this is normal math sqrt√(x)^2,
test value: 4^2 = 16, next root return 4
-8^2= 64,next root return 8
how to bitcoin Publickey x and y use to sqrt example: √(x,y)^2
how to calculate sqrt for bitcoin publickey teach me please
example1:x,y
px: e493dbf1c10d80f3581e4904930b1404cc6c13900ee0758474fa94abe8c4cd13 py: 51ed993ea0d455b75642e2098ea51448d967ae33bfbdfe40cfe97bdc47739922 #privatekey 4
px: 421f5fc9a21065445c96fdb91c0c1e2f2431741c72713b4b99ddcb316f31e9fc py: 2b90f16d11dabdb616f6db7e225d1e14743034b37b223115db20717ad1cd6781 #privatekey 4^2 = 16
ans
px: e493dbf1c10d80f3581e4904930b1404cc6c13900ee0758474fa94abe8c4cd13 py: 51ed993ea0d455b75642e2098ea51448d967ae33bfbdfe40cfe97bdc47739922 #privatekey √16 = 4
example2:
px: 2f01e5e15cca351daff3843fb70f3c2f0a1bdd05e5af888a67784ef3e10a2a01 py: a3b25758beac66b6d6c2f7d5ecd2ec4b3d1dec2945a489e84a25d3479342132b # -8
px: ed3bace23c5e17652e174c835fb72bf53ee306b3406a26890221b4cef7500f88 py: e57a6f571288ccffdcda5e8a7a1f87bf97bd17be084895d0fce17ad5e335286e # -8^ = 64
ans
px: 2f01e5e15cca351daff3843fb70f3c2f0a1bdd05e5af888a67784ef3e10a2a01 py: 5c4da8a741539949293d082a132d13b4c2e213d6ba5b7617b5da2cb76cbde904 # √64 = 8
how does work explain. do u understad my problem ,i speak little english
Topic: y coordinate calculation (PUBLIC KEY BITCOIN) (Read 940 times)
Here's the output
#mybadenglishwrite
other example
i am genarate rsz value,
step 1: rsz value in sample_rsz.txt get
step 2: rsz to private key hexconvert
step 3: cheak for balance
your not get rsz value in sample_rsz.txt please skip step1(and) write your code step2,step3
other help please solve:
iam run ImportError: No module named txnUtils
https://github.com/FoxxD3V/btc-rsz/blob/master/RawTX_RSZ.py
Code:
'Set X'
['0xaf5a13d03a858342aea7dcc0772d66d65b83f6fa17988568cc219866a99436ccL',
'0x680c20dcdca0813ae3450845c18c6b4975e96281313fb811dda958bca2222076L',
'0x8d485591727814848b4917388714866d9fd60f0269112edb646f3c13e06924f0L',']
'Set Y'
['0xc694e15f92cddfb68aebcc313f5594b987e7ae7d72f5bfc7b44b6adbd4301ee1L',
'0xe1bb14e7912ff0224f95d90c710ccf830bef75e1bfe16898adf80fe0d4b595c9L',
'0xf44e87d22618b5f5b6545cf5555092c64d279708eaf12a5518bbe9bca0d1aae2L']
['0xaf5a13d03a858342aea7dcc0772d66d65b83f6fa17988568cc219866a99436ccL',
'0x680c20dcdca0813ae3450845c18c6b4975e96281313fb811dda958bca2222076L',
'0x8d485591727814848b4917388714866d9fd60f0269112edb646f3c13e06924f0L',']
'Set Y'
['0xc694e15f92cddfb68aebcc313f5594b987e7ae7d72f5bfc7b44b6adbd4301ee1L',
'0xe1bb14e7912ff0224f95d90c710ccf830bef75e1bfe16898adf80fe0d4b595c9L',
'0xf44e87d22618b5f5b6545cf5555092c64d279708eaf12a5518bbe9bca0d1aae2L']
#mybadenglishwrite
other example
i am genarate rsz value,
step 1: rsz value in sample_rsz.txt get
step 2: rsz to private key hexconvert
step 3: cheak for balance
your not get rsz value in sample_rsz.txt please skip step1(and) write your code step2,step3
Code:
sample_rsz.txt
python getz_input.py -txid f9aa66876f79ed8870720e9019e769548f591d285cc2d16460c411c5da0912ca
Starting Program...
