Print Page - How Bitcoin Addresses are generated? Understand the Math behind Bitcoin

Title: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on February 04, 2020, 05:05:40 PM

How Bitcoin Addresses are Generated

This thread will only cover P2PKH address i.e. the bitcoin address starting with '1', also known as Legacy Address. I will create another thread in future about how to create P2SH or Bech32 addresses.

Ok! So let's start with the topic. To use Bitcoin, user generally needs two things: Private Key and Bitcoin Address. Bitcoin Address is an identifier which looks like this: 18J6ai34uzGofUuzbiwhXJzKzdx1efDBqA. User have to share it with sender to receive payment. Whereas private key is a key which user have to input in wallet to access the funds received.

You may be already knowing what I have just said above. But did you ever wonder how these pair of keys are generated? Let's dive deep into topic and create our own code for generating key pair. The main and the most important component of Bitcoin Address is Private Key. Let's discuss it first:

Private Key

In simple words, anything can be private key if it fulfills two conditions. Condition one, it must not be 0. Second, it must be lower than the value of N defined by SECG for secp256k1 curve. However, the value of N is very, very large so practically every 256-bits number is valid private key.

Now the question arises how to generate private key. As I said in the starting that anything can be private key. For example, this string: "I am a string to generate private key" can be converted into private key. All you have to do is, to convert this string into 256-bits value and check if it is lower than the N.

But is it suggested to generate private key this way? Actually no! It is popular saying that human is the worst random generator. If we use custom strings or numbers like this, it may be possible that someone else uses the exact same string which may result into compromise of private key. So better be safe than sorry and only rely on random generators to generate private key.

But again another problem arises. Most of the generators such as Math library of Javascript (Math.random() function) use fixed patterns to generate random number. So using such generators will generate more miseries than keys. :D

So what is the ultimate solution? The best way is to use the keys generated by wallets but if you want to independently dive into the quest, use secure generators like this one: strong pseudorandom generator (https://developer.mozilla.org/en-US/docs/Web/API/Crypto/getRandomValues).

Enough said on private keys, let's go to bitaddress.org and generate an address. First we will create address on bitaddress.org and then try to create the same through our own code to learn the mathematics behind key generation.

Here is the key pair I generated. You may find that there are more than one format for both public key and private key. Let's discuss about them in brief before jumping to the coding part:

https://webtricks.website/image/bitcoinKeys.png

1. Public Address

This is the P2PKH format of bitcoin address. It is widely used for sending/receiving bitcoins. Public Key once generated through Elliptic Curve cryptography is then hashed using sha-256 and ripemd-160 algorithm and later checksum is attached in the end of hash which forms public address. We will try to achieve that later in this thread with real code.

2. WIF Private Key

WIF or Wallet Import Format is the format of private key in which wallets such as Electrum import private key. If you paste the bare hex of private key then Electrum won't open the wallet. You have to convert private key into WIF format to use it in wallets. We will write code to convert private key into WIF too.

3. Uncompressed Public Key

Ok! So I haven't discussed so far how public key is generated. The process is actually complex. We take a special generator point defined as G by SECG which is located on secp256k1 curve i.e. one of the elliptic curve. Then we multiply this generator point with private key. The resulting multiplication will give us two coordinates, one is X and the other is Y. Uncompressed Public Key is nothing but : 04 + X + Y. So first two numbers of public key are 04 which signifies that key is uncompressed. Next 64 characters (32 bytes since every 2 characters of hex make 1 byte) are X coordinate and last 64 characters (32 bytes) are Y coordinate. Total length of uncompressed public key is 130 or 65 bytes.

4. Compressed Public Key

Since, it is possible to find Y coordinate if X coordinate is given. So we generally drop the Y coordinate from our public key. Hence, last 64 characters are removed. As a result, compressed public key is made up of 66 characters (32 bytes). First two characters can be either 02 or 03 (instead of 04) and the next 64 characters (32 bytes) will be X coordinate. If the value of Y coordinate is even then 02 is put. If the value of Y coordinate is odd then 03 is put. In the above photo, the value of Y-coordinate was odd so we have 03 in our key.

5. Private Key Hexadecimal Form

As we discussed earlier the private key must be 256-bits or 32 bytes (8 bits = 1 byte) which is when converted into hexadecimal form is of 64 characters. So you can convert any value into hex and it will be of 64 characters. This is very handy for our bitcoin code because we will use hex form of private key to start generating key pair. So as I was saying earlier that we can even use strings like "I am a string to generate private key" to generate private key, so here is the secret. We will first convert such strings into hex and then use 64 characters of hex to generate key pair.

