Topic: Pollard's kangaroo ECDLP solver - page 112. (Read 55599 times)
Guys, how are you from Public Keys, coordinates define? I tried how many on the site http://gobittest.appspot.com/Address I do not understand how??? Teach me please!
I can't get information from the file save.work I use the command -winfo(Kangaroo.exe -winfo save.work), the program just collapses without giving any result. You may need an additional parameter?
-snip-
-------
if some tool change pubkey inside save.work, and this save work recalculate within all his record, how much time its take to find changed pubkey for same 64 bit
if you change only pubkey it will be not working, due to wildDP produced from old pubkey.-------
if some tool change pubkey inside save.work, and this save work recalculate within all his record, how much time its take to find changed pubkey for same 64 bit
You need tame wild DP with known private key and than you can use this file agan but there will be only tame DP.
I think today about using experience and concluded that it might help, but not too much. The whole point of a kangaroo is the effect of a birthday paradox. And if we have no pairs in the working file, but only one view, then the help is not too big, I think.
-snip-
-------
if some tool change pubkey inside save.work, and this save work recalculate within all his record, how much time its take to find changed pubkey for same 64 bit
if you change only pubkey it will be not working, due to wildDP produced from old pubkey.-------
if some tool change pubkey inside save.work, and this save work recalculate within all his record, how much time its take to find changed pubkey for same 64 bit
You need tame wild DP with known private key and than you can use this file agan but there will be only tame DP.
I think today about using experience and concluded that it might help, but not too much. The whole point of a kangaroo is the effect of a birthday paradox. And if we have no pairs in the working file, but only one view, then the help is not too big, I think.
To Jean Luc
if checking 64 bit, and save.work file 1 gb and found in 6 min
./kangaroo -winfo save.work
Kangaroo v1.5
Loading: save.work
Version : 0
DP bits : 8
Start : 0
Stop : FFFFFFFFFFFFFFF
Key : 034B7DBF84F4AF9B9E5B9C15EEDE9C671FF5194FAF5290CE61DF4D2396A9FF22F0
Count : 8657043456 2^33.011
Time : 05:44
DP Size : 518.0/654.0MB
DP Count : 16908283 2^24.011
HT Max : 105 [@ 035B51]
HT Min : 31 [@ 03A140]
HT Avg : 64.50
HT SDev : 8.02
Kangaroos : 4194304 2^22.000
-------
if some tool change pubkey inside save.work, and this save work recalculate within all his record, how much time its take to find changed pubkey for same 64 bit
if checking 64 bit, and save.work file 1 gb and found in 6 min
./kangaroo -winfo save.work
Kangaroo v1.5
Loading: save.work
Version : 0
DP bits : 8
Start : 0
Stop : FFFFFFFFFFFFFFF
Key : 034B7DBF84F4AF9B9E5B9C15EEDE9C671FF5194FAF5290CE61DF4D2396A9FF22F0
Count : 8657043456 2^33.011
Time : 05:44
DP Size : 518.0/654.0MB
DP Count : 16908283 2^24.011
HT Max : 105 [@ 035B51]
HT Min : 31 [@ 03A140]
HT Avg : 64.50
HT SDev : 8.02
Kangaroos : 4194304 2^22.000
-------
if some tool change pubkey inside save.work, and this save work recalculate within all his record, how much time its take to find changed pubkey for same 64 bit
after finding 110 puzzle, forum seems silent, no further discussion related to dp, split, client server, chit chat, all goes to home as show ended, and winner goes for celebrate, and dev also goes to rest with family,
hope near to finding puzzle 115, all crowed gather again at cinema for next show end
hope near to finding puzzle 115, all crowed gather again at cinema for next show end
30 days.. 30 pages.. want news? doubling Ygrid gives +25% speed
Can you explain yourself better? What is 'Ygrid' ?
It's obvious for half a year and already known to those interested.
Setting -g X, Y ... Ultimately Y is 128, while raising this value to 256 or 512 increases the speed. What a sly man - he gave news.
It is time for those present to take off the pink glasses.
Half. From ZERO.