======================================================================
[Input Index #: 0]
R: 00823cd5826d4dda527055dd8c183c3911a7689c03250214c9928c502d556d5dcd
S: 708cbaadc433e75db1b2d2b49f1dcb29a6abcf830fb49b5e2f43edf58a9855f7
Z: cab8d8ead97afc124085bb98127ba0c4c8fc9e0f6908c88c43b24565f98b61f8
PubKey: 039c5889d0ea6c234f0986a519677ec17b8402762bb5e1c2fc85d74256bded7273
======================================================================
[Input Index #: 1]
R: 7020dab260a2621f0ba6ca9cb7117d9f0c3764cf802fbf9f1ec270b876e86478
S: 477b0abf12644608fd2a96c1b877aa6d38cc97beadb23f0935cae3d02da29e50
Z: ac1b62f6fe57a9e226460367fbe45dcad394ea167b44b607182390eec19817be
PubKey: 021af19d3e7658610ace22a8cac1a4349fc9ea253d60459d109d152a40df20a7b6
======================================================================
[Input Index #: 2]
R: 40381bfcdaa49e8dc464c7efa260c47ab943d87e55a7bfec9e50791c7a9b00c1
S: 48eaf79559aec14634c80ca1ac9acce1c70dac7f3f23e029bb3509e06826558e
Z: 8fe79999e5a085062b64a973fc7e1cfb96343383aa415e191f2c6fea9e91a1d5
PubKey: 031ab5e8b751a9d0fb1a7c8db749bf08d2f96adf700070ed98c192e2226ecaf54a
======================================================================
[Input Index #: 3]
R: 27a2026dc60891e753d5769654eae6fdb4273ad5e43b453c89f98ddf735a60d3
S: 287ee3d8394b8020bfa8eb2cbd1731de9b56ebfb7853e9c45a8429d444a4532d
Z: da97a9cf6cdc44477da5299626789bfbec96ad5108d8a38166901790e7ef25a1
PubKey: 036c134583e010e1a0a41ce03ab453d8aa09979e9929af208bf7130145aec27eec
======================================================================
[Input Index #: 4]
R: 125dd347afe4554df33946d3948e96b24fb852b97a0bfa2ea8d2f4efc7958f9d
S: 63ac3605c815a28c2721cfce08aacabf95fffcad9c33dd49f1d16110ac3c379e
Z: db2d008d6d0f78d6b766539099f6939a412d5fc75460ce7e8e42d3aec4fc4b54
PubKey: 0233244cb067b59e82de611f665284111b07b6867380efb9317cba100af345974c
======================================================================
[Input Index #: 5]
R: 00a264c4897e694fd13c6f0348977bad815499b0cd7df34fd5a4ee680463d3c30c
S: 72c579ee7c9cb502c903ac71d60d93834c2a9ce8a43215ed853c619337c1cfe8
Z: cf22845485cd95c625bf92c9a92b49f1166315d4545e404cd213bc4022ca32e5
PubKey: 0374d16a1603a5691eb73aa12be62e506792cff5772def92376d1dbf7d15a64a4d
======================================================================
[Input Index #: 6]
R: 6fc545a0360d77a92e5f00ad13f947c48d3d61605b091f43d3b8c9aeca68a3ea
S: 472db6ab16c4b34442a123764e871bbf1c866810996a3117c7a4937ef0b92b52
Z: 49acf9eb7e34189460d96ef1d8ce0d6bd35e5ff659da757775244aeb887b398d
PubKey: 0242ae9c0bd6300b20b08709546b79a02ef3a297a7eee1299121e2f79eb646c5b9
python getz_input.py -txid f9aa66876f79ed8870720e9019e769548f591d285cc2d16460c411c5da0912ca
Starting Program...
======================================================================
[Input Index #: 0]
R: 00823cd5826d4dda527055dd8c183c3911a7689c03250214c9928c502d556d5dcd
S: 708cbaadc433e75db1b2d2b49f1dcb29a6abcf830fb49b5e2f43edf58a9855f7
Z: cab8d8ead97afc124085bb98127ba0c4c8fc9e0f6908c88c43b24565f98b61f8
PubKey: 039c5889d0ea6c234f0986a519677ec17b8402762bb5e1c2fc85d74256bded7273
======================================================================
[Input Index #: 1]
R: 7020dab260a2621f0ba6ca9cb7117d9f0c3764cf802fbf9f1ec270b876e86478
S: 477b0abf12644608fd2a96c1b877aa6d38cc97beadb23f0935cae3d02da29e50
Z: ac1b62f6fe57a9e226460367fbe45dcad394ea167b44b607182390eec19817be
PubKey: 021af19d3e7658610ace22a8cac1a4349fc9ea253d60459d109d152a40df20a7b6
======================================================================
[Input Index #: 2]
R: 40381bfcdaa49e8dc464c7efa260c47ab943d87e55a7bfec9e50791c7a9b00c1
S: 48eaf79559aec14634c80ca1ac9acce1c70dac7f3f23e029bb3509e06826558e
Z: 8fe79999e5a085062b64a973fc7e1cfb96343383aa415e191f2c6fea9e91a1d5
