So What Is Base-45, And Where Is It Used?

If you are into Cybersecurity, Base-64 should be a well-known format, and often used to convert binary data into a text format. In Bitcoin, we use Base-58 for the Bitcoin address. But, what is Base-45?

Well, your vaccine status document probably contains a QR code, and which uses Base-45 format for the data coding [article]. With Base-45 format, we have 45 characters defined. The encoding table is [here]:

Value Encoding  Value Encoding  Value Encoding  Value Encoding
   00 0            12 C            24 O            36 Space
   01 1            13 D            25 P            37 $
   02 2            14 E            26 Q            38 %
   03 3            15 F            27 R            39 *
   04 4            16 G            28 S            40 +
   05 5            17 H            29 T            41 -
   06 6            18 I            30 U            42 .
   07 7            19 J            31 V            43 /
   08 8            20 K            32 W            44 :
   09 9            21 L            33 X
   10 A            22 M            34 Y
   11 B            23 N            35 Z

With this we take the data stream with two bytes [A, B] at a time, and and convert into [ C, D, E] and where:

(A*256) + B = C + (D*45) + (E*45*45).

For example, for “hello”, we have:

h         e         l         l         o
0110 1000 0110 0101 0110 1100 0110 1100 0110 1111

The first two bytes are A=64+32+8=104 and B=64+32+5 =101, and where:

(104*256)+101 = 26,725

We then divide by 45 and note the remainder:

26725 / 45 = 593 r 40 = ‘+’
593 /45 = 13 r 8 -> ‘8’
13/45 = 0 r 13 -> ‘D’

Thus “he” maps to “+8D” in Base-45. A full example is (note that there is a space in the encoded string) [here]:

h            e           l           l           o
0110 1000    0110 0101   0110 1100   0110 1100   0110 1111Message:  hello 68656c6c6f
Encoded:  +8D VDL2
Decode:   hello

The code is [here]:

import base45
import sys
message="hello"
if (len(sys.argv)>1):
 message=str(sys.argv[1])
en = base45.b45encode(message.encode())
print ("Message:\t",message,message.encode().hex()) 
print ("Encoded:\t",en.decode())
de = base45.b45decode(en)
print ("Decode:\t\t",de.decode())

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