6. Private Key Base64 Form

Not very popular format of private key. But we can even encode/decode our private key into Base64 using native conversion.

Enough for the head start. Now let's dive straight into code and generate the above key.

As I am fan of Javascript (because I think it is the easiest programming language and can be used in full-stack development), I will be using JS in Node.JS environment for this guide. But if you are comfortable with other language then you can easily interpret my JS code into your code. At last, if you aren't comfortable with coding at all then leave that, just read the text and pictures below and I promise you will have the best idea on how keys are generated.

Before starting let's prepare the setup. First step is to create a folder. Inside folder create a file with .js extension. File name can be anything like index.js or app.js.
Next step is to download node.js on your computer. It is very easy to download node.js, it is similar to downloading any other computer software. Next step is to download some code editor, I suggest Visual Studio Code (easy to use IDE).

Once the above steps are done, open the folder in Visual Studio Code and head to your terminal. There is inbuilt terminal in Visual Studio Code, you can use that too. If not, you can use native terminal of Mac or Windows but make sure you have opened the folder in terminal. Once folder is opened in both Visual Studio Code and terminal, run the following commands in terminal to install 2 dependencies for the project:

Code:

npm init -y
npm i ripemd160 --save
npm i bs58 --save

We need two hashing and one encoding functions in our code namely sha256, ripemd160 and base58 apart from elliptic curve cryptography. sha256 is already present in native crypto library of nodejs. We can either code other two on our own or just import them. For the simplicity of this guide, we installed ripemd160 and bs58 npm packages above and will use these in our code. I have verified the source code of both packages and it's completely safe to use these in code.

Now let's start the real fun. Open your file and start with the code. The code is in chronological order. The Step 1 code will go at the top of file and step 2 code will start where step one code ends and so on:

Step 1. Creating hashing functions

Code:

const crypto = require('crypto');
const RIPEMD160 = require('ripemd160');
const BS58 = require('bs58');

const sha256 = input => crypto.createHash('sha256').update(input).digest();

const ripemd160 = input => new RIPEMD160().update(input).digest();

const bs58 = input => BS58.encode(input);

Ok! So in first three lines of code, we have imported the code of all three hashing and encoding functions in our file. Next, we created functions for these. It is not mandatory to create functions but in that case we have to write whole code again and again whenever we need to hash something. For example, if we don't write these three functions then every time we have to create sha256 hash of something we have to write crypto.createHash('sha256').update(something).digest() but with above code, we just have to write sha256(something) from next time. Cool? Let's move forward.

Step 2. Creating Elliptic Curve Function

Code:

const generateECPoints = privateKey => {

    const Pcurve = BigInt('0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F');

    const Gx = BigInt('55066263022277343669578718895168534326250603453777594175500187360389116729240');
    const Gy = BigInt('32670510020758816978083085130507043184471273380659243275938904335757337482424');

    const G = [Gx, Gy];

    const modInverse = (a, n) => {

        a = (a % n + n) % n

        const dArray = [];
        let b = n;

        while(b) {
        [a, b] = [b, a % b];
        dArray.push({a, b});
        }

        if (a !== BigInt(1)) {
        return null;
        }

        let x = BigInt(1);
        let y = BigInt(0);

        for(let i = dArray.length - 2; i >= 0; --i) {
        [x, y] = [y,  x - y * BigInt(dArray[i].a / dArray[i].b)];
        }

        return (y % n + n) % n;
    }

    const modOf = (a,b) => {
        const r = ((a % b) + b)% b;
        return r;
    }

    const ECAdd = (a,b) => {
        const lamAdd = modOf((b[1] - a[1]) * BigInt(modInverse(b[0] - a[0], Pcurve)), Pcurve);
        const x = modOf((lamAdd*lamAdd - a[0] - b[0]), Pcurve);
        const y = modOf((lamAdd*(a[0] - x) - a[1]), Pcurve);
        return [x, y];
    }

    const ECDouble = a => {
        const lamda = modOf(((BigInt(3)*a[0]*a[0])*(modInverse(BigInt(2)*a[1], Pcurve))), Pcurve);
        const x = modOf((lamda*lamda - BigInt(2)*a[0]), Pcurve);
        const y = modOf((lamda*(a[0] - x) - a[1]), Pcurve);
        return [x, y];
    };

    const ECMultiply = (genPoint, pvtKey) => {
        const scalarBinary = BigInt('0x'+pvtKey).toString(2);
        let GP = genPoint;

        for (let i=1; i < scalarBinary.length; i++) {
            GP = ECDouble(GP)
            if (scalarBinary[i] === '1') {
                GP = ECAdd(GP, genPoint);
            }
        }
        return GP;
    }
    
    return ECMultiply(G, privateKey);
}

The above code is my version of Elliptic Curve Multiplication. This maybe only pure Javascript coding of elliptic curve you will find on the entire internet. I think it would be inappropriate to explain the whole above code in this thread as the main motive of this thread is to generate key pair. So for now use the above code as it is. I will create separate thread for Elliptic Curve Cryptography after 3-4 days and explain the same above code in that thread.

