Step by step guide to go from public key to a Bech32 encoded address

[Coding Enthusiast]

Bitcoin wiki has a pretty good step-by-step explanation of how to go from a public key to a base58_encoded address which contains the values for each step of the way[1]. But unfortunately I could not find anything similar for Bech32_encoding. Additionally I found the reference implementations a bit confusing[2]! The information is out there[3] but I feel like having it step-by-step like "[1]" can make it a lot easier specially for developers. For example during unit testing I was getting a different address (bc1qp63uahgrxged4z5jswyt5dn5v3lzsem6c0qqhg8) for below public key and I wasn't sure where the bug was coming from, this visualization helped me [4] realize I was appending the version byte before converting the bits instead of after. So hopefully these steps can help someone like me looking for them.

How to create a Bech32 address from a public key:

1. Having a compressed[5] public key (0x02 or 0x03 followed by 32 byte X coordinate):

Code:

0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

2. Perform SHA-256 hashing on the public key:

Code:

0f715baf5d4c2ed329785cef29e562f73488c8a2bb9dbc5700b361d54b9b0554

3. Perform RIPEMD-160 hashing on the result of SHA-256:

Code:

751e76e8199196d454941c45d1b3a323f1433bd6

4. The result of step 3 is an array of 8-bit unsigned integers (base 2^8=256) and Bech32 encoding converts this to an array of 5-bit unsigned integers (base 2^5=32) so we "squash" the bytes to get:
in hex:

Code:

0e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e16

in numbers:

Code:

14 20 15 07 13 26 00 25 18 06 11 13 08 21 04 20 03 17 02 29 03 12 29 03 04 15 24 20 06 14 30 22

5 bits binary:

Code:

01110 10100 01111 00111 01101 11010 00000 11001 10010 00110 01011 01101 01000 10101 00100 10100 00011 10001 00010 11101 00011 01100 11101 00011 00100 01111 11000 10100 00110 01110 11110 10110

5. Add the witness version byte in front of the step 4 result (current version is 0):

Code:

000e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e16

6. Compute the checksum by using the data from step 5 and the H.R.P (bc for MainNet and tb for TestNet)

Code:

0c0709110b15

7. Append the checksum to result of step 5 (we now have an array of 5-bit integers):

Code:

000e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e160c0709110b15

8. Map each value to its corresponding character in Bech32Chars (qpzry9x8gf2tvdw0s3jn54khce6mua7l) 00 -> q, 0e -> w,...

Code:

qw508d6qejxtdg4y5r3zarvary0c5xw7kv8f3t4

9. A Bech32_encoded address consists of 3 parts: HRP + Separator + Data:

Code:

bc1qw508d6qejxtdg4y5r3zarvary0c5xw7kv8f3t4

The final result from step 9 is the same as example in BIP173[6]

References:
[1] https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses
[2] https://github.com/sipa/bech32
[3] https://github.com/bitcoin/bips/blob/master/bip-0173.mediawiki
[4] https://en.bitcoin.it/w/images/en/4/48/Address_map.jpg
[5] Only compressed public keys are allowed: https://github.com/bitcoin/bips/blob/master/bip-0143.mediawiki#restrictions-on-public-key-type
[6] https://github.com/bitcoin/bips/blob/master/bip-0173.mediawiki#examples

[Coding Enthusiast]

Great guide and mostly it's easy to understand. But i don't understand the 8th steps, is it encode/decode result from Bech32 characters?

Yes. Note that step7 is the hexadecimal representation of an array of 5-bit integers {0, 14, 20, 15, 7, ..., 11, 21} so 0 is item at index 0 of B32Chars or the letter q and 14 is the character at index 14 or w, 20 is 5 and so on.
 In C♯

Code:

string B32Chars = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
StringBuilder result = new StringBuilder();
foreach (byte item in step7Array)
{
   result.Append(B32Chars[item]);
}

Basically this:
.join in python implementation (https://github.com/sipa/bech32/blob/master/ref/python/segwit_addr.py#L59)
or the for loop in JavaScript implementation (https://github.com/sipa/bech32/blob/master/ref/javascript/bech32.js#L74-L76)

[odolvlobo]

4. The result of step 3 is an array of 8-bit unsigned integers (base 2^8=256) and Bech32 encoding converts this to an array of 5-bit unsigned integers (base 2^5=32) so we "squash" the bytes to get:

I feel that your description is confusing. You write "array of 5-bit integers", but displaying the results as a hex string implies that it is a string of 8-bit values. I recommend inserting spaces between each value to emphasize that each element is distinct, and perhaps using decimal values to avoid implying that the values could lie outside of the range 0 - 31.

