Hi,
How to Calculate x ,y in Addresses,can you explain more.. if any code in git-hub
can you explain step by guide please..
I am New to bitcoin ....
please inbox me to learn something...
Topic: Half of any bitcoin (crypto) public key - (public key half) - page 3. (Read 2449 times)
2^-1 (mod n) = 57896044618658097711785492504343953926418782139537452191302581570759080747169
2 * 57896044618658097711785492504343953926418782139537452191302581570759080747169 = 1 (mod n)
Multiplying a point by this number will "half" the point.
2 * 57896044618658097711785492504343953926418782139537452191302581570759080747169 = 1 (mod n)
Multiplying a point by this number will "half" the point.
The goal is to "half" the point. You want to find the point Q where 2Q = P, your original point.
So you compute 2^-1 (mod n) where n is the order of the group (see the secp256k1 parameters: https://en.bitcoin.it/wiki/Secp256k1)
2^1 is the multiplicative inverse of 2 (mod n). 2 x 2^1 = 1 (mod n). When you do the scalar multiplication it cancels out a factor of 2.
2Q = P
(2^-1)2Q = (2^-1)P
Q = (2^-1)P
Hope that makes sense.
So you compute 2^-1 (mod n) where n is the order of the group (see the secp256k1 parameters: https://en.bitcoin.it/wiki/Secp256k1)
2^1 is the multiplicative inverse of 2 (mod n). 2 x 2^1 = 1 (mod n). When you do the scalar multiplication it cancels out a factor of 2.
2Q = P
(2^-1)2Q = (2^-1)P
Q = (2^-1)P
Hope that makes sense.
here the another answer
https://crypto.stackexchange.com/questions/59972/half-of-any-bitcoin-crypto-public-key-public-key-half-is-possible
ECC is cryptography over an elliptic curve group.
Firstly you have an elliptic curve, e.g. Bitcoin uses a Koblitz curve secp256k1 y2=x3+7.
The group is defined over curve points over a finite field Fp (integer modular p). The group elements are points on the curve. A point in the affine form consists of two coordinates P=(x,y) where x,y∈Fp.
For group elements, you can do point addition P+Q, as well as scalar multiplication sP, where s is an integer in Zn where n is the order of the group (how many elements in the group).
A public key in bitcoin is a point P. To do P2, you multiply 12 to P where 12 is the multiplicative inverse of 2 in Zn. It is an integer that can be found using the extended Euclidean algorithm and is 57896044618658097711785492504343953926418782139537452191302581570759080747169 in the case of secp256k1.
but in crypt o ,
private key 3
x = f9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9
y = 388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672
half of the above public key is 1 given below
x = 79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
y = 483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
but the output is
x = c62c910e502cb615a27c58512b6cc2c94f5742f76cb3d12ec993400a3695d413
y = 17f3dadd767275ddd3b23f46723631778bf01dadaebb9a953cf068712457c010
what wrong in this how to correct this
3/2 = 1
The goal is to "half" the point. You want to find the point Q where 2Q = P, your original point.
So you compute 2^-1 (mod n) where n is the order of the group (see the secp256k1 parameters: https://en.bitcoin.it/wiki/Secp256k1)
2^1 is the multiplicative inverse of 2 (mod n). 2 x 2^1 = 1 (mod n). When you do the scalar multiplication it cancels out a factor of 2.
2Q = P
(2^-1)2Q = (2^-1)P
Q = (2^-1)P
Hope that makes sense.
So you compute 2^-1 (mod n) where n is the order of the group (see the secp256k1 parameters: https://en.bitcoin.it/wiki/Secp256k1)
2^1 is the multiplicative inverse of 2 (mod n). 2 x 2^1 = 1 (mod n). When you do the scalar multiplication it cancels out a factor of 2.
2Q = P
(2^-1)2Q = (2^-1)P
Q = (2^-1)P
Hope that makes sense.
Sure, just multiply the point by 2^-1 (mod n).
How its possible there is scalar addition, subtraction and multiplication only , can you explain more (multiply the point by 2^-1 (mod n))
Sure, just multiply the point by 2^-1 (mod n).
To get half of any given bitcoin (crypt o) public key is possible, Technically it's possible, we made that. The public key that's in the bitcoin network.
Public key x and y == Double(Half of the Public key x and y)
Example's:
Address
Public key in network
Public key x and y
Half of the above public key
Address
Public key in network
Public key x and y
Half of the above public key
Half of the above public key
Address
Public key in network
Public key x and y
half of the above public key
Public key x and y == Double(Half of the Public key x and y)
Example's:
Address
Code:
1HQ3Go3ggs8pFnXuHVHRytPCq5fGG8Hbhx
Public key in network
Code:
02545d2c25b98ec8827f2d9bee22b7a9fb98091b2008bc45b3b806d44624dc038c
Public key x and y
Code:
x = 545d2c25b98ec8827f2d9bee22b7a9fb98091b2008bc45b3b806d44624dc038c
y = f1e18224b09ed00841c5407e571829e41876d44522f97e05e405a91ef38d4f00
Half of the above public key
Code:
x = 8f870b1693cb408f96a3da9e3623b6d0315a403395d79f412f26044210bcddd2
y = 8a0a3e2399787a1f084d53500bc577ba1cc4e19ab7b2d9a2bd327e5e56e8afa0
Address
Code:
1JCe8z4jJVNXSjohjM4i9Hh813dLCNx2Sy
Public key in network
Code:
037f73b63c10ce53c1b73800751d859915badcf5423da1fd7fabfc8556a833f0bd
Public key x and y
Code:
x = 7f73b63c10ce53c1b73800751d859915badcf5423da1fd7fabfc8556a833f0bd
y = bb2402fa216c2eeafc8e5667c8290c8e28199cb7e48bef2fffbdee5dff0ad277
Half of the above public key
Code:
x = acbe1e6677d64cbbb501f3e1e43604bc478e57fcc473e78dd06a6cb3de223c6d
y = d3bf86be940c6a60352da18297d3c3c23a6db42e586fa74294c32a0d7c1b4a88
Half of the above public key
Code:
x = ae05a1d169edb67fe94fef428b6594ba218ce157bb04c8dac2889b805f6e8965
y = 18897d88bb3c44476d8c204bf29650f159c47f6138913ab04ba37fc7bf3081cb
Address
Code:
12ib7dApVFvg82TXKycWBNpN8kFyiAN1dr
Public key in network
Code:
04d6597d465408e6e11264c116dd98b539740e802dc756d7eb88741696e20dfe7d3588695d2e7ad23cbf0aa056d42afada63036d66a1d9b97070dd6bc0c87ceb0d
Public key x and y
Code:
x = d6597d465408e6e11264c116dd98b539740e802dc756d7eb88741696e20dfe7d
y = 3588695d2e7ad23cbf0aa056d42afada63036d66a1d9b97070dd6bc0c87ceb0d
half of the above public key
Code:
x = dc0f6e4ff971e22fffa77df43d24128046599f9b2299bc7a6fbc4e7e9fc4a0ff
y = 615f1884faa5197a00560ecb69f2b18ef223a3dfaee2407d4ea5a2286de2a41b
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