If you have followed my blockchain posts so far, you know how to create bitcoin transactions by assembling transaction inputs and transaction outputs into a transaction data structure and serializing it. However, there is one subtlety that we have ignored so far – what exactly do you sign?

You cannot sign the entire bitcoin transaction, simply because the signature is part of it! So there is a sort of chicken-or-egg problem. Instead, you need to build a transaction without the signature, serialize it, create a hash value, sign this hash value, then add the signature to the transaction and publish this transaction.

This is essentially how signing actually works. However, there are a few details that we still miss. So let us look at the source code of the reference client once more to make sure that we really understand how this works.

As a starting point, remember that there is a script opcode called `OP_CHECKSIG`

that verifies a signature. So let us look at the corresponding method which we find in `script/interpreter.cpp`

. When this opcode is executed, the function `EvalScript`

delegates to the method `TransactionSignatureChecker::CheckSig`

. This method removes the last byte of the signature script (which is the hash type) and then calls the function `SignatureHash`

. This function receives the following parameters (you might have to trace back a bit starting at `EvalScript`

to verify this):

- the script code of the public key script
- the transaction that is to be signed
- the index of the transaction input within that transaction to which the signature refers
- the hash type
- the amount
- a version number which is zero in our case and indicates whether the segregated witness feature is in effect
- a data structure that serves as a cache

We have not yet talked about the **hash type**. Essentially the hash type controls which parts of a transaction are included in the signature and therefore protected against being changed. The most common case is `SIGHASH_ALL = 1`

, and this is the value for this field that we assume in this post (if you understand this case, it will not be difficult to figure out the other cases as well).

In any case, the function `SignatureHash`

is what we are searching for. It serializes the transaction and creates a hash value which is then passed to the crytographic subroutines to actually verify the signature. This function again delegates the actual work to an instance of the helper class `CTransactionSignatureSerializer`

, more precisely to its method `Serialize`

. This method is in fact not very surprising.

template void Serialize(S &s) const { // Serialize nVersion ::Serialize(s, txTo.nVersion); // Serialize vin unsigned int nInputs = fAnyoneCanPay ? 1 : txTo.vin.size(); ::WriteCompactSize(s, nInputs); for (unsigned int nInput = 0; nInput < nInputs; nInput++) SerializeInput(s, nInput); // Serialize vout unsigned int nOutputs = fHashNone ? 0 : (fHashSingle ? nIn+1 : txTo.vout.size()); ::WriteCompactSize(s, nOutputs); for (unsigned int nOutput = 0; nOutput < nOutputs; nOutput++) SerializeOutput(s, nOutput); // Serialize nLockTime ::Serialize(s, txTo.nLockTime); }

Ignoring the flag fAnyoneCanPay, this method behaves similar to ordinary serialization – first the version number is written, then the number of inputs, followed by the actual inputs, then the number of outputs, the actual outputs and finally the lock time.

The actual difference to an ordinary transaction serialization is hidden in the method `SerializeInput`

.

template void SerializeInput(S &s, unsigned int nInput) const { // In case of SIGHASH_ANYONECANPAY, only the input being signed is serialized if (fAnyoneCanPay) nInput = nIn; // Serialize the prevout ::Serialize(s, txTo.vin[nInput].prevout); // Serialize the script if (nInput != nIn) // Blank out other inputs' signatures ::Serialize(s, CScript()); else SerializeScriptCode(s); // Serialize the nSequence if (nInput != nIn && (fHashSingle || fHashNone)) // let the others update at will ::Serialize(s, (int)0); else ::Serialize(s, txTo.vin[nInput].nSequence); }

Again, this starts out as usual by serializing the reference to the spent transaction output (transaction ID and index). However, we soon find the first difference – if the index of the transaction input to be signed differs from the input that is currently serialized, an empty script is serialized instead of the signature script – which translates into a single byte 0x0 which is the length of the empty script.

The second difference is located in the method `SerializeScriptCode`

. Here, instead of serializing the not yet existing signature, the content of the variable `scriptCode`

is serialized. Going back a bit, we see that this is the public key script of the corresponding transaction output! So basically, this script takes the position of the signature script in this serialization step.