For example:

4. The result of step 3 is an array of 8-bit unsigned integers (base 2^8=256) and Bech32 encoding converts this to an array of 5-bit unsigned integers (base 2^5=32) so we "squash" the bytes to get:

Code:

0e 14 0f 07 0d 1a 00 19 12 06 0b 0d 08 15 04 14 03 11 02 1d 03 0c 1d 03 04 0f 18 14 06 0e 1e 16

or even better:

4. The result of step 3 is an array of 8-bit unsigned integers (base 2^8=256) and Bech32 encoding converts this to an array of 5-bit unsigned integers (base 2^5=32) so we "squash" the bytes to get:

Code:

14 20 15 7 13 26 0 25 18 6 11 13 8 21 4 20 3 17 2 29 3 12 29 3 4 15 24 20 6 14 30 22

Also,

5. Add the witness version byte in front of the step 4 result (current version is 0):

Code:

000e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e16

I recommend removing "byte" since the witness version is not a byte. Note that bip-173 also calls it a "byte" when it isn't.

5. Add the witness version in front of the step 4 result (current version is 0):

Code:

0 14 20 15 7 13 26 0 25 18 6 11 13 8 21 4 20 3 17 2 29 3 12 29 3 4 15 24 20 6 14 30 22

[Coding Enthusiast]

I feel that your description is confusing. You write "array of 5-bit integers", but displaying the results as a hex string implies that it is a string of 8-bit values.

I get what you are talking about but base-16 is just another representation of an array of "numbers", it doesn't really make a difference if I write 14 12 15 with spaces or 0e 14 0f with or without spaces, they are both representing the same set of numbers in base-256. The only possible way to clarify things is if I start typing them in binary like this but that's just impossible to read:

Code:

01110 10100 01111 ...

Additionally hex or base-16 is a very easy and convenient way to transfer arrays of "numbers". For instance you can not input each of those "numbers" (14, 20, 15...) one by one in an array when coding, it would take a long time and it is easy to make a mistake. But you can very easily give your code the hexadecimal string representation of it and decode it into the array of "numbers" then treat those "numbers" however you like.

I am going to add both numbers and binary, maybe that helps visualizing it better.

I recommend removing "byte" since the witness version is not a byte. Note that bip-173 also calls it a "byte" when it isn't.

Well, "version byte" is the name of the "0" we are appending to it, I can't just change that name:
https://github.com/bitcoin/bips/blob/master/bip-0141.mediawiki#witness-program
https://github.com/bitcoin/bips/blob/master/bip-0142.mediawiki#rationale

[TheArchaeologist]

If you want to play around with this using Python you can check: https://github.com/mcdallas/cryptotools

Example:

Code:

>>> from ECDSA.secp256k1 import CURVE, PrivateKey

>>> private = PrivateKey.random()
>>> private.int()
8034465994996476238286561766373949549982328752707977290709076444881813294372

>>> public = private.to_public()
>>> public
PublicKey(102868560361119050321154887315228169307787313299675114268359376451780341556078, 83001804479408277471207716276761041184203185393579361784723900699449806360826)

>>> public.point in CURVE
True

>>> public.to_address('P2WPKH')
'bc1qh2egksgfejqpktc3kkdtuqqrukrpzzp9lr0phn'

[danda]

nice.  why not add to bitcoin wiki?

[denisdo95]

3. Perform RIPEMD-160 hashing on the result of SHA-256:

Code:

751e76e8199196d454941c45d1b3a323f1433bd6

4. The result of step 3 is an array of 8-bit unsigned integers (base 2^8=256) and Bech32 encoding converts this to an array of 5-bit unsigned integers (base 2^5=32) so we "squash" the bytes to get:
in hex:

Code:

0e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e16

Hey.

Please tell me, how did you get the string "0e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e16" from the string "751e76e8199196d454941c45d1b3a323f1433bd6"? What command do you need to execute for this?

[DannyHamilton]

3. Perform RIPEMD-160 hashing on the result of SHA-256:

Code:

751e76e8199196d454941c45d1b3a323f1433bd6

4. The result of step 3 is an array of 8-bit unsigned integers (base 2^8=256) and Bech32 encoding converts this to an array of 5-bit unsigned integers (base 2^5=32) so we "squash" the bytes to get:
in hex:

Code:

0e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e16

Hey.

