Topic: Strange pubkey (real existing or not) (Read 420 times)

And there is nothing special about public keys. In general public keys are just points(x,y) on the curve forming finite cyclic group of prime order(means any curve point except infinity point can be a generator and has the same order as G). in any way if you apply operations on any curve point you get another curve point. all valid points are  multiples of each other.  and you can of course take public key and go backwards to G with point subtraction and point scalar division recovering bits of private key. but to do that you need to know whether point has even or odd index in a subgroup S={ infinity_point, G, 2G, 3G, ..., (N-1)G } like in array. but no such method exists.

starting_y = 0x0
#starting_y = 55066263022277343669578718895168534326250603453777594175500187360389116729240
#starting_y = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2a
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
beta = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee

def oncurve(x,y): # Checks if point satifies x^3 +7 = y^2 , mod P
  x = (x*x*x+7) % p
  y = (y*y) % p
  return x==y
 
while starting_y < p:
    y = starting_y
    xcubed = (y*y - 7) % p
    x = pow(xcubed, (p + 2) * pow(9, p - 2, p) % p , p)
    #x = pow(xcubed, (p + 2) // 9 , p)
    plist = list()
    x1 = str(hex(x))[2:].zfill(64)
    plist.append(x1)
    x2 = str(hex((x * beta % p)))[2:].zfill(64)
    plist.append(x2)
    x3 = str(hex((x * beta * beta % p)))[2:].zfill(64)
    plist.append(x3)
    if (y**2) % p == (int(x1,16)**3 + 7) % p:
        print(f"Secp256k1 True Y Coordinate: {hex(y)[2:].zfill(64)} [{y}]")
        print(f'{x1}:{hex(y)[2:].zfill(64)}')
        print( oncurve( int(x1, 16),int(hex(y)[2:].zfill(64), 16)) )
        print(f'{x2}:{hex(y)[2:].zfill(64)}')
        print( oncurve( int(x2, 16),int(hex(y)[2:].zfill(64), 16)) )
        print(f'{x3}:{hex(y)[2:].zfill(64)}')
        print( oncurve( int(x3, 16),int(hex(y)[2:].zfill(64), 16)) )
        print('---------------------------------------------------------------------------------------------------------------------------------')
    starting_y += 1

you can check valid y-coordinates also.

Why brute forced?
Address is base58 encoded ripemd160 hash, which means that any base 58 text you may decode to hash160, calculate checksum, append to the known part (previously decoded text) and encode again using base 58.
That way you receive correctly generated address - hash160 from unknown source (as you do not know which pubkey hashed sha256 created that hash160) and corresponding checksum. 

To be clear the address you posted was not created from a public key because it would be impossible to find such a big HASH160 collision that corresponds to "759d6677091e973b9e9d99f19c68fbf43e3f05f9". What they did to create this address was to simply create the Base58 string then brute force the last couple of characters to have the correct checksum.

thank you very much 

Of course. If you know "trap addresses" like 1BitcoinEaterAddressDontSendf59kuE, then you should also understand, that it is possible to pick some public key that has unknown private key, so a "trap public key". For example:
As you can see, this key also exists. In theory, there is some valid (but unknown) private key, that can be used to unlock it, but in practice, if such keys will ever be spendable, then ECDSA will be gone.

So these public keys exist ??