But we are not yet done – let us return to the function `SignatureHash`

and see what it does close to the end.

CTransactionSignatureSerializer txTmp(txTo, scriptCode, nIn, nHashType); // Serialize and hash CHashWriter ss(SER_GETHASH, 0); ss << txTmp << nHashType; return ss.GetHash();

Using the operator <<, we see that the method `Serialize`

that we have just studied is invoked. However, we see that in addition, the hash type – which was stripped off at the beginning – is now added again at the end. All this is routed into a `CHashWriter`

which is defined in `hash.h`

and is essentially a wrapper around a 256 bit hashing routine. This hash is then returned to `TransactionSignatureChecker::CheckSig`

which then tries to verify the signature with that message.

After that tour through the reference client, let us try to verify the signature of a real transaction from the bitcoin network. In the library btc/script.py, I have implemented a function `signatureHash`

which does – for the special case discussed – the same as the function that we have just looked at. Using that function, it is now not difficult to verify a signature, given a transaction input and the corresponding spent output. Here is what we need to do in an ipython session, again assuming that you have downloaded my btc package.

First, we get our sample transaction that we have already used before and the transaction output spent by the first transaction input.

In [1]: import btc.utils In [2]: import btc.txn In [3]: raw = btc.utils.getRawTransaction("ed70b8c66a4b064cfe992a097b3406fa81ff09641fe55a709e4266167ef47891") In [4]: txn = btc.txn.txn() In [5]: txn.deserialize(raw) In [6]: txin = txn.getInputs()[0] In [7]: raw = btc.utils.getRawTransaction(txin.prevTxid) In [8]: prev = btc.txn.txn() In [9]: prev.deserialize(raw) In [10]: spentTxo = prev.getOutputs()[txin.getVout()]

Next, we determine the signature hash and interpret it as a big endian encoded integer.

In [11]: h = int.from_bytes(btc.script.signatureHash(txn, 0, spentTxo), "big")

Next we need to determine the other ingredients of the signature – the r and s values.

In [12]: r = txin.getScriptSig().getSignatureR() In [13]: s = txin.getScriptSig().getSignatureS()

Now we need the ECDSA cryptography library. We get the SECP256K1 curve and its parameters from there and determine the point on the curve that corresponds to the public key.

In [14]: import ecdsa In [15]: curve = ecdsa.curves.SECP256k1 In [16]: G = curve.generator In [17]: p = curve.curve.p() In [18]: txin.getScriptSig().getScriptType() Out[18]: 'P2PKH' In [19]: pubKey = txin.getScriptSig().getPubKeyHex() In [20]: pubKey Out[20]: '038c2d1cbe4d731c69e67d16c52682e01cb70b046ead63e90bf793f52f541dafbd'

We see that the first byte of the public key is 0x03. If you remember what we have learned about the public key encoding, this means that y is odd. We can therefore determine the x and y coordinate as follows.

In [21]: x = int.from_bytes(bytes.fromhex(pubKey[2:66]), 'big') In [22]: y = ecdsa.numbertheory.square_root_mod_prime((x**3 +7) % p , p) In [23]: y Out[23]: 91238655223056717466178782248030327689649326505413694215614940048183357985838 In [24]: y = (p - y) % p In [25]: y Out[25]: 24553434014259477957392202760657580163620658160226869823842643959725476685825 In [26]: assert(curve.curve.contains_point(x, y))

Now we are almost done.

In [27]: Q = ecdsa.ellipticcurve.Point(curve.curve, x, y) In [28]: pKey = ecdsa.ecdsa.Public_key(G, Q) In [29]: signature = ecdsa.ecdsa.Signature(r,s) In [30]: pKey.verifies(h, signature) Out[30]: True

So our signature is valid, as expected – after all this is a real transaction from the bitcoin network. The full source code for this exercise is also contained in btc/script.py in the function `verifySignature`

.

Of course we could now revert this process – given a transaction, we could use the function `signatureHash`

to create a hash value which we then sign using the ECDSA library. This now puts us in a position to actually create a transaction that we can then push into the bitcoin network. Now, this is clearly something you do not want to try in the real bitcoin network. Therefore I will show you in my next post how you can set up a small test network at home to be able to play with this without the risk of losing actual bitcoins.