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@ -681,13 +681,13 @@ The math of ECDSA is complex and difficult to understand. There are a number of
This is not just a theoretical possibility. We have seen this issue lead to exposure of private keys in a few different implementations of transaction signing algorithms in bitcoin. People have had funds stolen because of inadvertent re-use of a _k_ value. The most common reason for re-use of a _k_ value is an improperly initialized random-number generator. This is not just a theoretical possibility. We have seen this issue lead to exposure of private keys in a few different implementations of transaction signing algorithms in bitcoin. People have had funds stolen because of inadvertent re-use of a _k_ value. The most common reason for re-use of a _k_ value is an improperly initialized random-number generator.
((("warnings and cautions", "random number generation")))((("deterministic initialization")))To avoid this vulnerability, the industry best practice is to not generate _k_ with a random-number generator seeded with entropy, but instead to use a deterministic-random process seeded with the transaction data itself. That ensures that each transaction produces a different _k_. The industry-standard algorithm for deterministic initialization of _k_ is defined in https://tools.ietf.org/html/rfc6979[RFC 6979] published by the Internet Engineering Task Force. ((("warnings and cautions", "random number generation")))((("deterministic initialization")))To avoid this vulnerability, the industry best practice is to not generate _k_ with a random-number generator seeded with entropy, but instead to use a deterministic-random process seeded with the transaction data itself. That ensures that each transaction produces a different _k_. ((("RFC 6979")))The industry-standard algorithm for deterministic initialization of _k_ is defined in https://tools.ietf.org/html/rfc6979[RFC 6979] published by the Internet Engineering Task Force.
If you are implementing an algorithm to sign transactions in bitcoin, you _must_ use RFC6979 or a similarly deterministic-random algorithm to ensure you generate a different _k_ for each transaction.((("", startref="Tdigsig06"))) If you are implementing an algorithm to sign transactions in bitcoin, you _must_ use RFC6979 or a similarly deterministic-random algorithm to ensure you generate a different _k_ for each transaction.((("", startref="Tdigsig06")))
=== Bitcoin Addresses, Balances, and Other Abstractions === Bitcoin Addresses, Balances, and Other Abstractions
We began this chapter with the discovery that transactions look very different "behind the scenes" than how they are presented in wallets, blockchain explorers, and other user-facing applications. Many of the simplistic and familiar concepts from the earlier chapters, such as bitcoin addresses and balances, seem to be absent from the transaction structure. We saw that transactions don't contain bitcoin addresses, per se, but instead operate through scripts that lock and unlock discrete values of bitcoin. Balances are not present anywhere in this system and yet every wallet application prominently displays the balance of the user's wallet. ((("transactions", "higher-level abstractions", id="Thigher06")))We began this chapter with the discovery that transactions look very different "behind the scenes" than how they are presented in wallets, blockchain explorers, and other user-facing applications. Many of the simplistic and familiar concepts from the earlier chapters, such as bitcoin addresses and balances, seem to be absent from the transaction structure. We saw that transactions don't contain bitcoin addresses, per se, but instead operate through scripts that lock and unlock discrete values of bitcoin. Balances are not present anywhere in this system and yet every wallet application prominently displays the balance of the user's wallet.
Now that we have explored what is actually included in a bitcoin transaction, we can examine how the higher-level abstractions are derived from the seemingly primitive components of the transaction. Now that we have explored what is actually included in a bitcoin transaction, we can examine how the higher-level abstractions are derived from the seemingly primitive components of the transaction.
@ -721,4 +721,4 @@ In summary, the information presented to users through wallet applications, bloc
Every day, hundreds of transactions that do not contain Pay-to-Public-Key-Hash outputs are confirmed on the blockchain. The blockchain explorers often present these with red warning messages saying they cannot decode an address. The following link contains the most recent "strange transactions" that were not fully decoded: https://blockchain.info/strange-transactions[]. Every day, hundreds of transactions that do not contain Pay-to-Public-Key-Hash outputs are confirmed on the blockchain. The blockchain explorers often present these with red warning messages saying they cannot decode an address. The following link contains the most recent "strange transactions" that were not fully decoded: https://blockchain.info/strange-transactions[].
As we will see in the next chapter, these are not necessarily strange transactions. They are transactions that contain more complex locking scripts than the common Pay-to-Public-Key-Hash. We will learn how to decode and understand more complex scripts and the applications they support next.((("", startref="BCtransact06"))) As we will see in the next chapter, these are not necessarily strange transactions. They are transactions that contain more complex locking scripts than the common Pay-to-Public-Key-Hash. We will learn how to decode and understand more complex scripts and the applications they support next.((("", startref="BCtransact06")))((("", startref="Thigher06")))