Step 3. Generating X and Y coordinates of Public Key from above function and Private Key

Code:

const privateKey = "6EBD5FAB742ED0734B37C63BD2A3CE8797FE4AC63C9A99781F8BEDDF6307094E";
const publicKey = generateECPoints(privateKey);

In this step we have taken the hex value of private key (5th item from the image) and put it in generateECPoints function as created in Step 2. This will give us X and Y coordinates of Public Key which will look like this:
[26552980488606060638326679080566574626825610331305555186819497546906082384636n, 106820354128014061768597493909158935631153585355120117243602895828064095418195n]

You may notice n at the last of each coordinate. This n means we are dealing with extra large numbers here, known as Big Integers in Javascript. Also you may notice that these coordinates are not matching the X and Y in the image above. Well, we have generated numbers for now. We have to convert these into hexadecimals to get uncompressed key and compressed key. Let's do that in next step.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on February 04, 2020, 05:06:05 PM

Step 4. Creating Compressed and Uncompressed Public Key

Code:

const checkKey = key => key.length < 64 ? '0'.repeat(64 - key.length) : key;

const publicKeyX = checkKey(publicKey[0].toString(16));
const publicKeyY = checkKey(publicKey[1].toString(16));

const uncompressedKey = '04'+publicKeyX+publicKeyY;

let compressedKey;
if (publicKey[1]%BigInt(2)===BigInt(1)) {
  compressedKey = '03'+publicKeyX;
} else {
  compressedKey = '02'+publicKeyX;
}

Bingo! We have achieved the first target. We have created uncompressed and compressed public key. In the code above, we have first of all created checkKey function. This function is doing an interesting thing. It may be possible that while converting X and Y coordinates from number to hexadecimal that the resultant length of X and Y is not 64. But as we discussed previously that the length of uncompressed key is 130 where first two characters are 04 then 64 characters of X and then 64 of Y. So it fill the void, we are adding zeros if length is lower than 64. For example, if the length of X is 63 characters, we will add one 0 to make it 64.

Then we defined hexadecimal value of X coordinate as publicKeyX and Y as publicKeyY. You may see we using toString(16) in second and third line. This code is converting number to hex and then overall wrapper of checkkey is checking if the length is lower than 64 then add 0, if not then return same key.

Then we defined uncompressed key as uncompressedKey and then compressed key as 03+X if Y is odd and 02+X if Y is even.

Step 5. Generating P2PKH Key

Before starting with code let's discuss the process of generating P2PKH key. It is to notice that uncompressed and compressed key we generated in step 4 was not Bitcoin specific. There are several other services like Gmail or Facebook using Elliptic Curve cryptography to create public/private keys. However, this very step is where we will convert our public key into Bitcoin-specific format i.e. P2PKH. Following is the pictorial representation of the process, yes the artist is back :D

https://webtricks.website/image/keyGeneration.png

So we start with uncompressed key as generated in step 4 (we can also start with compressed key which will generate different P2PKH address but can be used interchangeably and belongs to same private key). Next we perform sha256 on the uncompressed key. Then ripemd160 hashing on the previous. Then we add 00 in front of previous hash. This is our 21-bytes of binary address. To generate next 4-bytes of binary address. We have to perform double sha256 hashing on first 21 bytes. Take the first 4 bytes of resulting hash i.e. first eight characters of the resulting hash and add it in the end of 21 bytes. Finally we get 25-bytes Binary address and we have to convert this into Base58 code. Now let's see the final code.

Code:

const keyHex = Buffer.from(uncompressedKey, 'hex');
const ripedHashedKey = ripemd160(sha256(keyHex));
const mainRipeKeyString = '00'+ripedHashedKey.toString('hex');
const mainRipeKey = Buffer.from(mainRipeKeyString, 'hex');
const doubleHashedKey = sha256(sha256(mainRipeKey)).toString('hex');
const checkSum = doubleHashedKey.substr(0, 8);
const binaryAddress = Buffer.from(mainRipeKeyString+checkSum, 'hex');
const publicAddress = bs58(binaryAddress);

The above code is nothing but the same 8 steps I detailed in picture above. Bingo! We have successfully generated our Bitcoin Address. Now let's move to final step and generate our WIF private key from hexadecimal of private key.