PubKey: 031ab5e8b751a9d0fb1a7c8db749bf08d2f96adf700070ed98c192e2226ecaf54a
======================================================================
[Input Index #: 3]
R: 27a2026dc60891e753d5769654eae6fdb4273ad5e43b453c89f98ddf735a60d3
S: 287ee3d8394b8020bfa8eb2cbd1731de9b56ebfb7853e9c45a8429d444a4532d
Z: da97a9cf6cdc44477da5299626789bfbec96ad5108d8a38166901790e7ef25a1
PubKey: 036c134583e010e1a0a41ce03ab453d8aa09979e9929af208bf7130145aec27eec
======================================================================
[Input Index #: 4]
R: 125dd347afe4554df33946d3948e96b24fb852b97a0bfa2ea8d2f4efc7958f9d
S: 63ac3605c815a28c2721cfce08aacabf95fffcad9c33dd49f1d16110ac3c379e
Z: db2d008d6d0f78d6b766539099f6939a412d5fc75460ce7e8e42d3aec4fc4b54
PubKey: 0233244cb067b59e82de611f665284111b07b6867380efb9317cba100af345974c
======================================================================
[Input Index #: 5]
R: 00a264c4897e694fd13c6f0348977bad815499b0cd7df34fd5a4ee680463d3c30c
S: 72c579ee7c9cb502c903ac71d60d93834c2a9ce8a43215ed853c619337c1cfe8
Z: cf22845485cd95c625bf92c9a92b49f1166315d4545e404cd213bc4022ca32e5
PubKey: 0374d16a1603a5691eb73aa12be62e506792cff5772def92376d1dbf7d15a64a4d
======================================================================
[Input Index #: 6]
R: 6fc545a0360d77a92e5f00ad13f947c48d3d61605b091f43d3b8c9aeca68a3ea
S: 472db6ab16c4b34442a123764e871bbf1c866810996a3117c7a4937ef0b92b52
Z: 49acf9eb7e34189460d96ef1d8ce0d6bd35e5ff659da757775244aeb887b398d
PubKey: 0242ae9c0bd6300b20b08709546b79a02ef3a297a7eee1299121e2f79eb646c5b9
other help please solve:
iam run ImportError: No module named txnUtils
https://github.com/FoxxD3V/btc-rsz/blob/master/RawTX_RSZ.py
thanks its work @ETFbitcoin
i need help, sample.txt file open next get x and y value same time,set value for setmy_x_value,setmy_y_value
#note without error..
sample x and y value.. sample.txt
filename ='sample.txt'
with open(filename) as f:
addf = f.read().split()
addf = set(addf) # this is my idea how to same time get x and y ?...setmy_x_value,setmy_y_value
#mybadenglish
example output... like tihs
i need help, sample.txt file open next get x and y value same time,set value for setmy_x_value,setmy_y_value
#note without error..sample x and y value.. sample.txt
Code:
('0xaf5a13d03a858342aea7dcc0772d66d65b83f6fa17988568cc219866a99436ccL', '0xc694e15f92cddfb68aebcc313f5594b987e7ae7d72f5bfc7b44b6adbd4301ee1L')
('0x680c20dcdca0813ae3450845c18c6b4975e96281313fb811dda958bca2222076L', '0xe1bb14e7912ff0224f95d90c710ccf830bef75e1bfe16898adf80fe0d4b595c9L')
('0x8d485591727814848b4917388714866d9fd60f0269112edb646f3c13e06924f0L', '0xf44e87d22618b5f5b6545cf5555092c64d279708eaf12a5518bbe9bca0d1aae2L')
('0xedb1bc4d3649221c13c65dcf79d7d2050cc734ab878f78ac90d1274356e65536L', '0x5ee7898c708f13ab827bffb1c411375e80155366f0d9b74769a25aa6b3f3e17bL')
('0xa3472f6ecc489b37a0059d3555e11fa44ba6fa139080ea91a84d5928ea1e4058L', '0xc822e040aef7a7a82cc0f7e1b91d2ce35e60f98cbb77b1127d5a69ecb51f62d8L')
('0x2f5410507ab547341c4cfd87c89381dff84609f0ba3b106d912ac8b3b939b139L', '0x79b0462c5105e546f827871efbf9bb53a83615f4fd90486afa6280a994c2fea2L')
('0x66c31d4feabd3f65a7d2ee4cb60f484a29c3485c555189ac993bb5465c21baafL', '0x90c2113380966bf3fffd18b8f94f49b4e21a22bf01c17cce17b8b1256a43d504L')
('0xef78c2ae7c2d1bed13f204e5ed6764c7a9b1c24690ab6fc259f4f4b3acc24e3dL', '0x5c3458d1124458f569fcabc4fab4872335a75e0834d4afa564c83d7d3833e7a4L')
('0x32253c8bcb7cc19c9b959537aafd738bbaba5943cace632248e3ecd03f7cd960L', '0x4dccceab7f7eb85a5d21a5a21c6ebc5ed53bbbd74784cd422e84edf8ef89bc3eL')
('0x9fbc293e6bdaffa96519a7538a7ece62d07a8182bf20494551f2894d39e3c75bL', '0x957beece6c39c7d41fc2c9c3a53796a45a7bef5d3baf8cbd95a32e999615f83L')
