lets learn about gen generation and elliptic curves!
figuring out what a point on a curve after a few hops means for us fans of encryption.
bitcoin is poison so it's good to understand why it's so hard to compute the private key from a public key.
the generate directory contains our code to generate test private and public keys
How can we know whether we have valid key pairs generated?
if we successfully generate btc valid keys, that's enough to confirm that the algorithms are right as rain!
we have a file which we can use to learn about details on the curve Secp256k1 used.
Obtain the group order n of the curve.
For Secp256k1 this is FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141.
In decimal the number is:
115792089237316195423570985008687907852837564279074904382605163141518161494337
Generate a cryptographically secure random number k between 1 and n-1.
Note that 2^255 < n < 2^256
The random number k above is our 'seed' number or private key?
As above this number is:
1 <= k <= n-1
We then compute the public key (x, y) via:
(x, y) = k*G, where G is the generator point of the secp256k1 curve, which is
0479BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8
OR
Gx = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
Gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
Worth noting is that because we use ECDSA, the key should be positive and should be less than the order of the curve. The order of secp256k1 is FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141, which is pretty big: almost any 32-byte number will be smaller than it.
Wow this is quite interesting - we use two hashing algorithms to hash the public key before appending a few tidbits to it to provide the final BTC address. Order matters so we do:
enc = RIPEMD-160(SHA-256(pubkey_x))
Hashing algorithm RIPEMD-160 Hashing algorithm SHA-256
These two one-way algorithms make it hard to guess even the public key used in Bitcoin or other cryptocurrencies.
stole some code here and there. e.g. protocoin generate private key generate bitcoin address