Step 6. Generating WIF from Private Key

Similar to the previous approach, let's discuss the process before actually moving to the code. Generating WIF from private key is actually simpler than previous step. Converting raw hex of private key into WIF actually has many benefit. First it is smaller and simpler than raw hex. Second it has inbuilt-checksum to verify that private key is valid. Let's see the pictorial representation from artist first:

https://webtricks.website/image/wifGeneration.png

First step is simple, we are taking hexadecimal form of private key and adding 80 in front of it. Note that all these addition we are making throughout code isn't actually numbers. They are hex codes, for example, 80 here when converted to decimal form is 128. Ok next, we are performing double rounds of sha256 hashing. Then we take first 4 bytes of the resultant hex and add them at the end of extended hex of private key. Finally we perform Base58 encoding on the result and we get our WIF key. Code time:

Code:

const pvtKeyExtended = "80"+privateKey;
const extended = Buffer.from(pvtKeyExtended, 'hex');
const hashedExtended = sha256(sha256(extended)).toString('hex');
const checksum = hashedExtended.substr(0, 8);
const finalHex = pvtKeyExtended+checksum;
const WIF = bs58(Buffer.from(finalHex, 'hex'));

Nothing special in code this time too. We are simply performing all six steps as mentioned in picture above. If you have any doubt regarding any code, you can ask in thread or PM me.

Good work! We have finally completed the process and generated our Bitcoin Address along with WIF Key. Great, now let's test the code next.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on February 04, 2020, 05:06:18 PM

TESTING

Code:

console.log(`This is Bitcoin Address: ${publicAddress}
This is WIF Key: ${WIF}
This is Uncompressed Public Key: ${uncompressedKey}
This is compressed Public Key: ${compressedKey}
Thisi is hexadecimal of Private Key: ${privateKey}`);

After writing above code in file, save the file and open terminal. Now run the following command in terminal. Make sure, folder is opened in terminal:

node index.js (file name can be different for you)

You will get address, WIF, public keys, private key in terminal and these will match bitaddress generated keys. You can try different private key. Just change the private key in Step 3 and you are good to go.

But let's not forget the fact that this thread is still for learning purpose. Always use the keys generated by wallets like Electrum and MyCelium, unless you are completely sure what are you doing.

Hope you liked this guide. Do let me know if you still get any doubts, I will address them.

For full code in order, visit: https://webtricks.website/keyGeneration.html

Watch code in action, visit: https://key-generation-by-webby.herokuapp.com/

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: BITCOIN4X on February 04, 2020, 05:14:26 PM

A good enough thread to learn in detail about bitcoin addresses. But I just want to tell you that I didnt like mathematics from school until now, because it only makes me dizzy and freezes my mind. :D
But on this occasion I will try to learn a little from the details you describe, hopefully I can understand it even if only a little.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: JeromeTash on February 04, 2020, 07:36:27 PM

Hi @webtricks, thanks for the detailed topic ;)
If i had 10 sMerits, i would send them all your way. Reading this along with the couple of videos i downloaded a few days ago will help me have a good understanding of how addresses are generated.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: hatshepsut93 on February 04, 2020, 09:08:53 PM

Nice guide, I'm a JS developer myself and I love how you made those ECC functions from scratch, very educating!

Quote from: webtricks on February 04, 2020, 05:05:40 PM

Code:

const convertPvtKey = pvtKey => {
        const hexKey = '0x'+pvtKey;
        const decimalKey = BigInt(hexKey).toString(10);
        return BigInt(decimalKey);
    }

Is this necessary? What's the point of converting a BigInt to decimal string only to convert it back to BigInt? In Javascript all numbers are always in base 10, so BigInt(hexKey) and BigInt(decimalKey) are already the same. For example:

Code:

console.log(BigInt("0xff") === 255n) //true

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: seoincorporation on February 04, 2020, 09:28:01 PM

hey, this is a great thread webtricks. The process could look complex, but once you do it the first time the next ones are an easy task. Would be nice if now you can explain to us the Math behind the brain wallets. I have seen software to make from brainwallets bitcoin addys, but i would like to understand how that process works.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: LoyceV on February 04, 2020, 09:50:56 PM

This is far more impressive than I expected on the Beginners board! That must have been a lot of work, well done!