ZERO (it's not even his equipment)
Congratulation and nice job
https://www.youtube.com/watch?v=q6mMh4pRki8
Babbler only. Be careful with zielar.
30 days.. 30 pages.. want news? doubling Ygrid gives +25% speed
Jean Luc should get at least half, IMO. He spent a lot of time developing the software and fixing bugs and adding features that other people requested.
Yes, definitely. No less than you for #59, #60, #61, #62 and #63. Half. From ZERO.
How much will jean_luc get 
?
Guess, what be.?great to hear
how much power cost do you have ?
Guess, what answer. how much power cost do you have ?
ZERO (it's not even his equipment)
I helped him a bit yesterday to have a clean setup.
God, he can't even run someone else's program.Congratulation and nice job
https://www.youtube.com/watch?v=q6mMh4pRki8
Babbler only. Be careful with zielar.
30 days.. 30 pages.. want news? doubling Ygrid gives +25% speed
What hurts you, son? Do you have any complex? You got zero because the work you did for me is unusable. Since shit is semi-certain and I didn't make anything out of it - what would you like?
Secondly - I was asked by JeanLucPons for an address to pay him for help ... I appreciate his help and consider it valuable (as opposed to your sticky thing).
He renounced it twice, however ... What do you say ... that I should transfer some sum to be burned to keep my honor?
You should not be interested in the source of my equipment. If I have access to it - it means I earned it and deserved it. You are an ordinary shit for me, to whom I will certainly not explain what and where. Get to work better and don't cry here, warning others before me, because I didn't hurt anyone, and you pour out your bitter regrets here because Your ass is jealous.
Get yourself together, Pull yourself together.
30 days.. 30 pages.. want news? doubling Ygrid gives +25% speed
Can you explain yourself better? What is 'Ygrid' ?
It is time for those present to take off the pink glasses.
Half. From ZERO.
ZERO (it's not even his equipment)
Congratulation and nice job
https://www.youtube.com/watch?v=q6mMh4pRki8
Babbler only. Be careful with zielar.
30 days.. 30 pages.. want news? doubling Ygrid gives +25% speed
Jean Luc should get at least half, IMO. He spent a lot of time developing the software and fixing bugs and adding features that other people requested.
Yes, definitely. No less than you for #59, #60, #61, #62 and #63. Half. From ZERO.
How much will jean_luc get ?
Guess, what be.?great to hear
how much power cost do you have ?
Guess, what answer. how much power cost do you have ?
ZERO (it's not even his equipment)
I helped him a bit yesterday to have a clean setup.
God, he can't even run someone else's program.Congratulation and nice job
https://www.youtube.com/watch?v=q6mMh4pRki8
Babbler only. Be careful with zielar.
30 days.. 30 pages.. want news? doubling Ygrid gives +25% speed
Can @zielar share of saved tables of 110 bit? 
Congratulation to @zielar and @JeanLuc!
Is this the correct x and y coords for pub 110?
Public Key : 0309976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Xcoordinate: 09976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Ycoordinate: 02EF58F7EEF3EBBC285602744AD51753BAD939C214FF6A465C384377ABDEA7B9
YesPublic Key : 0309976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Xcoordinate: 09976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Ycoordinate: 02EF58F7EEF3EBBC285602744AD51753BAD939C214FF6A465C384377ABDEA7B9
Is this the correct x and y coords for pub 110?
Public Key : 0309976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Xcoordinate: 09976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Ycoordinate: 02EF58F7EEF3EBBC285602744AD51753BAD939C214FF6A465C384377ABDEA7B9
Yes Public Key : 0309976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Xcoordinate: 09976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Ycoordinate: 02EF58F7EEF3EBBC285602744AD51753BAD939C214FF6A465C384377ABDEA7B9
Is this the correct x and y coords for pub 110?
Public Key : 0309976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Xcoordinate: 09976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Ycoordinate: 02EF58F7EEF3EBBC285602744AD51753BAD939C214FF6A465C384377ABDEA7B9
Public Key : 0309976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Xcoordinate: 09976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Ycoordinate: 02EF58F7EEF3EBBC285602744AD51753BAD939C214FF6A465C384377ABDEA7B9
About using an experience of previous work.
