A cryptographic hash function is a deterministic algorithm $h:\{0,1\}^{*} \to \{0,1\}^{n}$ that maps an input of arbitrary length (a byte string) to a fixed-length output called a digest (hash value). Determinism means identical inputs produce identical digests. In blockchain protocols, digest values are treated as commitments: changing any protocol-relevant byte changes the digest.

Cryptographic security is expressed in computational terms. Typical goals are: • Preimage resistance: given y, it is infeasible to find x such that $h(x)=y$. • Second-preimage resistance: given x, it is infeasible to find $x' \neq x$ with $h(x')=h(x)$. • Collision resistance: it is infeasible to find any distinct $x,x'$ such that $h(x)=h(x')$. Here, “infeasible” means no known practical algorithm can achieve the task within realistic resource limits.

1) Chain linkage: block headers include a field with the hash of the previous header. If any header byte changes, the new hash no longer matches, so tampering is detected by recomputation. 2) Transaction commitment: many transactions are summarized into a single Merkle root included in the header. A Merkle proof lets a light client verify that a transaction is included in the set committed by that root, without downloading the full block.