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: pooya87 on February 05, 2020, 05:16:03 AM

you did a good job again. just some thoughts:

Quote from: webtricks on February 04, 2020, 05:05:40 PM

Condition one, it must be of 256-bits.

this is misleading.
for example "1" is a valid private key and it is only 1 bit. don't confuse the padding done for encoding such as this: KwDiBf89QgGbjEhKnhXJuH7LrciVrZi3qYjgd9M7rFU73sVHnoWn with the value being 256-bit.
the only condition that a key has to satisfy is to be bigger than zero (since 0.G is not defined) and smaller than curve's order (ie. N).

Quote

1. Public Address

is original work of Satoshi

is it? i think the "original" design was using public keys (that is P2PK scripts) then using hash of public keys (that is P2PKH scripts) were proposed.
for instance if you check blocks 1, 2,... you can see they all have a P2PK output.

Quote

3. Uncompressed Public Key

04 + X + Y. So first two numbers of public key are 04 which signifies that key is uncompressed. Next 64 characters are X coordinate and last 64 characters are Y coordinate. Total length of uncompressed public key is 130.

it might be best if you talk only in terms of "bytes" instead of "hex chars". that means 04 followed by 32 byte X followed by 32 byte Y that makes the length 65 bytes. specially since you are going to explain in code and in code it is best (and also faster) to work with bytes not hex characters.

Quote

We need three hashing functions in our code namely sha256, ripemd160 and base58 apart from elliptic curve cryptography.

that is 2 hash functions, 1 encoding and 1 ECC :P

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on February 05, 2020, 06:25:25 AM

Quote from: hatshepsut93 on February 04, 2020, 09:08:53 PM

Nice guide, I'm a JS developer myself and I love how you made those ECC functions from scratch, very educating!

Quote from: webtricks on February 04, 2020, 05:05:40 PM

Code:

const convertPvtKey = pvtKey => {
        const hexKey = '0x'+pvtKey;
        const decimalKey = BigInt(hexKey).toString(10);
        return BigInt(decimalKey);
    }

Thanks for pointing out. Actually I created convertPvtKey function for testing purpose but forgot to remove it from final code. Now I have removed it and made necessary adjustment in ECMultiply function too. :)

Quote from: seoincorporation on February 04, 2020, 09:28:01 PM

OK! I will look into that and will create a thread if possible.

Quote from: pooya87 on February 05, 2020, 05:16:03 AM

~snipy~

Thanks for your additions once again. I made the necessary amendments in OP this time.

Quote from: pooya87 on February 05, 2020, 05:16:03 AM

Quote from: webtricks on February 04, 2020, 05:05:40 PM

We need three hashing functions in our code namely sha256, ripemd160 and base58 apart from elliptic curve cryptography.

that is 2 hash functions, 1 encoding and 1 ECC :P

Correct! Changed and updated.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: pooya87 on February 05, 2020, 07:19:33 AM

Code:

        for (let i=1; i < scalarBinary.length; i++) {
            GP = ECDouble(GP)
            if (scalarBinary[i] === '1') {
                GP = ECAdd(GP, genPoint);
            }
        }

just out of curiosity is there any particular reason why you chose decreasing index for your point multiplication using double-and-add method? (double first then add)

i am not familiar with Javascript but isn't "i" supposed to be index? then why start from 1 instead of 0.
could you test your code with the following private key to see you get the correct public key:

Code:

private key hex: eebd5fab742ed0734b37c63bd2a3ce8797fe4ac63c9a99781f8beddf6307094f
expected public key hex: 04e4706c62ee3c81fa9074a24479cd1f00c26babe97d64def3fb3d519fab1144f6955c75d5845b4966e08e308bd07440032b1ee35ad3259ce58e06c6072ee278ec

(i flipped the first and last bit of your test key)

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on February 05, 2020, 09:12:38 AM

Quote from: pooya87 on February 05, 2020, 07:19:33 AM

Code:

        for (let i=1; i < scalarBinary.length; i++) {
            GP = ECDouble(GP)
            if (scalarBinary[i] === '1') {
                GP = ECAdd(GP, genPoint);
            }
        }

I will create detailed thread on this code and elliptic curve in 3-4 days, most probably on Sunday. For the mean time, you can visit here, my approach is similar to first and third answer in this thread: https://bitcoin.stackexchange.com/questions/25024/how-do-you-get-a-bitcoin-public-key-from-a-private-key

Quote from: pooya87 on February 05, 2020, 07:19:33 AM

could you test your code with the following private key to see you get the correct public key:

Code:

private key hex: eebd5fab742ed0734b37c63bd2a3ce8797fe4ac63c9a99781f8beddf6307094f
expected public key hex: 04e4706c62ee3c81fa9074a24479cd1f00c26babe97d64def3fb3d519fab1144f6955c75d5845b4966e08e308bd07440032b1ee35ad3259ce58e06c6072ee278ec