Here is test, were all possible DPs from previous was put to next work.
Gain from pazzle#54 to #79
DP=20 for both variants.
Most likely because the range is increased by 32 times in the next puzzle, and all DPs are concentrated at the very beginning of the range. Perhaps experience can help in solving the next range, but not after 5 bits.
And here is result of 3 test randomly generated keys in range 64bit and with experience from the puzzle 79.
The result is that experience helps you find the key in the current range or in the previous one, but it is absolutely useless to search in the following range that is multiple large to the current one.
In other words, in order to solve the puzzle faster you need to move from end to beginning .. first 125, then 120, then 115 and then 110))
How do you (anyone/everyone) configure/modify previous DPs and apply them to another range? Is it done automatically somehow or do you have to manually tweak each previous DP to fit next range? This is interesting... Here is test, were all possible DPs from previous was put to next work.
Gain from pazzle#54 to #79
DP=20 for both variants.
Code:
pazzle#54
*original*
40000000000000
7fffffffffffff
0385a30d8413af4f8f9e6312400f2d194fe14f02e719b24c3f83bf1fd233a8f963
[Count 2^32.75]result>0x6ABE1F9B67E114
*shifted*
0
3fffffffffffff
04b1f8ba606a61026d1ecaa93d9e9ceb12260c33e92809ed1ecb0850a2856accc1ac46d892583d7fdd24a25a229b6ea8d17add77b1f410a9d30441e0acbec19c74
[Count 2^32.76]result>0x2ABE1F9B67E114 + 0x40000000000000 = 0x6abe1f9b67e114
pazzle#59
*original*
800000000000000
fffffffffffffff
0348e843dc5b1bd246e6309b4924b81543d02b16c8083df973a89ce2c7eb89a10d
[Count 2^34.63]result>0xFC07A1825367BBE
*shifted + experience*
0
7ffffffffffffff
042b90a8680d08cf81e15e209acadbb16b7bdff19787d6d13ca6a7852fee8d1013447a29425ea9773471ad9810d21a976cf5bd4bdb46d0c8ae537591dce43252f2
[Count 2^35.42]result>0x7C07A1825367BBE+0x800000000000000 = 0xfc07a1825367bbe
pazzle#64
*original*
10000000000000000
1ffffffffffffffff
0230210c23b1a047bc9bdbb13448e67deddc108946de6de639bcc75d47c0216b1b
[Count 2^34.49]result>0x1A838B13505B26867
*shifted + experience*
0
ffffffffffffffff
04e7daa14feea7f3e6b77aa3ff75989ac171d9b3f7a263e70eab001849f2f185449b51b0bc783313d9e201f1bc453d0e7c2bb94db007ab7a848a63b47d86f29416
[Count 2^36.70]result>0xA838B13505B26867+0x10000000000000000 = 0x1a838b13505b26867
pazzle#69
*original*
200000000000000000
3fffffffffffffffff
0290e6900a58d33393bc1097b5aed31f2e4e7cbd3e5466af958665bc0121248483
[Count 2^38.68]result>0x349B84B6431A6C4EF1
*shifted + experience*
0
1fffffffffffffffff
049ffc74f6136e60e9229a58544c0e9cffa5a9d955d949e75e4bccbe1c06b81c3402d4ba4d9f65b918376c0cbf6f8caa840a6261cf900f413fb5279bb243f20c4c
[Count 2^38.43]result>0x149B84B6431A6C4EF1+0x200000000000000000 = 0x349b84b6431a6c4ef1
pazzle#74
*original*
4000000000000000000
7ffffffffffffffffff
03726b574f193e374686d8e12bc6e4142adeb06770e0a2856f5e4ad89f66044755
[Count 2^38.56]result>0x4C5CE114686A1336E07
*shifted + experience*
0
3ffffffffffffffffff
04997bf5a3795f965c338f3739dae9e4cc202c2203100e6be8132a65bf2c3681d1fa67799ecfb697015037e44076c734ad2eef8c3b166e04b0a76d8c0de0e14dc2
[Count 2^40.32]result>0xC5CE114686A1336E07+0x4000000000000000000 = 0x4c5ce114686a1336e07
