I managed to write the below code which will create public and private keys

Private Key

$input = "satoshinakamoto";
$sha256 = hash("sha256", ($input));
echo "<strong>Private Key: </strong>".$sha256."<br/>";

Public Key

    $step1 = hexStringToByteString("0450863AD64A87AE8A2FE83C1AF1A8403CB53F53E486D8511DAD8A04887E5B23522CD470243453A299FA9E77237716103ABC11A1DF38855ED6F2EE187E9C582BA6");
    echo "<p><strong>Step 1:</strong> ".$step1."</p>";
    $step2 = hash("sha256", $step1);
    echo "<p><strong>Step 2: </strong>".$step2."</p>";
    $step3 = hash('ripemd160', hexStringToByteString($step2));
    echo "<p><strong>Step 3: </strong>".$step3."</p>";
    $step4 = '00'.$step3;
    echo "<p><strong>Step 4: </strong>".$step4."</p>";
    $step5 = hash("sha256", hexStringToByteString($step4));
    echo "<p><strong>Step 5: </strong>".$step5."</p>";
    $step6 = hash("sha256",hexStringToByteString($step5));
    echo "<p><strong>Step 6: </strong>".$step6."</p>";
    $step7 = substr($step6,0,8);
    echo "<p><strong>Step 7: </strong>".$step7."</p>";
    $step8 = $step4.$step7;
    echo "<p><strong>Step 8: </strong>".$step8."</p>";
    $step9 = bc_hexdec($step8);
    echo "<p><strong>Step 9: </strong>".$step9."</p>";
    $step10 = bc_base58_encode($step9);
    echo "<p><strong>Step 10: </strong>1".$step10."</p>";
    return $step10;

To generate public key I took reference from https://en.bitcoin.it/wiki/Technical_background_of_version_1_Bitcoin_addresses

In that link they provided Step by Step process and I followed the same and if I input from Step 1 in the link then I am able to convert the code to public key but I am not sure how to convert Step 0 to Step 1






Document says

Take the corresponding public key generated with it (65 bytes, 1 byte 0x04, 32 bytes corresponding to X coordinate, 32 bytes corresponding to Y coordinate)

What does that mean? How can I generate this value from Private Key.

Edit 1

This question says https://stackoverflow.com/questions/17672696/generating-bitcoin-address-from-ecdsa-public-key

Joining the Elliptic Public Key and I still don't understand what are they.

migrated from stackoverflow.com Apr 14 '16 at 8:04

This question came from our site for professional and enthusiast programmers.

  • 5
    DO NOT GENERATE PRIVATE KEYS BY HASHING STRINGS. This type of system is known as a brainwallet and it is broken. Any Bitcoins deposited in a wallet generated this way WILL be stolen. – duskwuff Feb 24 '16 at 4:57
  • @duskwuff - I know that, I am just using a string as example but I am looking for algorithm how the wallets are generated. I know about the vulnerabilities of brainwallet. I just need to know the formula for how that X and Y Coordinates are generated. – lock Feb 24 '16 at 6:43

Bitcoin uses point multiplication on the Elliptic Curve secp256k1 to generate a public key from a private key. Basically, this curve has a defined Generator point G, and a method for 'adding' two points together in a way to get a new point (EC Point Addition).

Your private key is just a number, aka a Scalar, so to get your public key you just add the generator point to itself privkey number of times - basically scalar multiplication on the Elliptic curve. At the end, you'll end up with a point on the curve, with an X and Y coordinate, and this point is your public key. Those two coordinates of your point are what is referred to by the document you quoted, using 32 bytes for each coordinate plus a prefix.

The 0x04 prefix used is to denote the fact this is an uncompressed private key. You can also form a compressed version, by just using the X coordinate with either 0x02 or 0x03 prefix, because the Elliptic curve has only 2 values for Y coordinate for each X coordinate (one positive and one negative), so it's trivial to recover the Y coordinate if you know the X coordinate and the sign (based on your choice of prefix).

your priv = 18E14A7B6A307F426A94F8114701E7C8E774E7F9A47E2C2035DB29A206321725
X = priv x 79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798
Y = priv x 483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8


  • 2
    Downvoted. You make it sound like you need to multiply the individual X and Y coordates of the generator with the private key as numbers. This is not correct; you need to perform an elliptic curve multiplication, which requires a repeated geometric construction. – Pieter Wuille Jun 13 '16 at 11:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.