('0x680c20dcdca0813ae3450845c18c6b4975e96281313fb811dda958bca2222076L', '0xe1bb14e7912ff0224f95d90c710ccf830bef75e1bfe16898adf80fe0d4b595c9L')
('0x8d485591727814848b4917388714866d9fd60f0269112edb646f3c13e06924f0L', '0xf44e87d22618b5f5b6545cf5555092c64d279708eaf12a5518bbe9bca0d1aae2L')
('0xedb1bc4d3649221c13c65dcf79d7d2050cc734ab878f78ac90d1274356e65536L', '0x5ee7898c708f13ab827bffb1c411375e80155366f0d9b74769a25aa6b3f3e17bL')
('0xa3472f6ecc489b37a0059d3555e11fa44ba6fa139080ea91a84d5928ea1e4058L', '0xc822e040aef7a7a82cc0f7e1b91d2ce35e60f98cbb77b1127d5a69ecb51f62d8L')
('0x2f5410507ab547341c4cfd87c89381dff84609f0ba3b106d912ac8b3b939b139L', '0x79b0462c5105e546f827871efbf9bb53a83615f4fd90486afa6280a994c2fea2L')
('0x66c31d4feabd3f65a7d2ee4cb60f484a29c3485c555189ac993bb5465c21baafL', '0x90c2113380966bf3fffd18b8f94f49b4e21a22bf01c17cce17b8b1256a43d504L')
('0xef78c2ae7c2d1bed13f204e5ed6764c7a9b1c24690ab6fc259f4f4b3acc24e3dL', '0x5c3458d1124458f569fcabc4fab4872335a75e0834d4afa564c83d7d3833e7a4L')
('0x32253c8bcb7cc19c9b959537aafd738bbaba5943cace632248e3ecd03f7cd960L', '0x4dccceab7f7eb85a5d21a5a21c6ebc5ed53bbbd74784cd422e84edf8ef89bc3eL')
('0x9fbc293e6bdaffa96519a7538a7ece62d07a8182bf20494551f2894d39e3c75bL', '0x957beece6c39c7d41fc2c9c3a53796a45a7bef5d3baf8cbd95a32e999615f83L')
filename ='sample.txt'
with open(filename) as f:
addf = f.read().split()
addf = set(addf) # this is my idea how to same time get x and y ?...setmy_x_value,setmy_y_value
#mybadenglish
example output... like tihs
Code:
>>> Point1 = Point(setmy_x_value, setmy_y_value)
>>> Point2 = Point(0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5, 0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a)
>>> Point3 = sub(Point1,Point2)
>>> hex(Point3.x),hex(Point3.y)
('0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798', '0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8')
>>> Point2 = Point(0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5, 0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a)
>>> Point3 = sub(Point1,Point2)
>>> hex(Point3.x),hex(Point3.y)
('0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798', '0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8')
script: y from x
Code:
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
x = 0x33709eb11e0d4439a729f21c2c443dedb727528229713f0065721ba8fa46f00e
ysquared = ((x*x*x+7) % p)
print ("ysquared= %s ", hex(ysquared) )
y = pow(ysquared, (p+1)/4, p)
print ("y1 = ",hex(y))
print ("y2 = ", hex(y * -1 % p))
y1 = y
y2 = (y * -1) % p
print(" ")
print("value x = ",hex(x))
print("value x = ",x)
print(" ")
if Integer(y1) % 2 == 0:
print("value 02 to y = ",hex(y1))
print("value 02 to y =",y1)
print(" ")
print("value 03 to y = ",hex(y2))
print("value 03 to y =",y2)
if Integer(y2) % 2 == 0:
print("value 02 to y = ",hex(y2))
print("value 02 to y =",y2)
print(" ")
print("value 03 to y = ",hex(y1))
print("value 03 to y =",y1)
#test
print (hex((x**3 + 7 - y1**2) % p) )
print (hex((x**3 + 7 - y2**2) % p))
x = 0x33709eb11e0d4439a729f21c2c443dedb727528229713f0065721ba8fa46f00e
ysquared = ((x*x*x+7) % p)
print ("ysquared= %s ", hex(ysquared) )
y = pow(ysquared, (p+1)/4, p)
print ("y1 = ",hex(y))
print ("y2 = ", hex(y * -1 % p))
y1 = y
y2 = (y * -1) % p
print(" ")
print("value x = ",hex(x))
print("value x = ",x)
print(" ")
if Integer(y1) % 2 == 0:
print("value 02 to y = ",hex(y1))
print("value 02 to y =",y1)
print(" ")
print("value 03 to y = ",hex(y2))
print("value 03 to y =",y2)
if Integer(y2) % 2 == 0:
print("value 02 to y = ",hex(y2))
print("value 02 to y =",y2)
print(" ")
print("value 03 to y = ",hex(y1))
print("value 03 to y =",y1)
#test
print (hex((x**3 + 7 - y1**2) % p) )
print (hex((x**3 + 7 - y2**2) % p))
i am run your code python and python2 both erro why?
