work would be equally applicable to base64url, as the difference between base64 and
base64url has little impact on encoding and decoding algorithms.
2.1. Character Encodings
Base64 was designed with the ASCII character encoding in mind [Josefsson 2006]. In a
document using the ASCII encoding, only seven of the eight bits of each byte is used.
By convention, each ASCII character has a corresponding byte value (also called code
point) in [0, 128).
There are several supersets to the ASCII character encoding (e.g., UTF-8 or ISO 8859-
1): they interpret strings of byte values in
[0, 128)
as ASCII strings. Only byte values
with the most significant bits set are interpreted differently (e.g., as accented characters
such as ’
´
e’). In other words, if we need to include an ASCII string within a string that
uses a superset of the ASCII character encoding, we only need to copy the byte values.
Thus base64 is practical with all ASCII supersets.
Most Web pages are served using the Unicode format UTF-8 [Davis 2012] which
supports up to
1 114 112
possible characters. Some programming languages (e.g., Go and
Python) also default on UTF-8. XML documents use UTF-8 by default. Conveniently,
UTF-8 is an ASCII superset. In UTF-8, only the ASCII characters can be represented
using a single byte. All non-ASCII characters in UTF-8 require from two to four bytes.
It might seem like base64 is suboptimal: there are many more than 64 distinct
characters. However, there are only 95 printable ASCII characters, and they include
the space and the quotes (
"
and
’
), the ampersand (
&
) and the less-than sign (
<
). Thus
there are only about 90 characters that are represented as a single byte in UTF-8 that
would be generally usable in HTML and XML. If we restrict the size of our table to a
power of two, for simplicity and computational efficiency, then 64 characters is best.
2.2. Efficient Scalar Encoding
Throughout, we consider byte values as unsigned integers in
[0, 256)
. Thus we can think
of encoding as mapping a stream of numbers in [0, 256) to ASCII characters.
In the main loop of the encoding Algorithm 1, we combine three-byte values
(s
i
, s
i+1
, s
i+2
) arithmetically into four values in [0, 64), that is
— s
i
÷ 4,
— ((s
i
× 16) mod 64) + (s
i+1
÷ 16),
— ((s
i+1
× 4) mod 64) + (s
i+2
÷ 64)
— and s
i+2
mod 64.
Then we pass these four values to the function
B
which looks up the corresponding
ASCII character. In practice, an encoder might implement the function
B
efficiently as
a lookup table, using a 64-byte array.
Thus, given three input bytes, we get four output characters:
—
The first character is generated from the six most significant bits of the first byte
value.
—
The second character is determined from the two least significant bits from the first
byte value and from the four most significant bits of the second byte value.
—
The third character represents the four least significant bits of the second byte value
and the two most significant bits from the third byte value.
—
The last character is determined by the six least significant bits from the third byte
value.
Thus if we write the byte values starting from the left, with the bits within each byte
written from the most significant to the least significant, we have that the first 6 bits
5
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