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Base45 Encoding

Tool for coding with Base45 encoding, using 45 ASCII characters, which has become known since its use in the European green pass/certificate.

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Base45 Encoding -

Tag(s) : Character Encoding

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# Base45 Encoding

## Base45 Decoder

 Results format ASCII (printable) characters Hexadecimal 00-7F-FF Decimal 0-127-255 Octal 000-177-377 Binary 00000000-11111111 Integer number File to download

## Base45 Encoder

### What is Base-45? (Definition)

Base-45 is a proposed encoding standard for encoding data with 45 characters. It has been proposed by Faltstrom, et al. as a compact encoding better suited than Base32 or Base64 for QR-codes.

### How to encrypt using Base-45 cipher?

The Base45 encoding consists in writing the data in base 45 and using the following list of symbols 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ $%*+-./: Which corresponds to the 45 characters that can be used in a QR-code in alphanumeric mode so the correspondance table IndexCharacter Base45 0 0 11 22 33 44 55 66 77 88 99 10A 11B 12C 13D 14E 15F 16G 17H 18I 19J 20K 21L 22M 23N 24O 25P 26Q 27R 28S 29T 30U 31V 32W 33X 34Y 35Z 36 37$
38%
39*
40+
41-
42.
43/
44:

Encoding begins by cutting the data to be encoded from left to right in groups of 2 bytes. If the data has an odd number of bytes, the last group is 1 byte in size.

Example: Encode the 3 characters B45, of ASCII code [66,52,53], which are then split [66,52],

Each pair of 2 bytes $[a, b]$ is interpreted as a number in base $256$ such that $n = (a \times 256) + b$ (in base 10) which can then be converted into base 45 via a triple $[c,d,e]$ such that $n = c + (d \times 45) + (e \times 45^2)$. The characters in the correspondence table for the values '[c, d, e]' are noted (in that order) as encoded text.

Any last single byte $a$ at the end of the data is also interpreted as a number in base 256 and converted to a pair $[b,c]$ such that $a = b + (45 \times c)$. The characters in the correspondence table for the values [b,c] are noted (in that order) as encoded text.

Example: The couple [66,52] corresponds to the number 66 * 256 + 52 = 16948 and 16948 = 28 + 16 * 45 + 8 * 45 ^ 2, so the triplet [28,16,8] that is equivalent to the characters S,G,8 in base45
The remaining byte  is written in base 45 as follows: 53 = 1 * 45 + 8, either the pair [1,8] or the characters 1,8 in base45. The full encoding of B45 in base45 is SG881

### How to decrypt Base-45 cipher?

For any string written in Base45, start by converting the characters into numeric values (according to the correspondence table).

Example: Decode SG881, or the values [28,16,8,8,1]

Divide the values into groups of 3, from left to right. If the last group of 3 is not complete, add zeros 0 at the end.

Example: [28,16,8,8,1] splits as [28,16,8],[8,1,0]

Interpret each group [c,d,e] as a number in base 45 as follows: $n = c + (d \times 45) + (e \times 45^2)$ and note the values $n$ obtained

Example: [28,16,8],[8,1,0] is converted to ,

Convert each number to base 256 (so in bytes)

Example: 16948 = 66 * 256 + 52 or [66,52] and 53 remains  in base 256

The decoded message is the set of bytes. It can be interpreted in ASCII code (or Unicode)

Example: [66,52,53] for the 3 ASCII characters B,4,5 (plaintext)

### How to recognize a Base-45 ciphertext? (Identification)

Base-45 uses the 36 uppercase alphanumeric characters 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ completed with the characters (space)', \$ (dollar), % (percent), * (asterisk), + (plus), - (minus/dash), . (period), / (slash) and : (colon).

Base-45 is optimized to transmit data with the alphanumeric mode of QR-codes.

It has been used in COVID-19 vaccines certificates and European Union green passes.

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