0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dd2cdf8a7e655dfd 17f80feaac26d4cc065f41920a77a956ab628bfff36266a2536
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dd3629c17aff2951 9620fd3cf774a16daf6d09098ff8f96cb90964da9ef49d0537f
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dd4429ad065739db d2fac7da8a48091c0b0fd82e317d80bef6b91c65374ed95ed29
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dd63e1e22b33054d 5972f0f3c10ef5574fcc94c802a81904c87f645b5ffdcdf64f0
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dd8216fe4e7738d2 98e327c2ee89382a8df4ed499a229844c8c2c85b0cfdddd4114
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dd917a28fa043138 2d13d5d82b8de5f1edc1754aaab600584f786d7fdf7c8095cc7
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dda7d609efc53d16 25c86b0d4cdbf2a296c95582083e8163b59ecc8b1f92b34b956
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dde943da481f1454 f7517c9700431ddc3c07bc777dfcfa943c0d23caa01bb59a2c2
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9ddf5758c0b451a7f ae10bc472df6d23fcc9b5f5e4a887f307bd996aa3f9f4f84b6b
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9de322af70ac334d7 cbe665261f0b584264e67dd1ec33bbd1ba7f09eae24e69898a4
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9de988bed5bcfc1ff 605f485ef451a93a0b456b99beb82c8545433df6b30b269581f
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9debb686f3146f96d eddff1187f5a2cd859da8d66f7263c32ade2455e53e587041c6
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dec1ff8df5630093 6a22bed781bd5c9ecb609674a2bdce67c37f63d88b61bc1e111
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9deeaafe2e4419cd7 3bbdf5aaac47b4690a3e42343ad98a3d895abe62d58700dd283
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9def16fa62af275fa 1495b079db595e14a344bbc003ec1262db6693f252c45a8e0a6
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9df0a2f432cb80527 6ffb26ebaeb85b4270cd5bfae9ba535498ed0e0ef5e8cea3904
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9df3e173309acf8eb e932752945afbe0feaa1e2ba0c906c8284378ff05f7d65fedee
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9df462ca18708cdd2 38aeaf2282d253e78d0edc82fdba6c5a02e01621f32a8ebd3a0
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9df526b234f162f99 2542be7643bd2e944d3ae6f52dbc65c4da736bd36fd76149e00
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9df616627f042bf7b 7f7b48491592085300fb6d25abfd114263fd2bc6d5bd2030363
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9df7d7ec45274f44a bf15ed7b7e42106956ab23c33022168d04bde530e34417139a9
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9df89878894810eee 5c59877ec7f9a8fa20ee16e1bfb8313dc06c78691d16a0923ea
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dfdc883b1c1bb23f 4c61259f16c15ad0f80f1abd624d3e4c8467c00546b75841ca0
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9dfe66b95aa44a265 4119dbbbf103a2d53f0b7325dedd8c2ef5114da08598e527293
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e01e44d47c3dca07 eafe600856d156c28e2ffd1645e10e86f24fdbd9d741a3bdc70
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e02bd1df49bff933 d11150268a2f66eb4d1a1ff0ea5d82cf6455a83b60f90b7bd53
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e06e73d954accb63 ac67b73edc558a6af04d361017ec2f3e14aa7593fb52cca508a
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e083435ed7584e38 8d8f1006168b3a2f685aeaac775eda4b7fa025a6b9af01e7cf8
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e0df2c54b18d5b3d 398de60bb8d2ef873740cf45115c724279aec91f0f3c5d55224
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e0e967d4fb8322f4 736b9fa3509b7f834676cc5b44b2959258864221bccbe94e763
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e11dafb4c7b6e4c2 b28758280a0c5471637e325c56a0679bd5e234c34be30b4df65
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e12bb0da85aa9089 e727bbcb74a74b12936f64c1ec8ac442cee4c2d5bd2b1a9381e
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e14b085a0d36c946 df402a51ade842b907dbe0c35299f2ee9c1a2ebee463c0e78fb
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e15eea3ff3bca293 ca6319e3ba367f60defa5e520fe371afa92cb7c3b7e2aae80cd
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e1732ecf324de9de 3896783876d600a67e5848293151b296b9ce3fd16b53d81bfa2
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e1ce3f20d10b8fb7 7d652fe9225a18f1b215511fe425455657d4bd5fccf318b0d87
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e1d4730f9069ec92 e13aa09943a5d44567abe21caeadb34347a22f0a20476379cba
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e1fdbe74f8efd61b 626f292e461f153ab600e3854e2a6223c31276e69de3eda02ab
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e21e2bc8f0c70df1 9f241ed12153b925295080a2206b9ed2a34cb4767d6d5d8c6f2
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e229532a4e03457f 3488e1be6dab0928a34a667f4f5d228cf3b893fc65c30b0ebcc
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e2432959dc185e7d ad6adaecb1fa5657338dc7fc79c499604292632d86942863d47
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e258e3c3fe07e1ed f7317e306e1f3a25db1bb3fc0464bed2d39706d32757583e37f
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e27fc09774b3312e a2ed51f3e6714e756b2e8d3dc38ca705058deb5b0230c6b24db
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e28a9e1ef953897a c39158e5d6c7f9f0973d8601a7b3b35e5b5245ae1fb284b8fe2
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e2abf8a724674791 1a6b9e02bb0869e5088aa4cd4fe503a5b975186722cb100f881
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e2d422f03bede2c3 5aaa5ace849c420da8f97044bba7a15df6f25e21e7009d3c76e
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0400000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9e3063fe3c27f5db6 6f1d409aeae4285fba655bd09c77e6aa97ad761cd5824ebb77c
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ftfy