?....NameError: name 'Integer' is not defined
Code:
user@me133:~/Downloads$ python 3.py
ysquared= %s 0x8ff5190f5e682d223717cd48318a53d918a5c48335924148963d7fc92c852e00
Traceback (most recent call last):
File "3.py", line 5, in
y = pow(ysquared, (p+1)/4, p)
TypeError: pow() 3rd argument not allowed unless all arguments are integers
user@me133:~/Downloads$ python2 3.py[
('ysquared= %s ', '0x8ff5190f5e682d223717cd48318a53d918a5c48335924148963d7fc92c852e00L')
('y1 = ', '0x4bb74cfb14940bce37a2468d7873ea0d0ac01a946607fd774ffb8cdbfb022eacL')
('y2 = ', '0xb448b304eb6bf431c85db972878c15f2f53fe56b99f80288b004732304fdcd83L')
('value x = ', '0xc0c686408d517dfd67c2367651380d00d126e4229631fd03f8ff35eef1a61e3cL')
('value x = ', 87194829221142880348582938487511785107150118762739500766654458540580527283772L)
Traceback (most recent call last):
File "3.py", line 15, in
if Integer(y1) % 2 == 0:
NameError: name 'Integer' is not defined
user@me133:~/Downloads$ python3 3.py
ysquared= %s 0x8ff5190f5e682d223717cd48318a53d918a5c48335924148963d7fc92c852e00
Traceback (most recent call last):
File "3.py", line 5, in
y = pow(ysquared, (p+1)/4, p)
TypeError: pow() 3rd argument not allowed unless all arguments are integers
ysquared= %s 0x8ff5190f5e682d223717cd48318a53d918a5c48335924148963d7fc92c852e00
Traceback (most recent call last):
File "3.py", line 5, in
y = pow(ysquared, (p+1)/4, p)
TypeError: pow() 3rd argument not allowed unless all arguments are integers
user@me133:~/Downloads$ python2 3.py[
('ysquared= %s ', '0x8ff5190f5e682d223717cd48318a53d918a5c48335924148963d7fc92c852e00L')
('y1 = ', '0x4bb74cfb14940bce37a2468d7873ea0d0ac01a946607fd774ffb8cdbfb022eacL')
('y2 = ', '0xb448b304eb6bf431c85db972878c15f2f53fe56b99f80288b004732304fdcd83L')
('value x = ', '0xc0c686408d517dfd67c2367651380d00d126e4229631fd03f8ff35eef1a61e3cL')
('value x = ', 87194829221142880348582938487511785107150118762739500766654458540580527283772L)
Traceback (most recent call last):
File "3.py", line 15, in
if Integer(y1) % 2 == 0:
NameError: name 'Integer' is not defined
user@me133:~/Downloads$ python3 3.py
ysquared= %s 0x8ff5190f5e682d223717cd48318a53d918a5c48335924148963d7fc92c852e00
Traceback (most recent call last):
File "3.py", line 5, in
y = pow(ysquared, (p+1)/4, p)
TypeError: pow() 3rd argument not allowed unless all arguments are integers
p (modulus) = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
n (order; size; the count of all possible EC points) = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
a (the constant "a" in y^2 ≡ x^3 + a*x + b (mod p)) = 0x0000000000000000000000000000000000000000000000000000000000000000
b (the constant "b" in y^2 ≡ x^3 + a*x + b (mod p)) = 0x0000000000000000000000000000000000000000000000000000000000000007
g (the curve generator point G {x, y}) = (0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798, 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)
h (cofactor, typically 1) = 01
please tell why use h = 1
a = 0
b = 7
what different
how to reverse calculate y^2 ≡ x^3 + a*x + b (mod p) share your code
n (order; size; the count of all possible EC points) = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
a (the constant "a" in y^2 ≡ x^3 + a*x + b (mod p)) = 0x0000000000000000000000000000000000000000000000000000000000000000
b (the constant "b" in y^2 ≡ x^3 + a*x + b (mod p)) = 0x0000000000000000000000000000000000000000000000000000000000000007
g (the curve generator point G {x, y}) = (0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798, 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8)
h (cofactor, typically 1) = 01
please tell why use h = 1
a = 0
b = 7
what different
how to reverse calculate y^2 ≡ x^3 + a*x + b (mod p) share your code
hi eny update Re: y coordinate calculation (PUBLIC KEY BITCOIN)
share me
share me
sorry for the basic question.
how did you get 28948022309329048855892746252171976963317496166410141009864396001977208667916 ?
I get it, its P/4 ..
how did you get 28948022309329048855892746252171976963317496166410141009864396001977208667916 ?
sorry for the basic question.
how did you get 28948022309329048855892746252171976963317496166410141009864396001977208667916 ?
how did you get 28948022309329048855892746252171976963317496166410141009864396001977208667916 ?
I get it, its P/4 ..
I would like to understand the math behind this...
Simply and objectively!In decimal for ease.
