Edited ch06.asciidoc with Atlas code editor

ch06.asciidoc

@@ -496,7 +496,7 @@ image::images/mbc2_0606.png["Tx_Script_P2PubKeyHash_2"]
 [[digital_sigs]]
 === Digital Signatures (ECDSA)
 
-((("transactions", "digital signatures", id="Tdigsig06")))So far, we have not delved into any detail about "digital signatures." In this section we look at how digital signatures work and how they can present proof of ownership of a private key without revealing that private key.
+((("transactions", "digital signatures and", id="Tdigsig06")))So far, we have not delved into any detail about "digital signatures." In this section we look at how digital signatures work and how they can present proof of ownership of a private key without revealing that private key.
 
 ((("digital signatures", "algorithm used")))((("Elliptic Curve Digital Signature Algorithm (ECDSA)")))The digital signature algorithm used in bitcoin is the _Elliptic Curve Digital Signature Algorithm_, or _ECDSA_. ECDSA is the algorithm used for digital signatures based on elliptic curve private/public key pairs, as described in <<elliptic_curve>>. ECDSA is used by the script functions +OP_CHECKSIG+, +OP_CHECKSIGVERIFY+, +OP_CHECKMULTISIG+, and +OP_CHECKMULTISIGVERIFY+. Any time you see those in a locking script, the unlocking script must contain an ECDSA signature.
 
@@ -519,7 +519,7 @@ _Source: https://en.wikipedia.org/wiki/Digital_signature_
 
 ==== How Digital Signatures Work
 
-((("digital signatures", "how they work")))((("transactions", "digital signatures", "operation of")))A digital signature is a _mathematical scheme_ that consists of two parts. The first part is an algorithm for creating a signature, using a private key (the signing key), from a message (the transaction). The second part is an algorithm that allows anyone to verify the signature, given also the message and a public key.
+((("digital signatures", "how they work")))A digital signature is a _mathematical scheme_ that consists of two parts. The first part is an algorithm for creating a signature, using a private key (the signing key), from a message (the transaction). The second part is an algorithm that allows anyone to verify the signature, given also the message and a public key.
 
 ===== Creating a digital signature
 
@@ -570,14 +570,14 @@ See if you can decode Alice's serialized (DER-encoded) signature using this list
 
 ==== Verifying the Signature
 
-((("digital signatures", "verifying")))((("transactions", "digital signatures", "verifying")))To verify the signature, one must have the signature (+R+ and +S+), the serialized transaction, and the public key (that corresponds to the private key used to create the signature). Essentially, verification of a signature means "Only the owner of the private key that generated this public key could have produced this signature on this transaction."
+((("digital signatures", "verifying")))To verify the signature, one must have the signature (+R+ and +S+), the serialized transaction, and the public key (that corresponds to the private key used to create the signature). Essentially, verification of a signature means "Only the owner of the private key that generated this public key could have produced this signature on this transaction."
 
 The signature verification algorithm takes the message (a hash of the transaction or parts of it), the signer's public key and the signature (+R+ and +S+ values) and returns TRUE if the signature is valid for this message and public key.
 
 [[sighash_types]]
 ==== Signature Hash Types (SIGHASH)
 
-((("transactions", "digital signatures", "signature hash types")))((("digital signatures", "signature hash types")))((("commitment")))Digital signatures are applied to messages, which in the case of bitcoin, are the transactions themselves. The signature implies a _commitment_ by the signer to specific transaction data. In the simplest form, the signature applies to the entire transaction, thereby committing all the inputs, outputs, and other transaction fields. But, a signature can commit to only a subset of the data in a transaction, which is useful for a number of scenarios as we will see in this section.
+((("digital signatures", "signature hash types")))((("commitment")))Digital signatures are applied to messages, which in the case of bitcoin, are the transactions themselves. The signature implies a _commitment_ by the signer to specific transaction data. In the simplest form, the signature applies to the entire transaction, thereby committing all the inputs, outputs, and other transaction fields. But, a signature can commit to only a subset of the data in a transaction, which is useful for a number of scenarios as we will see in this section.
 
 ((("SIGHASH flags")))Bitcoin signatures have a way of indicating which part of a transaction's data is included in the hash signed by the private key, through the use of a +SIGHASH+ flag. The +SIGHASH+ flag is a single byte that is appended to the signature. Every signature has a +SIGHASH+ flag and the flag can be different from to input to input. A transaction with three signed inputs may have three signatures with different +SIGHASH+ flags, each signature signing (committing) different parts of the transaction.
 
@@ -632,7 +632,7 @@ You will not see +SIGHASH+ flags presented as an option in a user's wallet appli
 [[ecdsa_math]]
 ==== ECDSA Math
 
-((("transactions", "digital signatures", "ECDSA math")))((("Elliptic Curve Digital Signature Algorithm (ECDSA)")))As mentioned previously, signatures are created by a mathematical function F~sig~, that produces a signature composed of two values _R_ and _S_. In this section we look at the function F~sig~ in more detail.
+((("Elliptic Curve Digital Signature Algorithm (ECDSA)")))As mentioned previously, signatures are created by a mathematical function F~sig~, that produces a signature composed of two values _R_ and _S_. In this section we look at the function F~sig~ in more detail.
 
 ((("public and private keys", "key pairs", "ephemeral")))The signature algorithm first generates an _ephemeral_ (temporary) private public key pair. This temporary key pair is used in the calculation of the _R_ and _S_ values, after a transformation involving the signing private key and the transaction hash.
 
@@ -672,7 +672,7 @@ The math of ECDSA is complex and difficult to understand. There are a number of
 
 ==== The Importance of Randomness in Signatures
 
-((("transactions", "digital signatures", "randomness in")))((("digital signatures", "randomness in")))As we saw in <<ecdsa_math>>, the signature generation algorithm uses a random key _k_, as the basis for an ephemeral private/public key pair. The value of _k_ is not important, _as long as it is random_. Specifically, if the same value _k_ is used to produce two signatures on different messages (transactions), then the signing private key can be calculated by anyone. Re-use of the same value for _k_ in a signature algorithm leads to exposure of the private key!
+((("digital signatures", "randomness in")))As we saw in <<ecdsa_math>>, the signature generation algorithm uses a random key _k_, as the basis for an ephemeral private/public key pair. The value of _k_ is not important, _as long as it is random_. Specifically, if the same value _k_ is used to produce two signatures on different messages (transactions), then the signing private key can be calculated by anyone. Re-use of the same value for _k_ in a signature algorithm leads to exposure of the private key!
 
 [WARNING]
 ====