Try putting in your two private keys as two very small numbers - say "2" and "5". The resulting private key are either "7" (2+5) or "A" (2*5 - in hex of course). Sure, it then uses elliptic curve multiplication to turn those private keys in to public keys, but the process it uses of multiplying the two private keys is just straight forward arithmetic multiplication.

Try using the numbers

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364140

and

1

as your two private keys.

You will see that One + Two gives you the curve order (

*n*) which is invalid and therefore gives no public key, whereas One x Two gives the FFFF...4140 number above (

*n*-1) which is the highest valid private key and does generate a public key.

You also mentioned that its entirely possible to generate a non-valid private key, can you provide an example on how you would do so since the hex for this key is zero and no library will allow you to do so unless it was not coded correctly?

Any number higher than

*n*-1 is a non-valid private key. It is possible to

*generate* such a key, but I never said it would be possible to

*use* such a key. Some pieces of software will calculate the private key modulo

*n* though, and so turn a non-valid private key in to a valid one. You can try this on the gobittest page by using the private keys

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364140

and

2

The private key generated from One + Two wraps back around and gives the private key "1".

Thank you for the detailed explication, what you said makes sense but what I don't understand is why would multiplying the key I mentioned by 12345 (or 3039 in hex) gives zero? I tried it with a python lib and it gave a different result actually but very similar public address.

The public address produced by gobittest for the zero key is

*049663999D864D6D1A79FFB0C547D19CB5A51123888AD4BDAE5CCEDB61CC3239BA4182C2088B09D 67ADEDF1BDC543B5F336D017017FF8D83E44D75A00A3D6BEE* and the public key produced by the python lib is

*049663999d864d6d1a79ffb0c547d19cb5a51123888ad4bdae5ccedb61cc3239ba004182c2088b0 9d67adedf1bdc543b5f336d017017ff8d83e44d75a00a3d6bee*

If you mean this page on gobittest

https://gobittest.appspot.com/PrivateKey, I entered the uncompressed WIF inside it and it gave me a private key of 9F23FFFFFFFFFFFFFFFFFFFFFFFFFFFFEF4D21CEC75756599124A862727EE62F6E5C. That private key isn't on the curve, so it's technically point at infinity (

I'm not sure if this is correct though). So if you multiply it by any number

you will also get point at infinity (stack exchange), which gobittest just writes as 0.

I dont know that the private key is for 04065f53171dcd7d03a71e93d74394694e6af13aef4030ce9faa3db65d627ecbcfcd75a3048ff8a

0d87bff6ec60d900e86523e3165e5bebc3bbdfc199d3a998063 but its definitely not what you mentioned. So what I'm wondering is why multiplying this by dec 12345 yeild point at infinity on gobittest

[moderator's note: consecutive posts merged]