pazzle#79
*original*
80000000000000000000
ffffffffffffffffffff
037e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc
[Count 2^39.25]result>0xEA1A5C66DCC11B5AD180
*shifted + experience*
0
7fffffffffffffffffff
043aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256def6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9
[Count 2^41.87]result>0x6A1A5C66DCC11B5AD180+0x80000000000000000000 = 0xea1a5c66dcc11b5ad180
So as you can see an experience didn`t help to solve next pazzle faster.*original*
40000000000000
7fffffffffffff
0385a30d8413af4f8f9e6312400f2d194fe14f02e719b24c3f83bf1fd233a8f963
[Count 2^32.75]result>0x6ABE1F9B67E114
*shifted*
0
3fffffffffffff
04b1f8ba606a61026d1ecaa93d9e9ceb12260c33e92809ed1ecb0850a2856accc1ac46d892583d7fdd24a25a229b6ea8d17add77b1f410a9d30441e0acbec19c74
[Count 2^32.76]result>0x2ABE1F9B67E114 + 0x40000000000000 = 0x6abe1f9b67e114
pazzle#59
*original*
800000000000000
fffffffffffffff
0348e843dc5b1bd246e6309b4924b81543d02b16c8083df973a89ce2c7eb89a10d
[Count 2^34.63]result>0xFC07A1825367BBE
*shifted + experience*
0
7ffffffffffffff
042b90a8680d08cf81e15e209acadbb16b7bdff19787d6d13ca6a7852fee8d1013447a29425ea9773471ad9810d21a976cf5bd4bdb46d0c8ae537591dce43252f2
[Count 2^35.42]result>0x7C07A1825367BBE+0x800000000000000 = 0xfc07a1825367bbe
pazzle#64
*original*
10000000000000000
1ffffffffffffffff
0230210c23b1a047bc9bdbb13448e67deddc108946de6de639bcc75d47c0216b1b
[Count 2^34.49]result>0x1A838B13505B26867
*shifted + experience*
0
ffffffffffffffff
04e7daa14feea7f3e6b77aa3ff75989ac171d9b3f7a263e70eab001849f2f185449b51b0bc783313d9e201f1bc453d0e7c2bb94db007ab7a848a63b47d86f29416
[Count 2^36.70]result>0xA838B13505B26867+0x10000000000000000 = 0x1a838b13505b26867
pazzle#69
*original*
200000000000000000
3fffffffffffffffff
0290e6900a58d33393bc1097b5aed31f2e4e7cbd3e5466af958665bc0121248483
[Count 2^38.68]result>0x349B84B6431A6C4EF1
*shifted + experience*
0
1fffffffffffffffff
049ffc74f6136e60e9229a58544c0e9cffa5a9d955d949e75e4bccbe1c06b81c3402d4ba4d9f65b918376c0cbf6f8caa840a6261cf900f413fb5279bb243f20c4c
[Count 2^38.43]result>0x149B84B6431A6C4EF1+0x200000000000000000 = 0x349b84b6431a6c4ef1
pazzle#74
*original*
4000000000000000000
7ffffffffffffffffff
03726b574f193e374686d8e12bc6e4142adeb06770e0a2856f5e4ad89f66044755
[Count 2^38.56]result>0x4C5CE114686A1336E07
*shifted + experience*
0
3ffffffffffffffffff
04997bf5a3795f965c338f3739dae9e4cc202c2203100e6be8132a65bf2c3681d1fa67799ecfb697015037e44076c734ad2eef8c3b166e04b0a76d8c0de0e14dc2
[Count 2^40.32]result>0xC5CE114686A1336E07+0x4000000000000000000 = 0x4c5ce114686a1336e07
pazzle#79
*original*
80000000000000000000
ffffffffffffffffffff
037e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc
[Count 2^39.25]result>0xEA1A5C66DCC11B5AD180
*shifted + experience*
0
7fffffffffffffffffff
043aeb4f818ca91912a3e50d1b3db196696f82713bae00ba2b53c09a23f1d284a085b2197137256def6c05a0f105e1b1eee9c10d23b7a4911040a23e891ebb3dc9
[Count 2^41.87]result>0x6A1A5C66DCC11B5AD180+0x80000000000000000000 = 0xea1a5c66dcc11b5ad180
Most likely because the range is increased by 32 times in the next puzzle, and all DPs are concentrated at the very beginning of the range. Perhaps experience can help in solving the next range, but not after 5 bits.
