entirely what you're wanting to do. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 07, 2015, 11:36:20 PM pythonpro1337: The 'p' in (mod p) is 2^255 - 19 and he's not searching for 10 but rather some arbitrarily large number such as 83402281777707715381485212681368749158073214888176003645002923212220704930559
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on February 08, 2015, 02:45:45 AM pythonpro1337: The 'p' in (mod p) is 2^255 - 19 and he's not searching for 10 but rather some arbitrarily large number such as 83402281777707715381485212681368749158073214888176003645002923212220704930559 Alright, though OP did say any formula we produce should work "in all cases," which I take to mean for general p and general x. Having re-read the thread, I noticed a few things I missed earlier. Are you essentially trying to find a general method for quickly finding the discrete logarithm? Are you looking to break elliptic curve cryptography? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on February 08, 2015, 06:51:15 AM As much as I'd like to help, if I were able to find an efficient way to find the discrete logarithm, I'd publish a paper on it and hope it was enough for a Fields Medal. :P
While a good quantum algorithm is known due to Shor, there is no known general way to find the discrete logarithm "quickly" on a classical computer. People with a lot more experience than I have (or anyone else here has) in group theory, cryptography, etc., have worked on this without success, so I wouldn't bank on getting help here. Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: ndnh on February 08, 2015, 07:08:13 AM pythonpro1337: The 'p' in (mod p) is 2^255 - 19 and he's not searching for 10 but rather some arbitrarily large number such as 83402281777707715381485212681368749158073214888176003645002923212220704930559 Alright, though OP did say any formula we produce should work "in all cases," which I take to mean for general p and general x. Having re-read the thread, I noticed a few things I missed earlier. Are you essentially trying to find a general method for quickly finding the discrete logarithm? Are you looking to break elliptic curve cryptography? Yes, I think he is looking to break ECC. I understand the issue you had, I also misinterpreted the question twice. I think I could attempt this if I had a supercomputer? Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on February 08, 2015, 07:37:56 AM indeed it would require all the computers and severs powers combined all over the world to get this number, you would be talking about infecting the whole internet with a worm and telling the zombies to run this script to find the algorithm in unison statically. would be impossible but it COULD BE POSSIBLE. just saying your chances are not in any lifetimes generation soon. sorry this bounty will run till the year 3567 A.D. we just dont have the technology to solve this in any way!
CASE CLOSED!!!! Title: This message was too old and has been purged Post by: Evil-Knievel on February 08, 2015, 08:03:32 AM This message was too old and has been purged
Title: This message was too old and has been purged Post by: Evil-Knievel on February 08, 2015, 08:04:27 AM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: pythonpro1337 on February 08, 2015, 08:18:32 AM Lol, pythoncoderpro changes his messages arbitrarily. See my last quote for his original message. so what are you trying to say? i type from computer or phone phone uses correct punctuation automatically where as im lazy when i type on the pc who cares Title: This message was too old and has been purged Post by: Evil-Knievel on February 08, 2015, 10:45:22 AM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Pallie on February 11, 2015, 01:29:58 PM I have two questions:
Is the x, for which we search the number of iterations, an integer? Does the solution have to be either a formula or a program? Because I might have one that is neither. Title: This message was too old and has been purged Post by: Evil-Knievel on February 11, 2015, 01:32:30 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: jsmit332 on February 12, 2015, 04:50:08 PM I have two questions: Is the x, for which we search the number of iterations an integer? Does the solution have to be either a formula or a program? Because I might have one that is neither. It must be an integer, as we are working in the ring Z/pZ I bet it's 2 ;D Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Jesse James on February 13, 2015, 03:21:10 AM Though you possibly qualified it by saying "at least in the context of...", I just thought I'd note that 2 is not necessarily a generator of ℤp× where p is prime. Consider, for example, p = 7. My bad, pythonpro1337 is correct. However, 2 is a generator of the multiplicative group of integers modulo 7237005577332262213973186563042994240857116359379907606001950938285454250989 (the order of the Curve25519 elliptic curve group), so the rest of my argument (https://bitcointalk.org/index.php?topic=939215.msg10372118#msg10372118) holds. Proof For convenience: N = 7237005577332262213973186563042994240857116359379907606001950938285454250989 Note that saying 2 is a generator of ℤN× is the same as saying 2 is primitive root modulo N. Since N is prime, ϕ(N) = N-1 If 2 isn't a primitive root then then it's order must divide N-1. Given the prime factorization of N-1 = 276602624281642239937218680557139826668747 * 198211423230930754013084525763697 * 33 * 2 * 2 and the fact that: 2(N-1)/276602624281642239937218680557139826668747 ≢ 1 (mod N) 2(N-1)/198211423230930754013084525763697 ≢ 1 (mod N) 2(N-1)/33 ≢ 1 (mod N) 2(N-1)/2 ≢ 1 (mod N) We can conclude that 2 is indeed a primitive root (and thus a generator of ℤN×). Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: bitspill on February 13, 2015, 05:23:22 AM An approach idea. Take an arbitrary x value (the one that is looked for, and find the point, that caused that value when inserted into the formula. In Mathematica that would be: Solve[(x*x - 1)^2/(4*x*(x*x + 486662*x + 1)) == THEVALUETOLOOKFOR, Modulus -> 2^255 - 19] Then go back the whole chain, unti you reach x=9. This can sometimes be tricky, that is why you probably have to think about it further. Only working in the case that it's a doubled value this should find the answer without brute forcing. Disclaimer: I don't have Mathematica to test rather I'm writing based on documentation. G = THEVALUETOLOOKFOR; _x = G; _i = 0; While[_x!=9, _x = Solve[(x*x - 1)^2/(4*x*(x*x + 486662*x + 1)) == _x, x, Modulus -> 2^255 - 19]; _i++]; Print["G (", G, ") is x=9 doubled ", _i, " times"] Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: Vortex20000 on February 21, 2015, 12:56:42 AM You guys are getting paid, what, ~7-8k USD, to crack ECC? Sorry, just read like 50% of this thread. Fun bounty though.
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: excword on February 21, 2015, 02:49:30 PM This bounty is still running. Interesting.
Title: This message was too old and has been purged Post by: Evil-Knievel on February 21, 2015, 04:08:58 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: dothebeats on February 22, 2015, 11:25:51 AM Reading the whole thread makes me want to learn math more and understand the different jargon laid before my own eyes. Fun bounty, Evil-Knievel. Inspired me to sharpen my mathematical skills.
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: larry12 on February 24, 2015, 07:06:16 PM Let me try. If not work i will try again tomorrow. ;)
C++ Code: #include<iostream.h> BTC ADDRESS : 1CeWcoy5Lv7PoZJ9JqqSsjBz7gfrLCoJpj Title: This message was too old and has been purged Post by: Evil-Knievel on February 24, 2015, 07:14:21 PM This message was too old and has been purged
Title: Re: [30 BTC Bounty] - Find a mathematical / algorithmical formula Post by: larry12 on February 24, 2015, 07:16:43 PM Hmm... yes you're right..... ;)
Ok. I will try again tomorrow when i have more time. The bounty is too good not to try again ;D Have a nice day. ;) |