Your question is wrong. What you are posting is supposed to be the x coordinate of a point (x and y coordinates) that is only valid if it is located on the elliptic curve used by bitcoin called secp256k1. In order to check if a point is on curve you have to solve the curve's equation which is y² = x³ + 7.
So basically you cube your x and add 7 to it then you check to see if it has an square root modulo p.

0200000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c68  1LQiRWwELhChkpuAaC6tFpSDqpdjR3fYiC
0200000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c6a  172N3FM1uEjzSx28Tg1aoSzDqgmd9yqqCa

Does it really exist in the 2^256?

It just so happens that at the line of symmetry of private keys, there are two public keys with the same Y but differing X, as demonstrated in the posts above. In this example the "odd X" key came before the "even X" key, but this pattern is not repeated across the other private keys.

Naturally, one will find that by taking the recirpocal (subtracting by the key order i.e. num. priv keys) of the key will induce the opposite parity of X but preserve the Y value. It is not possible with current methods to determine which private keys are going to have even X, and which ones will have odd X.

I don't see anything strange here. You have a key pair and you negate it and it still has the same x coordinate and a different y; which is how it is supposed to work.

Then you try different x values for a public key and some of them are valid in the equation y^2 = x^3 + ax + b (mod p). The x values you choose are not special, you could have decremented it so much to reach the following and it still be a valid x for example.

To answer your question, you can make an address out of any public key, whether it is valid or not. An address is simply an encoded hash of a public key.

The public key 0400...00 is not valid, but its address is 16QaFeudRUt8NYy2yzjm3BMvG4xBbAsBFM

FYI, there are numerous typos in your post.

1. Your private key:

2. Public key of 7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0:

2. Public key of 7fffffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1:

Hello, I would like to have more information about the public key:

By choosing half of 2^256 private keys:

7fffffffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a0 has for public key: 03000000000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63

the public key is a little strange but let us say that it is simply the symmetry which makes that and thus if I increase of 1 the private key: 7fffffffffffffffffffffffff5d576e7357a4501ddfe92f46681b20a1 it has for public key:
0300000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c63

what is normal is the symmetry.

the strange thing is that if I add 1 to the public key :
0300000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c64

apparently it exists because it is connected to this bitcoin address:
13vSJ5pXUcUqiKoFN1gm7ffHVpK45G7b3e.

My question is this:
Does this public key really exist or not ?
And would they be positioned at strategic points ?

because if I continue it works

0200000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c68  1LQiRWwELhChkpuAaC6tFpSDqpdjR3fYiC
0200000000000000000000003b78ce563f89a0ed9414f5aa28ad0d96d6795f9c6a  172N3FM1uEjzSx28Tg1aoSzDqgmd9yqqCa
...........