Blockchains are trusted without a central authority because of mathematics, not because of any company or government. Cryptography is the toolkit that makes the shared record tamper-evident, proves who owns what, and lets strangers transact safely. Every wallet, transaction and block you will meet later relies on it.
You'll start with cryptographic hash functions: how they turn any input into a fixed-size fingerprint, and why that fingerprint is practically impossible to reverse or fake. Then you'll walk through SHA-256 step by step, the hash function at the heart of Bitcoin. From there the module covers public-key cryptography, where a private key and a public key work as a pair, and finishes with digital signatures and elliptic curves, which let you prove ownership of funds without ever revealing your private key.
With these building blocks in place, you'll be ready for the next module, Consensus Mechanisms, which shows how a network of nodes agrees on which blocks to accept.
What a hash function is, why the same input always gives the same output, and why hashes work as digital fingerprints for blocks and transactions.
A detailed walkthrough of the SHA-256 algorithm with a worked example, showing how Bitcoin's hash function processes data into a 256-bit result.
How public and private keys work as a pair, and how two parties can agree on a shared secret over an open channel using Diffie-Hellman key exchange.
How elliptic curve cryptography signs data so anyone can verify who signed it, while the private key stays secret. This is how Bitcoin transactions are authorized.