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I'm trying to create Bob's first receive (ephemeral) address according to the BIP 47 spec after the Notification Transaction has taken place, which I believe to be:

141fi7TY3h936vRUKh1qfUZr8rSBuYbVBK

according to these test vectors. I have been unable to calculate the correct ephemeral public key (B') corresponding to this address via:

B' = B + sG

or the correct private key (b') for the ephemeral address via:

b' = b + s

The variables I have come up with so far for this first address include:

// Alice selects the 0th private key derived from her payment code:
a = 8d6a8ecd8ee5e0042ad0cb56e3a971c760b5145c3917a8e7beaf0ed92d7a520c

// Alice selects the next unused public key derived from Bob's payment code, 
// starting from zero:
B = 024ce8e3b04ea205ff49f529950616c3db615b1e37753858cc60c1ce64d17e2ad8

// Alice calculates a secret point:
S = 03f5bb84706ee366052471e6139e6a9a969d586e5fe6471a9b96c3d8caefe86fef

// Alice calculates a scalar shared secret using the x value of S:
// x value = f5bb84706ee366052471e6139e6a9a969d586e5fe6471a9b96c3d8caefe86fef
// SHA256(x value)
s = d24366e662da47c0cccca4cc2d2d817af54e4d21039c0cc4fc441624efe273f7

// s multiplied by generator point
sG = 0283850c6835576554261fbab5845a099638859528b2725455e6a48e7566415c02

// Alice uses the scalar shared secret to calculate the ephemeral public key 
// used to generate the P2PKH address for this transaction:
B' = 0344b4795e48df097bd87e6cf87a70e4f0c30b2d847b6e34cddde64af10296952d



// Bob's first private key
b = 04448fd1be0c9c13a5ca0b530e464b619dc091b299b98c5cab9978b32b4a1b8b

b' = d687f6b820e6e3d47296b01f3b73ccdc930eded39d559921a7dd8ed81b2c8f82

Are any of these variables incorrect, and if so, how are the correct ones obtained?

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  • how did you come up with S = 03f5bb84706ee366052471e6139e6a9a969d586e5fe6471a9b96c3d8caefe86fef the shared secretes in the test vectors are supposed to be different. which software / lib are u using? Commented Feb 23, 2019 at 16:27
  • Multiplied the point "B" (pub key) times scalar "a" (private key). They are supposed to be different? I'm using Core Bitcoin for iOS.
    – user31364
    Commented Feb 23, 2019 at 16:30

1 Answer 1

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+50

Felix Engelmann and I sat down tonight and we used bx via libbitcoin. We have been able to produce the address from the test vector and exactly your intermediate results

a='8d6a8ecd8ee5e0042ad0cb56e3a971c760b5145c3917a8e7beaf0ed92d7a520c'
B='024ce8e3b04ea205ff49f529950616c3db615b1e37753858cc60c1ce64d17e2ad8'
S=$(bx ec-multiply $B $a)
echo $S
> 03f5bb84706ee366052471e6139e6a9a969d586e5fe6471a9b96c3d8caefe86fef

s=$(bx sha256 'f5bb84706ee366052471e6139e6a9a969d586e5fe6471a9b96c3d8caefe86fef')
echo $s
> d24366e662da47c0cccca4cc2d2d817af54e4d21039c0cc4fc441624efe273f7

sG=$(bx ec-to-public $s)
echo $sG
> 0283850c6835576554261fbab5845a099638859528b2725455e6a48e7566415c02

B_prime=$(bx ec-add $B $s)
echo $B_prime
> 0344b4795e48df097bd87e6cf87a70e4f0c30b2d847b6e34cddde64af10296952d

addr=$(bx ec-to-address -v 0 $B_prime)
echo $addr
> 141fi7TY3h936vRUKh1qfUZr8rSBuYbVBK

Note that our value for B_prime was 0344b4795e48df097bd87e6cf87a70e4f0c30b2d847b6e34cddde64af10296952d as you suggested. Actually encoding it to a Bitcoin address seemed a little bit tricky as without passing -v 0 it would use a testnet address. Maybe you have a similar problem while using Bitcoin core? I don't know the API though for transforming a pub key / ec point to an Adress in Bitcoin core out of my head.

Anyway I think you did everything correctly and you just did a mistake in encoding the P2PKH address.

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    Beautiful! In knowing that my parameters matched yours, I became certain that it was simply that last step in creating the address that was causing me problems. Instead of creating a new key via BTCKey(curvePoint: BPrime), I tried a different initializer via BTCKey(publicKey: BPrime?.data), and it worked!. Gah, I knew it was something ridiculous. Never looked at the initializers because it just seemed straightforward.
    – user31364
    Commented Feb 24, 2019 at 20:35

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