All calculations:
p = 115792089237316195423570985008687907853269984665640564039457584007908834671663
-------------------------------------------------------------------------------------------------------------------------------------------------------
Private key : 1
Public key :
x = 55066263022277343669578718895168534326250603453777594175500187360389116729240
55066263022277343669578718895168534326250603453777594175500187360389116729240**3 + 7 =
32748224938747404814623910738487752935528512903530129802856995983256684603122**28948022309329048855892746252171976963317496166410141009864396001977208667916=
y = 32670510020758816978083085130507043184471273380659243275938904335757337482424
OKAY
---------------------------------------------------------------------------------------------------------------------------------------------------
Private key : 2
Public key :
x = 89565891926547004231252920425935692360644145829622209833684329913297188986597
89565891926547004231252920425935692360644145829622209833684329913297188986597**3 + 7 =
57199941671890039290383617934355424684258807805258215939368959893591666662646**28948022309329048855892746252171976963317496166410141009864396001977208667916=
y = 12158399299693830322967808612713398636155367887041628176798871954788371653930
OKAY
-------------------------------------------------------------------------------------------------------------------------------------------------
Private key : 3
Public key :
x = 112711660439710606056748659173929673102114977341539408544630613555209775888121
112711660439710606056748659173929673102114977341539408544630613555209775888121**3 + 7 =
104193826873522593991639737736096919049125888873761064059040146529970392609905**28948022309329048855892746252171976963317496166410141009864396001977208667916=
y = 90209061256745311731914079131285931446821116410824268969537695047367247992253
NO OKAY
------------------------------------------------------------------------------------------------------------------------------------------------
Why did the y value of private key 3 need to be inverted?
What math or method is used to know whether or not I will need to invert the y value?
Simply and objectively!In decimal for ease.
All calculations:
p = 115792089237316195423570985008687907853269984665640564039457584007908834671663
-------------------------------------------------------------------------------------------------------------------------------------------------------
Private key : 1
Public key :
x = 55066263022277343669578718895168534326250603453777594175500187360389116729240
55066263022277343669578718895168534326250603453777594175500187360389116729240**3 + 7 =
32748224938747404814623910738487752935528512903530129802856995983256684603122**28948022309329048855892746252171976963317496166410141009864396001977208667916=
y = 32670510020758816978083085130507043184471273380659243275938904335757337482424
OKAY
---------------------------------------------------------------------------------------------------------------------------------------------------
Private key : 2
Public key :
x = 89565891926547004231252920425935692360644145829622209833684329913297188986597
89565891926547004231252920425935692360644145829622209833684329913297188986597**3 + 7 =
57199941671890039290383617934355424684258807805258215939368959893591666662646**28948022309329048855892746252171976963317496166410141009864396001977208667916=
y = 12158399299693830322967808612713398636155367887041628176798871954788371653930
OKAY
-------------------------------------------------------------------------------------------------------------------------------------------------
Private key : 3
Public key :
x = 112711660439710606056748659173929673102114977341539408544630613555209775888121
112711660439710606056748659173929673102114977341539408544630613555209775888121**3 + 7 =
104193826873522593991639737736096919049125888873761064059040146529970392609905**28948022309329048855892746252171976963317496166410141009864396001977208667916=
y = 90209061256745311731914079131285931446821116410824268969537695047367247992253
NO OKAY
------------------------------------------------------------------------------------------------------------------------------------------------
Why did the y value of private key 3 need to be inverted?
What math or method is used to know whether or not I will need to invert the y value?
I send you pm, check your pm.
Thx
Now let's go on @_Counselor's example; if we take 0.5 and double it, we'll get 1. This means that we must find a number whose doubling will result in 1 in the finite field of secp256k1. In that case, it's - “7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1”. I'm trying to understand, though, how will you get 0.5 by having that hex and 1.
Once you move the 0.5 into the secp256k1 finite field, it is indistinguishable from that large number you quoted above. They are functionally equivalent.
We take 8 in the finite field of 47. We'll multiply 8 by 13 times => 8*13 = 104, 104 mod 47 = 10. Now let's find the multiplication inverse of 10 in that field:
10 * x = 8
How exactly can I solve this besides trying a different value each time? In the article, it tries 1, 2, 3... until it finds 29 which is suitable.
Let's consider a * x ≡ b (mod p), which means x ≡ b/a (mod p) for a ≠ 0.
There are two ways to find x.
First through Fermat's little theorem:
ap ≡ a (mod p)
ap-2 ≡ a-1 ≡ 1/a (mod p)
x ≡ b * ap-2 (mod p)
Second through Extended Euclidean algorithm:
x ≡ b * inverse(a, p) (mod p)
It's because -1 is outside of the range of remainders 0 to N-1, so it has to be shifted into this range, by repeatedly adding or subtracting N, until it becomes one of the numbers in that range (in this case, N-1).
So let me get this straight. If we want to represent -1 in a finite field [1, 47) whose acres are prime numbers, we'll have to deform it and include it into that range. In order to do so, we'll take -1 and add 47 to it, until it's included. In this case, -1 + 47 = 46. The result will never be 47, that's why I added parenthesis instead above.Now let's go on @_Counselor's example; if we take 0.5 and double it, we'll get 1. This means that we must find a number whose doubling will result in 1 in the finite field of secp256k1. In that case, it's - “7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1”. I'm trying to understand, though, how will you get 0.5 by having that hex and 1.
Sorry, but that's a bunch of new things introduced to my maths' knowledge. I'll try learnmeabitcoin.com's example with the modular inverse to possibly understand it better.