(i flipped the first and last bit of your test key)

I have deployed my code here:
https://key-generation-by-webby.herokuapp.com/ (It may take upto 10-15 seconds for this page to open because heroku sleeps server after 30 minutes of inactivity for free apps)

You can inspect the code and will find that pure Elliptic Curve code as I written above is generating public key from Private Key in front-end. Only P2PKH is being created in back-end because it is dependent on two npm packages. But only uncompressed public key is going in back-end to generate P2PKH, private key is not leaving the browser. It will work for the hex string of every private key. The key you provided is generating right public key.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: Pmalek on February 05, 2020, 09:27:39 AM

This is one of the best threads I have seen in a while. Thank you for taking the time to write such a detailed overview. This deserves to be shared and translated in multiple languages so that it reaches as many people as possible. When I have some more time, I will try to do my part in sharing it. Excellent work!

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: zasad@ on February 05, 2020, 11:21:10 AM

Thank you.
Russian translate
https://bitcointalk.org/index.php?topic=5223339

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: pooya87 on February 05, 2020, 01:17:54 PM

Quote from: webtricks on February 05, 2020, 09:12:38 AM

i do know the mechanics of elliptic curve cryptography, my curiosity was because i usually see implementations go from least significant bit up so the code is different (check bit > if_add > double instead of double > check bit > if_add)

Quote

yeah, it works fine. so i guess I can't read JavaScript :P

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: sujonali1819 on February 05, 2020, 02:07:51 PM

It’s a really heard job done by webtrics Since I have not much knowledge about Technical things, so I need more time to understand this ;D I will read more this thread to understand how actually it works. It's really a good job buddy. Keep it up and go ahead.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: hatshepsut93 on February 05, 2020, 02:57:57 PM

Quote from: webtricks on February 04, 2020, 05:05:40 PM

So what is the ultimate solution? The best way is to use the keys generated by wallets but if you want to independently dive into the quest, use secure generators like randomBytes npm module in Node.js.

randomBytes npm module is kinda useless in node, since it just calls node's own crypto module, so you can bypass that module and call it directly - https://nodejs.org/api/crypto.html#crypto_crypto_randombytes_size_callback

And browsers are also equipped with strong pseudorandom generator (https://developer.mozilla.org/en-US/docs/Web/API/Crypto/getRandomValues)- it is used in production by browser-based wallets like MEW and MetaMask.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: CucakRowo on February 05, 2020, 03:40:42 PM

Thank you for posting this extraordinary thread. I'm sure this thread consume your time a lots. You are cool. Once again, thank you.
(Finally, I have a nutritional thread to read before going to bed).

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: akirasendo17 on February 05, 2020, 10:14:14 PM

very impressive, the conversion of the bitcoin address is like conversion of ip v6, but more complex, thank you for the information,

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: Wexnident on February 08, 2020, 11:08:25 AM

Great post! Pretty nice how you both used codes and pictures to send the full message across to your viewers. Currently studying Fullstack javascript so I may try and read on about this sometime later after I finish studying it. Might turn out to be a good reference in terms of studying it.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: Vadi2323 on February 09, 2020, 09:12:35 AM

I use the words from that post (https://bitcointalk.org/index.php?topic=5223339.msg53777345#msg53777345) in Russian "Bitcoin turned 10 years old, and they all write instructions on how addresses are generated and even manage to get lost in terminology. For whom is this article? What is new in this information that the sectarians merited it together? How many more years does the community intend to chew on the ABC book?"

Quote from: A-Bolt on February 05, 2020, 11:34:52 AM

It is unfortunate that the technically illiterate article has earned so many Merits in the English-language part of the forum. Degradation is evident.

Quote from: A-Bolt on February 05, 2020, 12:46:33 PM

...
However, the author’s phrase:

Quote from: webtricks on February 04, 2020, 05:05:40 PM

This is the P2PKH format of public key. It is widely used for sending/receiving bitcoins. There are various rounds of different hashing algorithm involved to generate P2PKH key from hex of public key.

confirms my idea that the author has a terminological mess in his head about addresses and public keys.

Instead of the word address, the author uses the non-existent term P2PKH key, which misleads the reader.

