rfc9285v3.txt		rfc9285.txt
	Internet Engineering Task Force (IETF) P. Fältström		Internet Engineering Task Force (IETF) P. Fältström
	Request for Comments: 9285 Netnod		Request for Comments: 9285 Netnod
	Category: Informational F. Ljunggren		Category: Informational F. Ljunggren
	ISSN: 2070-1721 Kirei		ISSN: 2070-1721 Kirei
	D. van Gulik		D.W. van Gulik
	Webweaving		Webweaving
	August 2022		August 2022
	The Base45 Data Encoding		The Base45 Data Encoding
	Abstract		Abstract
	This document describes the Base45 encoding scheme, which is built		This document describes the Base45 encoding scheme, which is built
	upon the Base64, Base32, and Base16 encoding schemes.		upon the Base64, Base32, and Base16 encoding schemes.
	skipping to change at line 194 ¶		skipping to change at line 194 ¶
	Table 1: The Base45 Alphabet		Table 1: The Base45 Alphabet
	4.3. Encoding Examples		4.3. Encoding Examples
	It should be noted that although the examples are all text, Base45 is		It should be noted that although the examples are all text, Base45 is
	an encoding for binary data where each octet can have any value		an encoding for binary data where each octet can have any value
	0-255.		0-255.
	Encoding example 1:		Encoding example 1:
	The string "AB" is the byte sequence [[65 66]].		The string "AB" is the byte sequence [[65 66]]. If we look at all
	If we look at all 16 bits, we get 65 * 256 + 66 = 16706.		16 bits, we get 65 * 256 + 66 = 16706. 16706 equals 11 + (11 *
	16706 equals 11 + (11 * 45) + (8 * 45 * 45), so the sequence in		45) + (8 * 45 * 45), so the sequence in base 45 is [11 11 8].
	base 45 is [11 11 8].
	Referring to Table 1, we get the encoded string "BB8".		Referring to Table 1, we get the encoded string "BB8".
	+-----------+------------------+		+-----------+------------------+
	| AB | Initial string |		| AB | Initial string |
	+-----------+------------------+		+-----------+------------------+
	| [[65 66]] | Decimal value |		| [[65 66]] | Decimal value |
	+-----------+------------------+		+-----------+------------------+
	| [16706] | Value in base 16 |		| [16706] | Value in base 16 |
	+-----------+------------------+		+-----------+------------------+
	| [11 11 8] | Value in base 45 |		| [11 11 8] | Value in base 45 |
	+-----------+------------------+		+-----------+------------------+
	| BB8 | Encoded string |		| BB8 | Encoded string |
	+-----------+------------------+		+-----------+------------------+
	Table 2: Example 1 in Detail		Table 2: Example 1 in Detail
	Encoding example 2:		Encoding example 2:
	The string "Hello!!" as ASCII is the byte sequence [[72 101] [108		The string "Hello!!" as ASCII is the byte sequence [[72 101] [108
	108] [111 33] [33]].		108] [111 33] [33]]. If we look at this 16 bits at a time, we get
	If we look at this 16 bits at a time, we get [18533 27756 28449		[18533 27756 28449 33]. Note the 33 for the last byte. When
	33]. Note the 33 for the last byte.		looking at the values in base 45, we get [[38 6 9] [36 31 13] [9 2
	When looking at the values in base 45, we get [[38 6 9] [36 31 13]		14] [33 0]], where the last byte is represented by two values.
	[9 2 14] [33 0]], where the last byte is represented by two
	values.
	The resulting string "%69 VD92EX0" is created by looking up these		The resulting string "%69 VD92EX0" is created by looking up these
	values in Table 1. It should be noted it includes a space.		values in Table 1. It should be noted it includes a space.