We take 8 in the finite field of 47. We'll multiply 8 by 13 times => 8*13 = 104, 104 mod 47 = 10. Now let's find the multiplication inverse of 10 in that field:
10 * x = 8
How exactly can I solve this besides trying a different value each time? In the article, it tries 1, 2, 3... until it finds 29 which is suitable.
You may try it yourself with some EC calculator, just get a point from this privkey, then double it, you will get point from key "1".
I tried it with a secp256k1 calculator and verified it. So, what we're describing is called scalar multiplication? Shouldn't there be an inverse, where you can get -1 by only having - "fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140" - and 1? Quote
Pi and some other math constants actually can't be expressed like this unless you truncate it to some digits
In finite field, everything is truncated to the prime modulo. You have one and you have prime modulo plus one and that two values have exactly the same value in finite field. You can take a square root of something and it will be equal to some integer, because if you multiply that value by itself, you will get back the value you started with. The same with pi, e, and other constants. If you have some equation, for example that pi is a circumference divided by a diameter, then you can calculate better and better approximation, and finally you will end up with a number that cannot be better approximated, because by taking modulo you will lose precision. You can have pi defined as an infinite sum, where after some point, you will get all zeroes, because numbers will be too small to be expressed in this finite field.Finite fields are beautiful, because they are finite. You have well-defined precision set to 256-bit values and you will never need more precision than that if you stay in that field. Some values are undefined, for example there is no public key where x=5, so there is no value for the square root of 132 (y^2=x^3+7, x=5, y^2=132, y=sqrt(132) does not exist). But if it is possible to calculate some value (for example sqrt(2) exists), then it can be expressed as an integer.
If you don't mind could you explain it a little bit more? Or share me a link with useful content, if you're out of time.
Simple explanation.
Let's take a number like 0.5
What is 0.5? It is half of 1, so this number, then multiplied by two, will give 1.
Now we will find a number that satisfies this in the conditions of a finite field.
It will be "7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1" - if you double that number in secp256k1, you will get 1. So this enormous number also works just like 0.5.
You may try it yourself with some EC calculator, just get a point from this privkey, then double it, you will get point from key "1".
Some way we can explain "-1" as "fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140"
-1 + 1 = 0. If you add "1" and "fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140" you will get point at infinity, that is works on EC like zero.
Minus one is fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140
How? Don't I just convert the hexadecimal into decimal?It's because -1 is outside of the range of remainders 0 to N-1, so it has to be shifted into this range, by repeatedly adding or subtracting N, until it becomes one of the numbers in that range (in this case, N-1).
everything can be expressed as integers, even square roots and numbers like e, pi, logarithms, just everything.
If you don't mind could you explain it a little bit more? Or share me a link with useful content, if you're out of time.[Almost] all decimal numbers can be written as a fraction, with a numerator and denominator (Pi and some other math constants actually can't be expressed like this unless you truncate it to some digits).
So the decimal number is actually equivalent to: modinv(denominator) * numerator.
Where modinv is the modular inverse of the number with respect to N.
Is the mod supposed to be implied? Because, OP didn't write it.
Yes.
@OP, have you tried using Legendre numbers mod n to classify the private keys by their polarity? priv=1 gives an odd key (afaik), priv=2 gives an even key, so possibly odd keys have Legendre numbers of -1 and even numbers have them at 1.
I don't remember the polarity of the next few numbers from my head so it's worth a shot if you want to calculate them.
firstly everything is possible.
second:
"What I would really like is some method that would give me the correct y value... without having to invert or choose between y or -y (I THINK IT'S IMPOSSIBLE)" ---> if you do that means you break ecdsa. You trying solve problem that pubkey is in d
third -> you can check how many times is fliped (y) (as 02 to 03 and 03 to 02) depends on subgroup during adding point . but it is not possoble, you can't check n/2 subgrups -> hundreds years.. you know ... or you are immortal:D
Technically it's the second option
It will be square root modulo prime of 8
But, the square root of 8 is not an interval. Specifically, it is around 2.82. If you mod this with a prime number, such as 11, won't you get the same 2.82? (2.82 = (11 * 0) + 2.82)Please guide me I've messed things up again.
32748224938747404814623910738487752935528512903530129802856995983256684603122^
28948022309329048855892746252171976963317496166410141009864396001977208667916=
32670510020758816978083085130507043184471273380659243275938904335757337482424
The symbol that I colored red means power. The result from your process would give a much greater number, considered infinity. It doesn't give the blue one.28948022309329048855892746252171976963317496166410141009864396001977208667916=
32670510020758816978083085130507043184471273380659243275938904335757337482424
Public key equations are always modular... you forgot to include:
p = 115792089237316195423570985008687907853269984665640564039457584007908834671663
Minus one is fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140
How? Don't I just convert the hexadecimal into decimal?Code:
hex: fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140
dec: 115792089237316195423570985008687907852837564279074904382605163141518161494336
dec: 115792089237316195423570985008687907852837564279074904382605163141518161494336
You got me unprepared on this one. Still, I haven't learnt how they work. I know I shouldn't feel ridicule, but I do.
everything can be expressed as integers, even square roots and numbers like e, pi, logarithms, just everything.