Quote from: zasad@ on February 05, 2020, 11:21:10 AM

Thank you.
Russian translate
https://bitcointalk.org/index.php?topic=5223339

Russian translation

Quote from: LoyceV on February 04, 2020, 09:50:56 PM

This is far more impressive than I expected on the Beginners board! That must have been a lot of work, well done!

https://assets.podomatic.net/ts/3f/dd/d7/chaoscontinuum2/3000x3000-174x174+17+0_12306093.jpg

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: pooya87 on February 09, 2020, 09:49:04 AM

Quote from: Vadi2323 on February 09, 2020, 09:12:35 AM

Bitcoin turned 10 years old, and they all write instructions on how addresses are generated and even manage to get lost in terminology. For whom is this article? What is new in this information that the sectarians merited it together? How many more years does the community intend to chew on the ABC book?

Bitcoin is 11 years old not 10 and it is still Bitcoin that is that old not the newcomers who keep coming along every day! posts like this are giving them a simple look under the hood and if they weren't created here i assure you that most newcomers would never even see it elsewhere even though there are already many better instructions such as Mastering Bitcoin by A.A.

Quote from: A-Bolt on February 05, 2020, 11:34:52 AM

It is unfortunate that the technically illiterate article has earned so many Merits in the English-language part of the forum. Degradation is evident.

it may contain some small mistakes here and there and may not be as well versed as what experts have written but it is far from being "technically illiterate".

Quote from: A-Bolt on February 05, 2020, 12:46:33 PM

...
However, the author’s phrase:

Quote from: webtricks on February 04, 2020, 05:05:40 PM

if we are going to nitpick then we should do it correctly!
first of all the full text that should have been quoted is this:
1) [18J6ai34uzGofUuzbiwhXJzKzdx1efDBqA] Public Address: This is the P2PKH format of public key.
which makes it a lot more accurate. not to mention that the word "address" is already there!

secondly the word is not "address", the correct term is "script" since P2PKH is a script type not an address type, the term "address" is commonly used in its place to simplify it but since it is a nitpicking as i said the nit should be accurate itself!

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on February 09, 2020, 10:16:24 AM

Quote from: Vadi2323 on February 09, 2020, 09:12:35 AM

-snip-

Welcome to the thread. I was waiting for someone from that Russian community to finally come here and write the things rather than being cocky intellectuals in their own board. Google Translate translates Russian perfectly and I have already read everything discussed in Russian thread.

No doubt, whatever discussed among Russian folks is absolutely correct. I even made one edit already after reading reply in Russian board. If you guys have problem with any line or mistyped terminology then you are most welcome to reply here and I will correct the things. I already made 8 edits based on recommendations in the thread.

Now coming to the content of this thread. I completely disagree with the statement that this stuff is some basic bitcoin stuff. Go on and search 'Bitcoin for beginners' on Youtube and find a single video which explains the concept behind creating bitcoin address let alone the coding part. I bet you won't find any.

Secondly I am not some professional Bloomberg or BBC writer who is getting paid in K's for every article. This article contains over 21000 characters and everyone is allowed to make some conceptual mistakes when writing something that long. That's why I am open to edits.

Thirdly, I don't think mistakes highlighted is misguiding the reader at all. Technically yeah, that may be wrong a little bit but my motive was to make this thread accessible to everyone. If I just have to write the textbook terminology then Bitcoin Wiki is far better than writing own custom threads.

Lastly, picking a piece of thread may sound incorrect but read the whole thread and I cleared everything in detail as the thread progresses.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: Pmalek on February 14, 2020, 08:14:32 AM

I translated and posted the translation of your thread into the Croatian local forum. Excellent work once again!
This is the link to my translation:
https://bitcointalk.org/index.php?topic=5225719.0

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: rajasobdar786 on February 24, 2020, 05:37:08 AM

Very Nice post Sir!

Pretty nice how you Have used the codes and pictures to send the full message across to BitcoinTalk viewers.
im a newbie member and i want to write these type of post to give some info to beginners
well thank you for posting such a great informative post

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: johhnyUA on February 26, 2020, 04:25:00 PM

Quote from: webtricks on February 04, 2020, 05:05:40 PM

Public Key is the key that is shared to the sender and the world. Example: 18J6ai34uzGofUuzbiwhXJzKzdx1efDBqA. Whereas Private Key is the key which is used to access the funds received on Public Key.

Please, correct this in your post. If you done your guide to get merits, then you can leave it as is. But if you think, that some JS developer may read it and try to do something using your guide, then you don't have any other possibility except to change it.

18J6ai34uzGofUuzbiwhXJzKzdx1efDBqA is an address (abstract term) which is double hash of public key. (!!!)

