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September 22, 2015, 09:07:12 AM |
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Take a bitcoin public key (x, y) and its additive inverse (x, -y). How do you identify which is the positive point and which is the negative point?
Example
Private key 1 -> (x, y)
x = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798L
y = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8L
-y = 0xb7c52588d95c3b9aa25b0403f1eef75702e84bb7597aabe663b82f6f04ef2777L
Private key 2 -> (x, y)
x = 0xc6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5L
y = 0x1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52aL
-y = 0xe51e970159c23cc65c3a7be6b99315110809cd9acd992f1edc9bce55af301705L
Private key 3 -> (x, y)
x = 0xf9308a019258c31049344f85f89d5229b531c845836f99b08601f113bce036f9L
y = 0x388f7b0f632de8140fe337e62a37f3566500a99934c2231b6cb9fd7584b8e672L
-y = 0xc77084f09cd217ebf01cc819d5c80ca99aff5666cb3ddce4934602897b4715bdL
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Also, how can you identify which pub key is odd and which is even?
ex: private key 1 x,y is odd , private key 2 x,y is even (based with pub key)
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addition info :
bitcoin doubling pub key
In normal math number 7/2 results are 3 and 1 if we need 7 back 3*2 = 6 + 1 = 7
elliptical curve cryptography
private key 7 pub key are
x = 0x5cbdf0646e5db4eaa398f365f2ea7a0e3d419b7e0330e39ce92bddedcac4f9bcL
y = 0x6aebca40ba255960a3178d6d861a54dba813d0b813fde7b5a5082628087264daL
Getting 7 pub key back by , just doubling below given pub key to get 7 pub key
x = 0x592152c398d6c719636a03a6dad64246a5a6814aa62c156b0ce5332f6759b031L
y = 0x72dd2e1d26c233337760c49122a1df67d0aa792b453f97bd29765c83b47ba01dL
Like the same for 3,5,9,11......etc
Just education
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