And here is result of 3 test randomly generated keys in range 64bit and with experience from the puzzle 79.
Code:
***test 64bit****
*original*
10000000000000000
1ffffffffffffffff
035492d5b1c9e271d393ace35b32ed922e1ad202ff0c0aa05f53ba39edcabb003c
[Count 2^36.63]result>0x151881A76D2AEC2D9
*shifted + experience79bit*
0
ffffffffffffffff
049959d0a41a11f42a64f2a86c8133089e7fa508e53fb4afc64c03e5b4b109edd7b9c955dd43bca51b6db320602101d10585ebf60330bd3ea9d445b6cbb6e18932
[Count 2^34.63]result>0x51881A76D2AEC2D9+0x10000000000000000 = 0x151881a76d2aec2d9
***test 64bit****
*original*
10000000000000000
1ffffffffffffffff
03a643b91c86b76a71ec6f9c6a6d0a9ba71fcf3c69c11b919a252b44b76bfe9b6f
[Count 2^35.93]result>0x1CC24D7785E54FD54
*shifted + experience79bit*
0
ffffffffffffffff
0443814ed8fe2a1d4a36993911354fe8f7bf6daddbfcc3a1f814a3d3d32c7772eaa448c10af7a7f4f94da0c35e087cfba5310c81f86c4b0aaca9250476960305b7
[Count 2^34.87]result>0xCC24D7785E54FD54+0x10000000000000000 = 0x1cc24d7785e54fd54
***test 64bit****
*original*
10000000000000000
1ffffffffffffffff
035267fc38fc04ef271b54f5be8e482c46392ba97ca171e68d2408dd0717bd87cf
[Count 2^37.10]result>0x1114527E6BCFD0EAD
*shifted + experience79bit*
0
ffffffffffffffff
041c4f6e5f89465a941bb4291cf0266fff79c333e4dc1b30e5a8671b15504f364f1e5be5ba0cb4f8b19769ac5904aa465dab6fb3b8ace9862c704f8ea5a916d061
[Count 2^35.56]result>0x114527E6BCFD0EAD+0x10000000000000000 = 0x1114527e6bcfd0ead
In all three cases, experience helped me find the key faster.*original*
10000000000000000
1ffffffffffffffff
035492d5b1c9e271d393ace35b32ed922e1ad202ff0c0aa05f53ba39edcabb003c
[Count 2^36.63]result>0x151881A76D2AEC2D9
*shifted + experience79bit*
0
ffffffffffffffff
049959d0a41a11f42a64f2a86c8133089e7fa508e53fb4afc64c03e5b4b109edd7b9c955dd43bca51b6db320602101d10585ebf60330bd3ea9d445b6cbb6e18932
[Count 2^34.63]result>0x51881A76D2AEC2D9+0x10000000000000000 = 0x151881a76d2aec2d9
***test 64bit****
*original*
10000000000000000
1ffffffffffffffff
03a643b91c86b76a71ec6f9c6a6d0a9ba71fcf3c69c11b919a252b44b76bfe9b6f
[Count 2^35.93]result>0x1CC24D7785E54FD54
*shifted + experience79bit*
0
ffffffffffffffff
0443814ed8fe2a1d4a36993911354fe8f7bf6daddbfcc3a1f814a3d3d32c7772eaa448c10af7a7f4f94da0c35e087cfba5310c81f86c4b0aaca9250476960305b7
[Count 2^34.87]result>0xCC24D7785E54FD54+0x10000000000000000 = 0x1cc24d7785e54fd54
***test 64bit****
*original*
10000000000000000
1ffffffffffffffff
035267fc38fc04ef271b54f5be8e482c46392ba97ca171e68d2408dd0717bd87cf
[Count 2^37.10]result>0x1114527E6BCFD0EAD
*shifted + experience79bit*
0
ffffffffffffffff
041c4f6e5f89465a941bb4291cf0266fff79c333e4dc1b30e5a8671b15504f364f1e5be5ba0cb4f8b19769ac5904aa465dab6fb3b8ace9862c704f8ea5a916d061
[Count 2^35.56]result>0x114527E6BCFD0EAD+0x10000000000000000 = 0x1114527e6bcfd0ead
The result is that experience helps you find the key in the current range or in the previous one, but it is absolutely useless to search in the following range that is multiple large to the current one.
