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 in a way that a person can visually confirm the encoded data can be more beneficial than encoding it in binary form. 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 person, such as a developer or support technician, might need to visually confirm the information with low error rates. 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 the wrong 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 further system-specific encoding schemes. 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 when debugging systems. Fifth, unlike Base64, there is no byte 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 larger values. Finally, Base64 has eleven encoding variations that lead to confusion 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. Base58 encoding also has an average worst-case algorithm complexity that is O(n^2). For these reasons, developers might want to avoid using Base58 for encoding byte strings that are greater than 256 bytes in length. This document specifies the base 58 encoding scheme, including an introduction to the benefits of the approach, the encoding and decoding algorithm, alternative alphabets, and security considerations.

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, interpreted as a decimal value, from 0 to 57 maps to the alphabet above in the following way: Decimal Character Decimal Character 01 29W 12 30X 23 31Y 34 32Z 45 33a 56 34b 67 35c 78 36d 89 37e 9A 38f 10B 39g 11C 40h 12D 41i 13E 42j 14F 43k 15G 44m 16H 45n 17J 46o 18K 47p 19L 48q 20M 49r 21N 50s 22P 51t 23Q 52u 24R 53v 25S 54w 26T 55x 27U 56y 28V 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:

11233QC4

This section contains a variety of security considerations that implementers using this specification are advised to consider before deploying this technology in a production setting.

In general, when converting from a source base-encoding to a target base-encoding, if the target encoding is not the a numerical power of the source encoding, it is possible for the algorithm to degrade from linear algorithm complexity into quadratic algorithm complexity. That is, converting from base-2 (binary) to base-32 or base-64 can be done with a worst-case algorithm complexity of O(n) time, but converting from base-2 to base-58 has a worst-case complexity of O(n^2). In short, base-58 does not work well for encoding large byte values. Implementers are urged to ensure that their production software imposes limits on input size. Encoding values greater than 256 bytes in base58 is NOT RECOMMENDED.

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