modify rfc0016

[CHECKSUM] modify RFC0016:

• check that checksums do not begin with leading 1
• add test pubkeys

rfc/0016_public_key_checksum.md

@@ -39,6 +39,8 @@ When converting a public key to its binary representation, the length of the byt
   - If there is one leading non-zero byte and length is superior to 32, then the public key is not valid.
 
 ```python
+# you should install module base58
+import base58
 # convert public key string to bytes
 pubkey_byte = bytearray(base58.b58decode(pubkey))
 
@@ -105,13 +107,42 @@ To compute the checksum:
 
 0) use the binary representation of the public key :
 for simplification we use a pubkey that is 32 bits long once decoded.
-`pubkey = bytearray(base58.b58decode("J4c8CARmP9vAFNGtHRuzx14zvxojyRWHW2darguVqjtX"))`
+`pubkey = bytearray(base58.b58decode("J66fMDgSVVcdRgKucj1D5ssXAcQvg35JopvHNQo6cGY6"))`
 
-1) `sha256(pubkey)`
-`0x47c7aee49dfb9bea99949d04623281d8ad6188be8f6a698b0eb5994fa44d0a67`
+1) Hash the public key with sha256
+`sha256(pubkey)`
+`0x0daeb23dfe219d49d45af2367a56d3ef1086bbf2b2c128bc64625a4cef90c731`
+
+2) Encode the hash as base58
+`Base58.encode(sha256(pubkey))`
+`vQoY2iTFrYyBqSDAiWz9f9rRgNQm7FTsHTNpwqdEbct`
+
+2b) IF the public key is less than 44 char long, add leading "1" until it is 44 chars long.
+This aims at making checksums coherent among base58 implementations.
+`1vQoY2iTFrYyBqSDAiWz9f9rRgNQm7FTsHTNpwqdEbct`
+
+3) We only take the 3 first characters of this value to get the checksum
+`1vQ`
+
+## Test pubkeys
+
+Public keys associated to their correct checksum : 
+
+[
+    ["J4c8CARmP9vAFNGtHRuzx14zvxojyRWHW2darguVqjtX" , "5qC"],
+    ["12BjyvjoAf5qik7R8TKDJAHJugsX23YgJGi2LmBUv2nx" , "8BD"],
+    ["2BjyvjoAf5qik7R8TKDJAHJugsX23YgJGi2LmBUv2nx" , "8BD"],
+    # rare cases with numerous leading 1. 
+    ["111111111111111111111111111111111pubKey49311" , "C7L"],
+    ["11111111111111111111111111111111pubKey49311" , "C7L"],
+    # public key whose checksum may be wrong by beginning with 1
+    ["23iex3vD7sp9AK7wakwW1rj4F7RwYfQoXXR87Zttdte8", "14j"],
+    ["J66fMDgSVVcdRgKucj1D5ssXAcQvg35JopvHNQo6cGY6", "1vQ"],
+    # invalid public keys represented in 44 base58 chars. Should raise an error.
+    ["Z1111111111111111111111111111111111111111111" , None],
+    ["K1111111111111111111111111111111111111111111" , None],
+    # Should not raise an error.
+    ["J1111111111111111111111111111111111111111111" , "FqK"],
+]
 
-2) `Base58.encode(sha256(pubkey))`
-`5qCYkJMWgNA54gZz4HMQLbxL5btDmTS3EuHHCTcJaqGi`
 
-3)  We only take the 3 first characters of this value to get the checksum
-`5qC`