All of this story tell us something.

We now know that someone out there is able to crack aprox. 2^50 private keys in about 1 year.

(in a worst case scenario, also assuming that the one who cracked the 50 addresses brute forced all the possible addresses sequential)

As time goes by this capability will increase, it may take decades and decades or centuries but eventually it will be possible to crack 2^256 pvks.

The transaction referenced in this thread is a good reference to test how far the mankind cracking capabilities are.

As of now, we can enjoy the safety of bitcoin for a long long time

2^1   2   
2^2   4   
2^3   8   
2^4   16   
2^5   32   
2^6   64   
2^7   128   
2^8   256   
2^9   512   
2^10   1024   
2^11   2048   
2^12   4096   
2^13   8192   
2^14   16384   
2^15   32768   
2^16   65536   
2^17   131072   
2^18   262144   
2^19   524288   
2^20   1048576   
2^21   2097152   
2^22   4194304   
2^23   8388608   
2^24   16777216   
2^25   33554432   
2^26   67108864   
2^27   134217728   
2^28   268435456   
2^29   536870912   
2^30   1073741824   
2^31   2147483648   
2^32   4294967296   
2^33   8589934592   
2^34   17179869184   
2^35   34359738368   
2^36   68719476736   
2^37   137438953472   
2^38   274877906944   
2^39   549755813888   
2^40   1099511627776   
2^41   2199023255552   
2^42   4398046511104   
2^43   8796093022208   
2^44   17592186044416   
2^45   35184372088832   
2^46   70368744177664   
2^47   140737488355328   
2^48   281474976710656   
2^49   562949953421312   
2^50   1125899906842620   <- This is aprox. the number of bitcoins private keys someone is able to crack in about 1 year
2^51   2251799813685250   
2^52   4503599627370500   
2^53   9007199254740990   
2^54   18014398509482000   
2^55   36028797018964000   
2^56   72057594037927900   
2^57   144115188075856000   
2^58   288230376151712000   
2^59   576460752303423000   
2^60   1152921504606850000   
2^61   2305843009213690000   
2^62   4611686018427390000   
2^63   9223372036854780000   
2^64   18446744073709600000   
2^65   36893488147419100000   
2^66   73786976294838200000   
2^67   147573952589676000000   
2^68   295147905179353000000   
2^69   590295810358706000000   
2^70   1180591620717410000000   
2^71   2361183241434820000000   
2^72   4722366482869650000000   
2^73   9444732965739290000000   
2^74   18889465931478600000000   
2^75   37778931862957200000000   
2^76   75557863725914300000000   
2^77   151115727451829000000000   
2^78   302231454903657000000000   
2^79   604462909807315000000000   
2^80   1208925819614630000000000   
2^81   2417851639229260000000000   
2^82   4835703278458520000000000   
2^83   9671406556917030000000000   
2^84   19342813113834100000000000   
2^85   38685626227668100000000000   
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2^137   174224571863520000000000000000000000000000   
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2^142   5575186299632660000000000000000000000000000   
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2^144   22300745198530600000000000000000000000000000   
2^145   44601490397061200000000000000000000000000000   
2^146   89202980794122500000000000000000000000000000   
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2^156   91343852333181400000000000000000000000000000000   
2^157   182687704666363000000000000000000000000000000000   
2^158   365375409332726000000000000000000000000000000000   
2^159   730750818665451000000000000000000000000000000000   
2^160   1461501637330900000000000000000000000000000000000   
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2^162   5846006549323610000000000000000000000000000000000   
2^163   11692013098647200000000000000000000000000000000000   
2^164   23384026197294400000000000000000000000000000000000   
2^165   46768052394588900000000000000000000000000000000000   
2^166   93536104789177800000000000000000000000000000000000   
2^167   187072209578356000000000000000000000000000000000000   
2^168   374144419156711000000000000000000000000000000000000   
2^169   748288838313422000000000000000000000000000000000000   
2^170   1496577676626840000000000000000000000000000000000000   
2^171   2993155353253690000000000000000000000000000000000000   
2^172   5986310706507380000000000000000000000000000000000000   
2^173   11972621413014800000000000000000000000000000000000000   
2^174   23945242826029500000000000000000000000000000000000000   
2^175   47890485652059000000000000000000000000000000000000000   
2^176   95780971304118100000000000000000000000000000000000000   
2^177   191561942608236000000000000000000000000000000000000000   
2^178   383123885216472000000000000000000000000000000000000000   
2^179   766247770432944000000000000000000000000000000000000000   
2^180   1532495540865890000000000000000000000000000000000000000   
2^181   3064991081731780000000000000000000000000000000000000000   
2^182   6129982163463560000000000000000000000000000000000000000   
2^183   12259964326927100000000000000000000000000000000000000000   
2^184   24519928653854200000000000000000000000000000000000000000   
2^185   49039857307708400000000000000000000000000000000000000000   
2^186   98079714615416900000000000000000000000000000000000000000   
2^187   196159429230834000000000000000000000000000000000000000000   
2^188   392318858461668000000000000000000000000000000000000000000   
2^189   784637716923335000000000000000000000000000000000000000000   
