The Double-Hash Algorithm (HASH160)

Bitcoin does not use a single hash for its addresses. Instead, it uses a specific sequence known as HASH160. This choice was a deliberate design decision by Satoshi Nakamoto to combine the strengths of two different cryptographic families.

1. The Sequence

The math behind a Public Key Hash is: $$PKH = RIPEMD160(SHA256(PublicKey))$$

• Step 1: The raw bytes of the public key are put through the SHA256 algorithm. This produces a 32-byte output.

• Step 2: That 32-byte output is immediately put through the RIPEMD160 algorithm. This produces the final 20-byte output.

2. Why two different algorithms?

Using two different hashing families (NSA-designed SHA and European-designed RIPEMD) provides a "Safety Net."

• Cryptographic Heterogeneity: If a mathematical flaw is discovered in SHA256 in the future, the RIPEMD160 layer acts as a shield.

• Collision Resistance: SHA256 is extremely strong against collisions, while RIPEMD160 is excellent for producing short, unique fingerprints.

3. The 20-Byte Sweet Spot

Satoshi chose 20 bytes (160 bits) as the final length.

• 2^160 is a number so large that it is impossible to find two different public keys that result in the same hash (a collision).

• At the same time, it is small enough to keep the UTXO Set compact, allowing nodes to validate transactions faster.

4. Implementation in Scripts

In raw Bitcoin Script, this is represented by the opcode OP_HASH160.

• When a node sees OP_HASH160, it automatically performs both SHA256 and RIPEMD160 on the item at the top of the stack.

Algorithm	Developer	Output Size
SHA256	NSA (USA)	32 Bytes
RIPEMD160	KU Leuven (Belgium)	20 Bytes
Combined	HASH160	20 Bytes

In the next section, we will look at the Space Efficiency of this hash.