If you don't mind could you explain it a little bit more? Or share me a link with useful content, if you're out of time.No, because if you have a^b mod n
Is the mod supposed to be implied? Because, OP didn't write it. Quote
Specifically, it is around 2.82.
In finite field, all numbers are integers. There is no dot. Minus one is fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140, 0.5 is 7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1, everything can be expressed as integers, even square roots and numbers like e, pi, logarithms, just everything.Quote
The result from your process would give a much greater number, considered infinity.
No, because if you have a^b mod n, then you can check if b is even or odd. If b is odd, then you can calculate a*a^(b-1) mod n, in this way you have b-1 that is even. If b is even, you can calculate (a*a)^(b/2) mod n. If during multiplication you would get something bigger than n, then you take the result modulo n and proceed. Finally, you will always have a number modulo n, so it will always be in the correct range. It will be square root modulo prime of 8
But, the square root of 8 is not an interval. Specifically, it is around 2.82. If you mod this with a prime number, such as 11, won't you get the same 2.82? (2.82 = (11 * 0) + 2.82)Please guide me I've messed things up again.
32748224938747404814623910738487752935528512903530129802856995983256684603122^
28948022309329048855892746252171976963317496166410141009864396001977208667916=
32670510020758816978083085130507043184471273380659243275938904335757337482424
The symbol that I colored red means power. The result from your process would give a much greater number, considered infinity. It doesn't give the blue one. 28948022309329048855892746252171976963317496166410141009864396001977208667916=
32670510020758816978083085130507043184471273380659243275938904335757337482424
script : x from y
Code:
## Input
y = 0x3199555CE45C38B856C9F64AC6DB27000AB6CEA10CAD76B2B6E246C9A020E707
## Field parameters
# Field modulus
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
# Cube root of 1
beta = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee
## Actual code
xcubed = (y*y - 7) % p
print ("xcubed = 0x%x" % xcubed)
x = pow(xcubed, (p + 2) / 9, p)
print ("x1 = 0x%x" % x)
print ("x2 = 0x%x" % (x * beta % p))
print ("x3 = 0x%x" % (x * beta * beta % p))
y = 0x3199555CE45C38B856C9F64AC6DB27000AB6CEA10CAD76B2B6E246C9A020E707
## Field parameters
# Field modulus
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
# Cube root of 1
beta = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee
## Actual code
xcubed = (y*y - 7) % p
print ("xcubed = 0x%x" % xcubed)
x = pow(xcubed, (p + 2) / 9, p)
print ("x1 = 0x%x" % x)
print ("x2 = 0x%x" % (x * beta % p))
print ("x3 = 0x%x" % (x * beta * beta % p))
script: y from x
Code:
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
x = 0x33709eb11e0d4439a729f21c2c443dedb727528229713f0065721ba8fa46f00e
ysquared = ((x*x*x+7) % p)
print ("ysquared= %s ", hex(ysquared) )
y = pow(ysquared, (p+1)/4, p)
print ("y1 = ",hex(y))
print ("y2 = ", hex(y * -1 % p))
y1 = y
y2 = (y * -1) % p
print(" ")
print("value x = ",hex(x))
print("value x = ",x)
print(" ")
if Integer(y1) % 2 == 0:
print("value 02 to y = ",hex(y1))
print("value 02 to y =",y1)
print(" ")
print("value 03 to y = ",hex(y2))
print("value 03 to y =",y2)
if Integer(y2) % 2 == 0:
print("value 02 to y = ",hex(y2))
print("value 02 to y =",y2)
print(" ")
print("value 03 to y = ",hex(y1))
print("value 03 to y =",y1)
#test
print (hex((x**3 + 7 - y1**2) % p) )
print (hex((x**3 + 7 - y2**2) % p))
x = 0x33709eb11e0d4439a729f21c2c443dedb727528229713f0065721ba8fa46f00e
ysquared = ((x*x*x+7) % p)
print ("ysquared= %s ", hex(ysquared) )
y = pow(ysquared, (p+1)/4, p)
print ("y1 = ",hex(y))
print ("y2 = ", hex(y * -1 % p))
y1 = y
y2 = (y * -1) % p
print(" ")
print("value x = ",hex(x))
print("value x = ",x)
print(" ")
if Integer(y1) % 2 == 0:
print("value 02 to y = ",hex(y1))
print("value 02 to y =",y1)
print(" ")
print("value 03 to y = ",hex(y2))
print("value 03 to y =",y2)
if Integer(y2) % 2 == 0:
print("value 02 to y = ",hex(y2))
print("value 02 to y =",y2)
print(" ")
print("value 03 to y = ",hex(y1))
print("value 03 to y =",y1)
#test
print (hex((x**3 + 7 - y1**2) % p) )
print (hex((x**3 + 7 - y2**2) % p))
Thanks for the script ... but I already have the first and the second I already knew
What I would really like is some method that would give me the correct y value... without having to invert or choose between y or -y (I THINK IT'S IMPOSSIBLE)
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