2^190   1569275433846670000000000000000000000000000000000000000000   
2^191   3138550867693340000000000000000000000000000000000000000000   
2^192   6277101735386680000000000000000000000000000000000000000000   
2^193   12554203470773400000000000000000000000000000000000000000000   
2^194   25108406941546700000000000000000000000000000000000000000000   
2^195   50216813883093400000000000000000000000000000000000000000000   
2^196   100433627766187000000000000000000000000000000000000000000000   
2^197   200867255532374000000000000000000000000000000000000000000000   
2^198   401734511064748000000000000000000000000000000000000000000000   
2^199   803469022129495000000000000000000000000000000000000000000000   
2^200   1606938044258990000000000000000000000000000000000000000000000   
2^201   3213876088517980000000000000000000000000000000000000000000000   
2^202   6427752177035960000000000000000000000000000000000000000000000   
2^203   12855504354071900000000000000000000000000000000000000000000000   
2^204   25711008708143800000000000000000000000000000000000000000000000   
2^205   51422017416287700000000000000000000000000000000000000000000000   
2^206   102844034832575000000000000000000000000000000000000000000000000   
2^207   205688069665151000000000000000000000000000000000000000000000000   
2^208   411376139330302000000000000000000000000000000000000000000000000   
2^209   822752278660603000000000000000000000000000000000000000000000000   
2^210   1645504557321210000000000000000000000000000000000000000000000000   
2^211   3291009114642410000000000000000000000000000000000000000000000000   
2^212   6582018229284820000000000000000000000000000000000000000000000000   
2^213   13164036458569600000000000000000000000000000000000000000000000000   
2^214   26328072917139300000000000000000000000000000000000000000000000000   
2^215   52656145834278600000000000000000000000000000000000000000000000000   
2^216   105312291668557000000000000000000000000000000000000000000000000000   
2^217   210624583337114000000000000000000000000000000000000000000000000000   
2^218   421249166674229000000000000000000000000000000000000000000000000000   
2^219   842498333348457000000000000000000000000000000000000000000000000000   
2^220   1684996666696910000000000000000000000000000000000000000000000000000   
2^221   3369993333393830000000000000000000000000000000000000000000000000000   
2^222   6739986666787660000000000000000000000000000000000000000000000000000   
2^223   13479973333575300000000000000000000000000000000000000000000000000000   
2^224   26959946667150600000000000000000000000000000000000000000000000000000   
2^225   53919893334301300000000000000000000000000000000000000000000000000000   
2^226   107839786668603000000000000000000000000000000000000000000000000000000   
2^227   215679573337205000000000000000000000000000000000000000000000000000000   
2^228   431359146674410000000000000000000000000000000000000000000000000000000   
2^229   862718293348820000000000000000000000000000000000000000000000000000000   
2^230   1725436586697640000000000000000000000000000000000000000000000000000000   
2^231   3450873173395280000000000000000000000000000000000000000000000000000000   
2^232   6901746346790560000000000000000000000000000000000000000000000000000000   
2^233   13803492693581100000000000000000000000000000000000000000000000000000000   
2^234   27606985387162300000000000000000000000000000000000000000000000000000000   
2^235   55213970774324500000000000000000000000000000000000000000000000000000000   
2^236   110427941548649000000000000000000000000000000000000000000000000000000000   
2^237   220855883097298000000000000000000000000000000000000000000000000000000000   
2^238   441711766194596000000000000000000000000000000000000000000000000000000000   
2^239   883423532389192000000000000000000000000000000000000000000000000000000000   
2^240   1766847064778380000000000000000000000000000000000000000000000000000000000   
2^241   3533694129556770000000000000000000000000000000000000000000000000000000000   
2^242   7067388259113540000000000000000000000000000000000000000000000000000000000   
2^243   14134776518227100000000000000000000000000000000000000000000000000000000000   
2^244   28269553036454100000000000000000000000000000000000000000000000000000000000   
2^245   56539106072908300000000000000000000000000000000000000000000000000000000000   
2^246   113078212145817000000000000000000000000000000000000000000000000000000000000   
2^247   226156424291633000000000000000000000000000000000000000000000000000000000000   
2^248   452312848583266000000000000000000000000000000000000000000000000000000000000   
2^249   904625697166533000000000000000000000000000000000000000000000000000000000000   
2^250   1809251394333070000000000000000000000000000000000000000000000000000000000000   
2^251   3618502788666130000000000000000000000000000000000000000000000000000000000000   
2^252   7237005577332260000000000000000000000000000000000000000000000000000000000000   
2^253   14474011154664500000000000000000000000000000000000000000000000000000000000000   
2^254   28948022309329000000000000000000000000000000000000000000000000000000000000000   
2^255   57896044618658100000000000000000000000000000000000000000000000000000000000000   
2^256   115792089237316000000000000000000000000000000000000000000000000000000000000000   <- And this is how safe bitcoin is.

