The Base58 Encoding Scheme

When trasmitting data, it can be useful to encode the data in a way that survives lower fidelity transmission mechanisms. For example, encoding data using a human alphabet, or encoding the data in a way that a human being can visually confirm the encoded data while reducing the opportunity to make a mistake. The Base58 encoding scheme is similar to the Base64 encoding scheme in that it can translate any binary data to a text string. It is different from Base64 in that the conversion alphabet has been carefully picked to work well in environments where a human being, such as a developer or other human being, might need to work with the information. Base58 is designed with a number of usability characteristics in mind that Base64 does not consider. First, similar looking letters are omitted such as 0 (zero), O (capital o), I (capital i) and l (lower case L). Doing so eliminates the possibility of a human being mistaking similar characters for a different character. Second, the non-alphanumeric characters + (plus), = (equals), and / (slash) are omitted to make it possible to use Base58 values in all modern file systems and URL schemes without the need for translation. Third, by using only alphanumeric characters, easy double-click or double tap selection is possible in modern computer interfaces. Fourth, social messaging systems do not line break on alphanumeric strings making it easier to e-mail or message Base58 values for debugging or sharing purposes. Fifth, unlike Base64, there is no padding making many Base58 values smaller (on average) or the same size as Base64 values for values up to 64 bytes, and less than 2% larger for values larger than 256 bytes. Finally, Base64 has eleven encoding variations that lead to miscommunication among developers on which variety of Base64 to use. This specification asserts that there is just one simple encoding mechanism for Base58, making implementations and developer interactions simpler. While Base58 does have a number of beneficial usability features, it is not always a good choice for an encoding format. For example, when encoding large amounts of data, it is 2% less efficient than base64. Developers might avoid Base58 if a 2% increase in efficiency over large data sets is desired.

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119.

The Base58 alphabet consists of the following characters:

123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz Each byte value from 0 to 57 maps to the alphabet above in the following way: Byte Character Byte Character Byte Character Byte Character 01 12 23 34 45 56 67 78 89 9A 10B 11C 12D 13E 14F 15G 16H 17J 18K 19L 20M 21N 22P 23Q 24R 25S 26T 27U 28V 29W 30X 31Y 32Z 33a 34b 35c 36d 37e 38f 39g 40h 41i 42j 43k 44m 45n 46o 47p 48q 49r 50s 51t 52u 53v 54w 55x 56y 57z Other application-specific alphabets for Base58, such as the Ripple alphabet and the Flickr alphabet exist. Those alphabets, while valid in their own application spaces, are not valid encoding formats for this specification and MUST NOT be used. Supporting more than one Base58 encoding alphabet would harm interoperability.

To encode an array of bytes to a Base58 encoded value, run the following algorithm. All mathematical operations MUST be performed using integer arithmetic. Start by initializing a 'zero_counter' to zero (0x0), an 'encoding_flag' to zero (0x0), a 'b58_bytes' array, a 'b58_encoding' array, and a 'carry' value to zero (0x0). For each byte in the array of bytes and while 'carry' does not equal zero (0x0) after the first iteration: If 'encoding_flag' is not set, and if the byte is a zero (0x0), increment the value of 'zero_counter'. If the value is not zero (0x0), set 'encoding_flag' to true (0x1). If 'encoding_flag' is set, multiply the current byte value by 256 and add it to 'carry'. Set the corresponding byte value in 'b58_bytes' to the value of 'carry' modulus 58. Set 'carry' to the value of 'carry' divided by 58. Once the 'b58_bytes' array has been constructed, generate the final 'b58_encoding' using the following algorithm. Set the first 'zero_counter' bytes in 'b58_encoding' to '1'. Then, for every byte in 'b58_array', map the byte value using the Base58 alphabet in the previous section to its corresponding character in 'b58_encoding'. Return 'b58_encoding' as the Base58 representation of the input array of bytes.

To decode a Base58 encoded array of bytes to a decoded array of bytes, run the following algorithm. All mathematical operations MUST be performed using integer arithmetic. Start by initializing a 'raw_bytes' array, and a 'carry' value to zero (0x0). For each input byte in the array of input bytes: Set 'carry' to the byte value associated with the input byte character. If a mapping does not exist, return an error code. While 'carry' does not equal zero and there are input bytes remaining: Multiply the input byte value by 58 and add it to 'carry'. Set the output byte value to 'carry' modulus 256. Set 'carry' to the value of 'carry' divided by 256. Set the corresponding byte value in 'raw_bytes' to the value of 'carry' modulus 58. Set 'carry' to the value of 'carry' divided by 58.

The following examples can be used as test vectors for the algorithms in this specification: The Base58 encoded value for "Hello World!" is:

2NEpo7TZRRrLZSi2U The Base58 encoded value for "The quick brown fox jumps over the lazy dog." is:

USm3fpXnKG5EUBx2ndxBDMPVciP5hGey2Jh4NDv6gmeo1LkMeiKrLJUUBk6Z The Base58 encoded value for 0x0000287fb4cd is:

111233QC4

Thanks to Satoshi Nakamoto for inventing the Base58 encoding format and the Bitcoin community for popularizing its usage.