For anyone who wrote at least 1 line of code in their life it's obvious that such incorrect information will result in butthurt. You shouldn't misunderstand people who will try to use you guide. Thanks

The later review will appear soon

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on February 26, 2020, 05:35:20 PM

Quote from: johhnyUA on February 26, 2020, 04:25:00 PM

Quote from: webtricks on February 04, 2020, 05:05:40 PM

Please, correct this in your post. If you done your guide to get merits, then you can leave it as is. But if you think, that some JS developer may read it and try to do something using your guide, then you don't have any other possibility except to chenge it.

18J6ai34uzGofUuzbiwhXJzKzdx1efDBqA is an address (abstract term) which is double hash of public key. (!!!)

For anyone who wrote at least 1 line of code in their life it's obvious that such incorrect information will result in butthurt. You shouldn't misunderstand people who will try to use you guide. Thanks

The later review will appear soon

Glad you came by. Thanks for your edits, I made necessary changes in introduction as well as point (1) i.e. the definition of Public Address. Please check and tell me if anything else needed correction. While writing such lengthy guide, it is normal to do such mistakes. As I said earlier, this guide have over 21K characters and I manually typed each line.

PS: I am never looking for merits. If I was really a merit hunter then you would most probably be seeing 2000+ merits on my profile, it won't be difficult for me. However, I don't have such temptations.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: jenskohl on February 28, 2020, 12:17:20 PM

Overall this make me dizzy, "this need for further study" my brain said. First time reading about this on how the address generated from.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on February 28, 2020, 06:31:20 PM

Quote from: jenskohl on February 28, 2020, 12:17:20 PM

Overall this make me dizzy, "this need for further study" my brain said. First time reading about this on how the address generated from.

Yeah! Topic is a little bit excessively detailed. There are surely easy way to do so. For example, you can do what this thread is doing in few lines with Python by importing libraries. But that isn't the purpose of this thread. Rather I tried to go under the hood by writing bare implementation of every code. Right from taking random string, creating private key with it, using elliptic curve cryptography then deriving bitcoin address and WIF. Everything is written from scratch so that non-technical members can actually see how everything really happens.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: johhnyUA on March 12, 2020, 08:39:29 PM

Quote from: webtricks on February 26, 2020, 05:35:20 PM

Yep, now everything is pretty good. I remember that i had some more remarks about your text, and i will try too look into it a bit later, but for now i'm a little busy. But yeah, intro is now looking good.

Quote from: webtricks on February 04, 2020, 05:05:40 PM

Ok! So let's start with the topic. To use Bitcoin, user generally needs two things: Private Key and Bitcoin Address. Bitcoin Address is an identifier which looks like this: 18J6ai34uzGofUuzbiwhXJzKzdx1efDBqA. User have to share it with sender to receive payment. Whereas private key is a key which user have to input in wallet to access the funds received.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: Polar91 on March 30, 2020, 07:19:13 AM

Filipino Translation: https://bitcointalk.org/index.php?topic=5236264

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on July 22, 2020, 08:38:00 PM

Bump!

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: Lordhermes on July 23, 2020, 12:45:11 PM

Wow, this is really a good teachings that requires a big sum for before learning, we got it here free from OP, nice one, you really a life changing person that love inspiring people with secrets behind bitcoin addresses generation, thank you.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: Maus0728 on July 23, 2020, 01:33:20 PM

Quote from: webtricks on July 22, 2020, 08:38:00 PM

Bump!

Thanks for bumping! I am having trouble finding your thread.

You did this program using Java right? Do you have any resources that offers specific function that is used to generate bitcoin addresses using C++ library? Though I quite understand what is the process of address generation under the hood, I think it would be a good experience for me to create similar program that is written using C++.

Thank you so much.

Title: Re: How Bitcoin Addresses are generated? Understand the Math behind Bitcoin
Post by: webtricks on July 24, 2020, 05:24:06 PM

Quote from: Lordhermes on July 23, 2020, 12:45:11 PM

I'm glad you liked it!

Quote from: Maus0728 on July 23, 2020, 01:33:20 PM

Quote from: webtricks on July 22, 2020, 08:38:00 PM

Bump!

I have written code in Javascript and NodeJS (not Java). Yes, there is an extensive and well-maintained Bitcoin Library in C++ namely libbitcoin (https://github.com/libbitcoin/libbitcoin-system). Then of course, you have Bitcoin Core. You can easily create Bitcoin Addresses in both of these. Both got some cool pre-written C++ functions. But if you are interested in writing everything from scratch like I did in OP then I don't think there is any specific resource available in C++. Maybe somebody has written an article on the same which you maybe able to find on Search Engine. :)

Bitcoin Forum

Other => Beginners & Help => Topic started by: webtricks on February 04, 2020, 05:05:40 PM