In other words, in order to solve the puzzle faster you need to move from end to beginning .. first 125, then 120, then 115 and then 110))
No "v1.9alpha" in GITHUB !!!! 110 racked with NEW VERSION WHAT NOT AVAILABLE, may just now not aval-l maybe forever !!!
Cobras...the 1.9alpha isn't an official release. Jean Luc made some changes to the code but has not released it as an official release yet. When he tweaks the code, he updates his source code/repository.
look here, on line 22:
https://github.com/JeanLucPons/Kangaroo/blob/master/Constants.h
so if you download source code and compile, your compiled version will also say 1.9alpha.
Hope that helps.
No "v1.9alpha" in GITHUB !!!! 110 racked with NEW VERSION WHAT NOT AVAILABLE, may just now not aval-l maybe forever !!!
Congrates to winner
giving you new thinking level for 115, from my previous research, some friends here tested but hard for them to believe earlier, just for information
check my 2048 pubkeys list
https://anonfiles.com/a750taA8n6/100bit_txt dated November 09, 2019, 06:35:23 PM
refrence
https://bitcointalksearch.org/topic/m.53030914
privatekey 110
hex: 35c0d7234df7deb0f20cf7062444
hex: 00000000000000000000000000000000000035c0d7234df7deb0f20cf7062444
dec: 1090246098153987172547740458951748 / 1024
dec: 1064693455228503098191152791945.06640625
hex: D7035C8D37DF7AC3C833DC189
pubkey: 03bb788bea10bedfc4f32aee0f542fc9a0749b5db72a8b094cbbad9fde366f6fa4
hex: D7035C8D37DF7AC3C833DC188
pubkey: 02f2c172df4c4553891bd3c5e8a668a8fd5f5a46d0bc6b109649507180011301ac
check my created 100 bit 02f2...301ac and 03bb788... 6fa4 listed in 2048 corresponding keys to 110 puzzle
@brainlessgiving you new thinking level for 115, from my previous research, some friends here tested but hard for them to believe earlier, just for information
check my 2048 pubkeys list
https://anonfiles.com/a750taA8n6/100bit_txt dated November 09, 2019, 06:35:23 PM
refrence
https://bitcointalksearch.org/topic/m.53030914
privatekey 110
hex: 35c0d7234df7deb0f20cf7062444
hex: 00000000000000000000000000000000000035c0d7234df7deb0f20cf7062444
dec: 1090246098153987172547740458951748 / 1024
dec: 1064693455228503098191152791945.06640625
hex: D7035C8D37DF7AC3C833DC189
pubkey: 03bb788bea10bedfc4f32aee0f542fc9a0749b5db72a8b094cbbad9fde366f6fa4
hex: D7035C8D37DF7AC3C833DC188
pubkey: 02f2c172df4c4553891bd3c5e8a668a8fd5f5a46d0bc6b109649507180011301ac
check my created 100 bit 02f2...301ac and 03bb788... 6fa4 listed in 2048 corresponding keys to 110 puzzle
The solution set to your list is [(110_bit_private_key - 2i)/(1024)] modulo (secp256k1_group_order). This adds no new information to help solve the problem.
Nice job!
How much will jean_luc get?
How much will jean_luc get
?How much he wants
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