Cryptographic Foundations

Blockchain technology is built on a foundation of cryptographic primitives. Understanding hashing, digital signatures, and Merkle trees is essential to grasping how blockchains achieve security, integrity, and trustlessness.

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Cryptographic Hash Functions

A hash function takes an input of any size and produces a fixed-size output (the hash or digest). In blockchain, hash functions serve as the backbone of data integrity.

Properties of Cryptographic Hash Functions

Property	Description
Deterministic	The same input always produces the same output
Fixed output size	Regardless of input size, the hash is always the same length
Pre-image resistance	Given a hash, it is computationally infeasible to find the original input
Second pre-image resistance	Given an input, it is infeasible to find a different input with the same hash
Collision resistance	It is infeasible to find any two different inputs that produce the same hash
Avalanche effect	A tiny change in input produces a drastically different output

SHA-256 in Action

SHA-256 is the hash function used by Bitcoin. It always produces a 256-bit (32-byte) output:

Input:  "Hello"
SHA-256: 185f8db32271fe25f561a6fc938b2e264306ec304eda518007d1764826381969

Input:  "Hello!"
SHA-256: 334d016f755cd6dc58c53a86e183882f8ec14f52fb05345887c8a5edd42c87b7

Notice how adding a single character completely changes the hash — this is the avalanche effect.

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Hash Functions Used in Blockchain

Blockchain	Hash Function	Output Size
Bitcoin	SHA-256 (double hashed)	256 bits
Ethereum	Keccak-256	256 bits
Litecoin	Scrypt (memory-hard)	256 bits
Zcash	Equihash	Variable
IOTA	Curl-P / Kerl	243 trits

Note: Ethereum uses Keccak-256, which is closely related to but not identical to the NIST SHA-3 standard. The difference is in the padding scheme.

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Digital Signatures

Digital signatures allow blockchain participants to prove ownership of their funds and authorise transactions without revealing their private key.

How Digital Signatures Work in Blockchain

1. Sender hashes the transaction data
2. Sender signs the hash with their private key  -->  Signature
3. Transaction + Signature are broadcast to the network
4. Validators verify the signature using the sender's public key

ECDSA (Elliptic Curve Digital Signature Algorithm)

Bitcoin and Ethereum both use ECDSA with the secp256k1 curve:

Parameter	Value
Curve	secp256k1
Private key size	256 bits (32 bytes)
Public key size	512 bits uncompressed / 257 bits compressed
Signature size	~512 bits (two 256-bit integers: r, s)

Key Pair Generation