Please tell me, how did you get the string "0e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e16" from the string "751e76e8199196d454941c45d1b3a323f1433bd6"? What command do you need to execute for this?

Here's a simple way to understand it...

Convert the first value from a hex value to an array of bits where: 0 = 0000, 1=0001, 2=0010, 3-0011, 4=0100, etc
   7    5    1    e    7    6    e ...
0111 0101 0001 1110 0111 0110 1110 ...

Change the spacing of the 1's and zeros so that they are grouped 5 in a set instead of 4:
01110 10100 01111 00111 01101 110 ...

Convert each set of 5 into a hex value:
01110 10100 01111 00111 01101 110...
   0e    14    0f    07    0d    ...   

[denisdo95]

Here's a simple way to understand it...

Convert the first value from a hex value to an array of bits where: 0 = 0000, 1=0001, 2=0010, 3-0011, 4=0100, etc
   7    5    1    e    7    6    e ...
0111 0101 0001 1110 0111 0110 1110 ...

Change the spacing of the 1's and zeros so that they are grouped 5 in a set instead of 4:
01110 10100 01111 00111 01101 110 ...

Convert each set of 5 into a hex value:
01110 10100 01111 00111 01101 110...
   0e    14    0f    07    0d    ...   

Thank You Man! You best! 

[TsaPaka]

Thank you because I could understand until the last soft fork.
I explain here how a segwit address in P2WSH format is derived so as not to mix the segwit between P2WPKH and P2WSH.
Note that the guide explained above generates in P2WPKH format about 42 characters but P2WSH format about 62 characters.

https://bitcointalk.org/index.php?topic=5227953

[MixMAx123]

I have now successfully reached step 5.
I have: 000e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e16

Now I do not come to step 6.
When I calculate: SHA256 (SHA256 (000e140f070d1a001912060b0d081504140311021d030c1d03040f1814060e1e16)) = 103ede5cc41abfd088a368bb40df3d52e5614460521d88daa202917c7f3de88d.

The first 6 bytes are then with me: 10 3e de 5c c4 1a
And this is a different number than yours.
What am I doing wrong?

[Coding Enthusiast]

What am I doing wrong?

The encoding is Bech-32 not Base-58 and there is no SHA256 in this encoding, there is only playing around with bits. Read BIP-173 for details of how you should compute the checksum.

[Headphones]

Hey, great post! It's really useful.

I'm trying to decode a bech32 address tb1qwm3dqje4wc7cs2u9sv39yh2as8ae0ntzqkjunw into the h160 of the public key, which is step 3 in your guide, using the reference implementation in python.

I end up with an array of integers: [118, 226, 208, 75, 53, 118, 61, 136, 43, 133, 131, 34, 82, 93, 93, 129, 251, 151, 205, 98] which I think corresponds with step 4 of your guide.

How do I go from the array of numbers into the hex version of the h160 which according to https://slowli.github.io/bech32-buffer/ should be: 751e76e8199196d454941c45d1b3a323f1433bd6

Any help would be appreciated!

[Coding Enthusiast]

I'm trying to decode a bech32 address tb1qwm3dqje4wc7cs2u9sv39yh2as8ae0ntzqkjunw into the h160 of the public key

Same process steps in reverse:
Map each character to its index in Bech-32 charset after removing hrp (q=0; w=14,...):

Code:

0 14 27 17 13 0 18...

The result is in base-32 (5-bits group) and has to be converted back to base-256 (8-bits or 1 octet/byte group).
Also since this is an address, the first item is the witness version that has to be dropped and evaluated separately.

Code:

14 = 01110
27 = 11011
17 = 10001
13 = 01101
0  = 00000
18 = 10010
25 = 11001
...

Select 8-bits at a time:

Code:

01110110 11100010 11010000 01001011 ...
118      226      208      75 ...

which is  0x76e2d0... in hex and the same result that the site you linked gives.

PS. The additional steps to expand H.R.P and compute and verify checksum are skipped for simplicity but are mandatory.

How do I go from the array of numbers into the hex version of the h160 which according to https://slowli.github.io/bech32-buffer/ should be: 751e76e8199196d454941c45d1b3a323f1433bd6

Try again, when decoding Bech32=tb1qwm3dqje4wc7cs2u9sv39yh2as8ae0ntzqkjunw it returns 0x76e2d04b35763d882b858322525d5d81fb97cd62 as data (hexadecimal).

[Headphones]

Thank you for this! It's now working 

I'm trying to decode a bech32 address tb1qwm3dqje4wc7cs2u9sv39yh2as8ae0ntzqkjunw into the h160 of the public key

Same process steps in reverse:
Map each character to its index in Bech-32 charset after removing hrp (q=0; w=14,...):

Code:

0 14 27 17 13 0 18...

The result is in base-32 (5-bits group) and has to be converted back to base-256 (8-bits or 1 octet/byte group).
Also since this is an address, the first item is the witness version that has to be dropped and evaluated separately.

Code:

14 = 01110
27 = 11011
17 = 10001
13 = 01101
0  = 00000
18 = 10010
25 = 11001
...

Select 8-bits at a time:

Code:

01110110 11100010 11010000 01001011 ...
118      226      208      75 ...

which is  0x76e2d0... in hex and the same result that the site you linked gives.

PS. The additional steps to expand H.R.P and compute and verify checksum are skipped for simplicity but are mandatory.

How do I go from the array of numbers into the hex version of the h160 which according to https://slowli.github.io/bech32-buffer/ should be: 751e76e8199196d454941c45d1b3a323f1433bd6

Try again, when decoding Bech32=tb1qwm3dqje4wc7cs2u9sv39yh2as8ae0ntzqkjunw it returns 0x76e2d04b35763d882b858322525d5d81fb97cd62 as data (hexadecimal).

[oosinoots]

How do I compute the checksum? The bip 173 page has the code in python which I do not understand. Can you explain the process so I could code in Java/Kotlin?

[odolvlobo]

How do I compute the checksum? The bip 173 page has the code in python which I do not understand. Can you explain the process so I could code in Java/Kotlin?

The BIP also links to a C version if that helps: https://github.com/sipa/bech32/tree/master/ref/c

[Coding Enthusiast]

How do I compute the checksum? The bip 173 page has the code in python which I do not understand. Can you explain the process so I could code in Java/Kotlin?

I haven't seen a Java/Kotlic implementation but apart from the C implementation there is JavaScript and my own C# implementations that are similar languages.

The process is:
"Expand HRP" by converting its N base-256 (8-bit) representation to 2N+1 base-32 (5-bit).
For example bc which is 0x6263 or 0b01100010_01100011 becomes 0x0303000203
In this process for each octet the highest 3 bits are placed in first half of the result and the remaining (low) 5 bits in second half. In the example above:
b=0x62=0b01100010 -> 0x0303000203 and
c=0x63=0b01100011 -> 0x0303000203
The two halves are separated with a zero (the value at the middle is always 0) -> 0x0303000203

Now we can compute checksum of [expanded HRP] | [base32 data] | [6x zeros] (note that "|" is concatenation).
The process is best explained by code

Code:

private static uint Polymod(byte[] data)
{
    uint chk = 1;
    foreach (byte b in data)
    {
        uint temp = chk >> 25;
        chk = ((chk & 0x1ffffff) << 5) ^ b;
        for (int i = 0; i < 5; i++)
        {
            if (((temp >> i) & 1) == 1)
            {
                chk ^= generator[i];
            }
        }
    }
    return chk;
}

The actual checksum used in encoding is the result of "polymod" XORed with a constant. This constant is 0x01 for Bech32 (BIP-173) encoding just flipping the least significant bit and is 0x2bc830a3 for Bech32m (BIP-350) encoding. The former is used for witness version 0 addresses and the later for 1+. This is basically the only difference that was introduced in BIP-350.

[MixMAx123]

How do I compute the checksum? The bip 173 page has the code in python which I do not understand. Can you explain the process so I could code in Java/Kotlin?

Here it is in Java
https://github.com/MrMaxweII/Bitcoin-Address-Generator/blob/master/src/BTClib3001/Bech32Address.java

[larry_vw_1955]

@Coding Enthusiast do you have any plan to create Bech32m version of this guide since the BIP already created and few wallet already implement it?

i dont understand why they needed to have bech32m if they already have bech32. the more address types that get created i think the worse that is for bitcoin not better. i dont know if anyone else feel that way or not especially though if the address type that is being changed had some type of issue with it that motivated the creation of a related address typing. but i guess they'll keep going. watch out for bech32P anytime soon.