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[[ch04_keys_addresses]]
== Keys, Addresses
((("bitcoin", "keys and addresses", id="BCkeys04")))((("cryptography", "defined")))((("cryptography", see="also keys and addresses")))You may have heard that bitcoin is based on _cryptography_, which is a branch of mathematics used extensively in computer security. Cryptography means "secret writing" in Greek, but the science of cryptography encompasses more than just secret writing, which is referred to as encryption. Cryptography can also be used to prove knowledge of a secret without revealing that secret (digital signatures), or prove the authenticity of data (digital fingerprints). These types of cryptographic proofs are the mathematical tools critical to bitcoin and used extensively in bitcoin applications. Ironically, encryption is not an important part of bitcoin, as its communications and transaction data are not encrypted and do not need to be encrypted to protect the funds. In this chapter we will introduce some of the cryptography used in bitcoin to control ownership of funds, in the form of keys, addresses, and wallets.
((("bitcoin", "keys and addresses", id="BCkeys04")))((("cryptography", "defined")))((("cryptography", see="also keys and addresses")))You may have heard that bitcoin is based on _cryptography_, which is a branch of mathematics used extensively in computer security. Cryptography means "secret writing" in Greek, but the science of cryptography encompasses more than just secret writing, which is referred to as encryption. Cryptography can also be used to prove knowledge of a secret without revealing that secret (digital signatures), or prove the authenticity of data (digital fingerprints). These types of cryptographic proofs are the mathematical tools critical to bitcoin and used extensively in bitcoin applications. ((("encryption")))((("encryption", see="also keys and addresses")))Ironically, encryption is not an important part of bitcoin, as its communications and transaction data are not encrypted and do not need to be encrypted to protect the funds. In this chapter we will introduce some of the cryptography used in bitcoin to control ownership of funds, in the form of keys, addresses, and wallets.
=== Introduction
Ownership of bitcoin is established through _digital keys_, _bitcoin addresses_, and _digital signatures_. The digital keys are not actually stored in the network, but are instead created and stored by users in a file, or simple database, called a _wallet_. The digital keys in a user's wallet are completely independent of the bitcoin protocol and can be generated and managed by the user's wallet software without reference to the blockchain or access to the internet. Keys enable many of the interesting properties of bitcoin, including decentralized trust and control, ownership attestation, and the cryptographic-proof security model.
((("digital keys", see="keys and addresses")))((("keys and addresses", "overview of", id="KAover04")))Ownership of bitcoin is established through _digital keys_, _bitcoin addresses_, and _digital signatures_. The digital keys are not actually stored in the network, but are instead created and stored by users in a file, or simple database, called a _wallet_. The digital keys in a user's wallet are completely independent of the bitcoin protocol and can be generated and managed by the user's wallet software without reference to the blockchain or access to the internet. Keys enable many of the interesting properties of bitcoin, including decentralized trust and control, ownership attestation, and the cryptographic-proof security model.
Every bitcoin transaction requires a valid digital signature to be included in the blockchain, which can only be generated with a secret key; therefore, anyone with a copy of that key has control of the bitcoin in that account. The digital signature used to spend funds is also referred to as a _witness_, a term used in cryptography. The witness data in a bitcoin transaction testifies to the true ownership of the funds being spent.
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[TIP]
====
Most bitcoin implementations use the http://bit.ly/1ql7bn8[OpenSSL cryptographic library] to do the elliptic curve math. For example, to derive the public key, the function +EC_POINT_mul()+ is used.
Most bitcoin implementations use the http://bit.ly/1ql7bn8[OpenSSL cryptographic library] to do the elliptic curve math. For example, to derive the public key, the function +EC_POINT_mul()+ is used.((("", startref="KAover04")))
====
[[ecc_illustrated]]