	+---------------------------------------+------------------+		+---------------------------------------+------------------+
	| Hello!! | Initial string |		| Hello!! | Initial string |
	+---------------------------------------+------------------+		+---------------------------------------+------------------+
	| [[72 101] [108 108] [111 33] [33]] | Decimal value |		| [[72 101] [108 108] [111 33] [33]] | Decimal value |
	+---------------------------------------+------------------+		+---------------------------------------+------------------+
	| [18533 27756 28449 33] | Value in base 16 |		| [18533 27756 28449 33] | Value in base 16 |
	+---------------------------------------+------------------+		+---------------------------------------+------------------+
	| [[38 6 9] [36 31 13] [9 2 14] [33 0]] | Value in base 45 |		| [[38 6 9] [36 31 13] [9 2 14] [33 0]] | Value in base 45 |
	+---------------------------------------+------------------+		+---------------------------------------+------------------+
	| %69 VD92EX0 | Encoded string |		| %69 VD92EX0 | Encoded string |
	+---------------------------------------+------------------+		+---------------------------------------+------------------+
	Table 3: Example 2 in Detail		Table 3: Example 2 in Detail
	Encoding example 3:		Encoding example 3:
	The string "base-45" as ASCII is the byte sequence [[98 97] [115		The string "base-45" as ASCII is the byte sequence [[98 97] [115
	101] [45 52] [53]].		101] [45 52] [53]]. If we look at this two bytes at a time, we
	If we look at this two bytes at a time, we get [25185 29541 11572		get [25185 29541 11572 53]. Note the 53 for the last byte. When
	53]. Note the 53 for the last byte.		looking at the values in base 45, we get [[30 19 12] [21 26 14] [7
	When looking at the values in base 45, we get [[30 19 12] [21 26		32 5] [8 1]] where the last byte is represented by two values.
	14] [7 32 5] [8 1]] where the last byte is represented by two
	values.
	Referring to Table 1, we get the encoded string "UJCLQE7W581".		Referring to Table 1, we get the encoded string "UJCLQE7W581".
	+----------------------------------------+------------------+		+----------------------------------------+------------------+
	| base-45 | Initial string |		| base-45 | Initial string |
	+----------------------------------------+------------------+		+----------------------------------------+------------------+
	| [[98 97] [115 101] [45 52] [53]] | Decimal value |		| [[98 97] [115 101] [45 52] [53]] | Decimal value |
	+----------------------------------------+------------------+		+----------------------------------------+------------------+
	| [25185 29541 11572 53] | Value in base 16 |		| [25185 29541 11572 53] | Value in base 16 |
	+----------------------------------------+------------------+		+----------------------------------------+------------------+
	| [[30 19 12] [21 26 14] [7 32 5] [8 1]] | Value in base 45 |		| [[30 19 12] [21 26 14] [7 32 5] [8 1]] | Value in base 45 |
	skipping to change at line 270 ¶		skipping to change at line 265 ¶
	| UJCLQE7W581 | Encoded string |		| UJCLQE7W581 | Encoded string |
	+----------------------------------------+------------------+		+----------------------------------------+------------------+
	Table 4: Example 3 in Detail		Table 4: Example 3 in Detail
	4.4. Decoding Example		4.4. Decoding Example
	Decoding example 1:		Decoding example 1:
	The string "QED8WEX0" represents, when looked up in Table 1, the		The string "QED8WEX0" represents, when looked up in Table 1, the
	values [26 14 13 8 32 14 33 0].		values [26 14 13 8 32 14 33 0]. We arrange the numbers in chunks
	We arrange the numbers in chunks of three, except for the last one		of three, except for the last one which can be two numbers, and
	which can be two numbers, and get [[26 14 13] [8 32 14] [33 0]].		get [[26 14 13] [8 32 14] [33 0]]. In base 45, we get [26981
	In base 45, we get [26981 29798 33] where the bytes are [[105 101]		29798 33] where the bytes are [[105 101] [116 102] [33]]. If we
	[116 102] [33]].		look at the ASCII values, we get the string "ietf!".
	If we look at the ASCII values, we get the string "ietf!".
	+-------------------------------+------------------------+		+-------------------------------+------------------------+
	| QED8WEX0 | Initial string |		| QED8WEX0 | Initial string |
	+-------------------------------+------------------------+		+-------------------------------+------------------------+
	| [26 14 13 8 32 14 33 0] | Looked up values |		| [26 14 13 8 32 14 33 0] | Looked up values |
	+-------------------------------+------------------------+		+-------------------------------+------------------------+
	| [[26 14 13] [8 32 14] [33 0]] | Groups of three |		| [[26 14 13] [8 32 14] [33 0]] | Groups of three |
	+-------------------------------+------------------------+		+-------------------------------+------------------------+
	| [26981 29798 33] | Interpreted as base 45 |		| [26981 29798 33] | Interpreted as base 45 |
	+-------------------------------+------------------------+		+-------------------------------+------------------------+
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