Base 58 Encoding

Base 58 Encoding

A modified Base 58 encoding known as Base58Check is used for encoding byte arrays in Bitcoin into human-readable strings. A Bitcoin address is a Base58Check-encoded string with a 20-byte payload, which is the hash of the associated public key.

Base58Check has the following features:

• An arbitrarily sized payload.
• A symbol alphabet consisting of easily distinguished uppercase and lowercase letters (0OIl are not used)
• One byte of version/application information. Bitcoin addresses use 0x00 for this byte.
• Four bytes (32 bits) of hash-based error checking code. This code can be used to automatically correct typographical errors.
• Preservation of leading zeroes in the data.

A Base58Check string is created from a version/application byte and payload as follows.

1. Take the version/application byte and payload bytes, and concatenate them together.
2. Take the first four bytes of SHA256(SHA256(results of step 1))
3. Concatenate the results of step 1 and the results of step 2 together.
4. Treating the byte array as a big-endian base-256 number, convert the base-256 to base-58 using normal mathematical steps and the base-58 alphabet described below.
5. Count the number of leading zero bytes that were the result of step 3 (for Bitcoin addresses, there will always be at least one: the version/application byte). Each leading zero byte shall be represented by the character '1' in the final result.
6. Concatenate the 1's from step 5 with the results of step 4. This is the Base58Check result.

A Bitcoin address is the Base58Check encoding of the hash of the associated public key. Specifically, it is Base58Check(0,RIPEMD160(SHA256(public key))), with the following constraints:

• RIPEMD160 and SHA256 in this case are always exactly 20 and 32 unsigned bytes respectively. (Beware of bignumber implementations that clip leading 0x00 bytes, or prepend extra 0x00 bytes to indicate sign.)
• 0 refers to the version/application byte.
• "public key" is always represented as 65 bytes: the constant 0x04, followed by a 32-byte x-coordinate, then a 32-byte y-coordinate, both of which are unsigned big-endian integers.

Because of the 0x00 version/application byte, Bitcoin addresses always start with the digit '1'.

Base58_check encoding is also used for encoding private keys in the Wallet Import Format. This is formed exactly the same as a Bitcoin address, except that 0x80 is used for the version/application byte, and the payload is 32 bytes instead of 20 (a private key is a 32-byte unsigned big-endian integer). Such encodings will always yield a string that starts with '5', or more specifically, either '5H', '5J', or '5K'.

Base58 symbol chart

The Base58 symbol chart used in Bitcoin is specific to the Bitcoin project and is not intended to be the same as any other Base58 implementation used outside the context of Bitcoin.

Code	Character	Code	Character	Code	Character	Code	Character
0	1	1	2	2	3	3	4
4	5	5	6	6	7	7	8
8	9	9	A	10	B	11	C
12	D	13	E	14	F	15	G
16	H	17	J	18	K	19	L
20	M	21	N	22	P	23	Q
24	R	25	S	26	T	27	U
28	V	29	W	30	X	31	Y
32	Z	33	a	34	b	35	c
36	d	37	e	38	f	39	g
40	h	41	i	42	j	43	k
44	m	45	n	46	o	47	p
48	q	49	r	50	s	51	t
52	u	53	v	54	w	55	x
56	y	57	z

The algorithm for encoding address_byte_string (consisting of 0x01 + hash + 4-byte_check_code) is

   code_string = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"
   x = convert_bytes_to_big_integer(hash_result)
   
   output_string = ""
   
   while(x > 0) 
       {
           (x, remainder) = divide(x, 58)
           output_string.append(output_string[remainder])
       }
   
   repeat(number_of_leading_zero_bytes_in_hash)
       {
       output_string.append(code_string[0]);
       }
   
   output_string.reverse();

Source

https://github.com/bitcoin/bitcoin/blob/master/src/base58.h