Probably only two guys know that (who cracked and who owns), and they are probably not among us in this forum.

It's impossible to say whether or not any future mathematicians will be able to discover any weaknesses in the ECDSA algorithm with the secp256k1 curve.

It will not, however, ever be possible to brute-force attempt 2²⁵⁶ possibilities.


2¹⁶⁰ is the security level of version 1 bitcoin addresses.


Nope.

That's how secure an ECDSA public key is, but version 1 bitcoin addresses use a 160 bit hash of that public key, so the security is reduced to 2¹⁶⁰.

So a version 1 bitcoin address has a security level of 2¹⁶⁰, but how to make sure you have a security of 2²⁵⁶? From when on was the version 1 bitcoin address abandoned and we are sure to enjoy increased security?

Maybe I'm understanding this wrong and everybody is using version 1 addresses, but I would rather know for sure I'm using the safest keys possible.

After some analysis I believe the underlying sequence is probably random.  It may have been a PRNG instead of a RNG but that would not help us much.  It would be great if we had all 50 actual values to work with.

Even though the security of Bitcoin is reduced to "only" 2¹⁶⁰ by the selected second hashing algorithm it is actually more secure in other ways due to the selection of two different hashing algorithms in the public key to Bitcoin address step since both algorithms need to be broken in order to break that step.

Every step of the way everything possible was done to ensure that Bitcoin was secure.  For example Bitcoin is one of the only systems in existence that uses the secp256k1 curve instead of the secp256r1 curve that is used by almost everyone else.  But this was a very wise decision in light of recent leaks about the NSA and their underhanded practices with respect to the cryptography they produce or help produce.

secp256r1 was designed by the NSA, secp256k1 was not.

Very good info, thanks.

I also got to similar conclusion, doesn't look like this will be solvable without years of brute force.

It would be great if the guy that cracked the #50 shows up here and tell us the results.


Exactly, was going to reply similar post.

There are many laws in the universe that we still don't know, finding them can completely rewrite everything.

Just look at all the quantum field and you will see how many unanswered questions are there.

Off topic but interesting:

https://www.youtube.com/watch?v=DfPeprQ7oGc

We all will be long gone when that happens to tell you "I told you so" 

About the puzzle, the final verdict is that it is unsolvable without brute force, same opinion all?

Good luck with this, cause i havn't got a baldy what the heck yous are talking about.