Add a link to the appendix

bip-0000.mediawiki

@@ -88,7 +88,7 @@ Bob must include the same ''outpoint_hash'' when scanning.
 
 ''' Using all inputs '''
 
-In our simplified example we have been referring to Alice’s transactions as having only one input ''A'', but in reality a Bitcoin transaction can have many inputs. Instead of requiring Alice to pick a particular input and requiring Bob to check each input separately, we can instead require Alice to perform the tweak with the sum of the input public keys<ref name="other_inputs">'''What about inputs without public keys?''' Inputs without public keys can still be spent in the transaction but are simply ignored in the ''Silent Payments'' protocol.</ref>. This significantly reduces Bob's scanning requirement, makes light client support more feasible<ref name="using_all_inputs">'''How does using all inputs help light clients?''' If Alice uses a random input for the tweak, Bob necessarily has to have access to and check all transaction inputs, which requires performing an ECC multiplication per input. If instead Alice performs the tweak with the sum of the input public keys, Bob only needs the summed 32 byte public key per transaction and only does one ECC multiplication per transaction. Bob can then use BIP158 block filters to determine if any of the outputs exist in a block and thus avoids downloading transactions which don't belong to him.</ref>, and protects Alice's privacy in collaborative transaction protocols such as CoinJoin<ref name=""all_inputs_and_coinjoin">'''Why does using all inputs matter for CoinJoin?''' If Alice uses a random input to create the output for Bob, this necessarily reveals to Bob which input Alice has control of. If Alice is paying Bob as part of a CoinJoin, this would reveal which input belongs to her, degrading the anonymity set of the CoinJoin and giving Bob more information about Alice. If instead all inputs are used, Bob has no way of knowing which input(s) belong to Alice. This comes at the cost of increased complexity as the CoinJoin participants now need to coordinate to create the silent payment output and would need to use [https://gist.github.com/RubenSomsen/be7a4760dd4596d06963d67baf140406 Blind-Diffie-Hellman] to prevent the other participants from learning who Alice is paying</ref>.
+In our simplified example we have been referring to Alice’s transactions as having only one input ''A'', but in reality a Bitcoin transaction can have many inputs. Instead of requiring Alice to pick a particular input and requiring Bob to check each input separately, we can instead require Alice to perform the tweak with the sum of the input public keys<ref name="other_inputs">'''What about inputs without public keys?''' Inputs without public keys can still be spent in the transaction but are simply ignored in the ''Silent Payments'' protocol.</ref>. This significantly reduces Bob's scanning requirement, makes light client support more feasible<ref name="using_all_inputs">'''How does using all inputs help light clients?''' If Alice uses a random input for the tweak, Bob necessarily has to have access to and check all transaction inputs, which requires performing an ECC multiplication per input. If instead Alice performs the tweak with the sum of the input public keys, Bob only needs the summed 32 byte public key per transaction and only does one ECC multiplication per transaction. Bob can then use BIP158 block filters to determine if any of the outputs exist in a block and thus avoids downloading transactions which don't belong to him. It is still an open question as to how Bob can source the 32 bytes per transaction in a trustless manner, see [[#appendix-a-light-client-support|Appendix A: Light Client Support]] for more details</ref>, and protects Alice's privacy in collaborative transaction protocols such as CoinJoin<ref name=""all_inputs_and_coinjoin">'''Why does using all inputs matter for CoinJoin?''' If Alice uses a random input to create the output for Bob, this necessarily reveals to Bob which input Alice has control of. If Alice is paying Bob as part of a CoinJoin, this would reveal which input belongs to her, degrading the anonymity set of the CoinJoin and giving Bob more information about Alice. If instead all inputs are used, Bob has no way of knowing which input(s) belong to Alice. This comes at the cost of increased complexity as the CoinJoin participants now need to coordinate to create the silent payment output and would need to use [https://gist.github.com/RubenSomsen/be7a4760dd4596d06963d67baf140406 Blind-Diffie-Hellman] to prevent the other participants from learning who Alice is paying</ref>.
 
 Alice performs the tweak with the sum of her input private keys in the following manner: