Cryptography

Cryptography is a branch of mathematics focused on techniques for securing information, such as encryption, decryption, and the creation and use of digital keys. In Bitcoin, cryptography forms the backbone of its decentralized, trustless, and permissionless design.

One key cryptographic tool in Bitcoin is public key cryptography. With this, every user can generate their own unique pair of keys: one public, one private. The public key acts like an address for receiving funds, while the private key is needed to spend them. There’s no central authority issuing these keys; anyone can join and use the system simply by generating keys, reinforcing Bitcoin’s open and permissionless character. This differs from traditional banks, where third parties control account creation and access.

Importantly, sharing your public key allows others to send you bitcoin without letting them access your funds—unlike the legacy banking system where sharing account details often grants others more control than you’d like. In Bitcoin, users don’t have to rely on trust in individuals or institutions; the cryptography itself offers strong guarantees.

Another central cryptographic tool in Bitcoin is the hash function. Hashes help maintain the blockchain’s security and immutability by linking each block to its predecessor: each block includes a hash of the previous block. If any data in a past block changes, its hash changes, which in turn changes the hash of every subsequent block. This makes it virtually impossible to alter past transactions without redoing all the computational work, keeping the blockchain tamper-resistant.

Mining in Bitcoin relies on both hash functions and a process called Proof-of-Work. Anyone with sufficient computing power can mine, and the mining process is probabilistic, with no one able to consistently game the system regardless of size. This openness and randomness protect the network from centralized control and attacks, making Bitcoin robust and decentralized.