Wallet import format
Wallet Import Format (WIF, also known as Wallet Export Format) is a way of encoding a private ECDSA key so as to make it easier to copy.
Private key to WIF
1 - Take a private key
0C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D
2 - Add a 0x80 byte in front of it
800C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D
3 - Perform SHA-256 hash on the extended key
8147786C4D15106333BF278D71DADAF1079EF2D2440A4DDE37D747DED5403592
4 - Perform SHA-256 hash on result of SHA-256 hash
507A5B8DFED0FC6FE8801743720CEDEC06AA5C6FCA72B07C49964492FB98A714
5 - Take the first 4 bytes of the second SHA-256 hash, this is the checksum
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6 - Add the 4 checksum bytes from point 5 at the end of the second SHA-256 hash from point 4
800C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D507A5B8D
7 - Convert the result from a byte string into a base58 string using Base58Check encoding. This is the Wallet Import Format
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WIF to private key
1 - Take a Wallet Import Format string
5HueCGU8rMjxEXxiPuD5BDku4MkFqeZyd4dZ1jvhTVqvbTLvyTJ
2 - Convert it to a byte string using Base58Check encoding
800C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D507A5B8D
3 - Drop the last 4 checksum bytes from the byte string
800C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D
4 - Drop the first byte (it should be 0x80). This is the private key
0C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D
WIF checksum checking
1 - Take the Wallet Import Format string
5HueCGU8rMjxEXxiPuD5BDku4MkFqeZyd4dZ1jvhTVqvbTLvyTJ
2 - Convert it to a byte string using Base58Check encoding
800C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D507A5B8D
3 - Drop the last 4 checksum bytes from the byte string
800C28FCA386C7A227600B2FE50B7CAE11EC86D3BF1FBE471BE89827E19D72AA1D
3 - Perform SHA-256 hash on the shortened string
8147786C4D15106333BF278D71DADAF1079EF2D2440A4DDE37D747DED5403592
4 - Perform SHA-256 hash on result of SHA-256 hash
507A5B8DFED0FC6FE8801743720CEDEC06AA5C6FCA72B07C49964492FB98A714
5 - Take the first 4 bytes of the second SHA-256 hash, this is the checksum
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6 - Make sure it is the same, as the last 4 bytes from point 2
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7 - If they are, and the byte string from point 2 starts with 0x80, there is no error.