Compressed Public Keys (The Efficiency Upgrade)

Around 2012, Bitcoin developers realized they could cut the size of public keys in half without losing any security. This led to the Compressed Public Key format, which is the standard for almost all Bitcoin transactions today.

1. The 33-Byte Structure

A compressed public key consists of:

1. Prefix (1 byte): Either 0x02 or 0x03.

2. X-Coordinate (32 bytes): The horizontal position.

Total Size: 33 Bytes.

2. The Mathematical Magic

The secp256k1 curve follows the equation: $$y^2 = x^3 + 7 \pmod p$$

Because this is a symmetric curve, for every valid X, there are only two possible values for Y:

• A Positive (Even) value.

• A Negative (Odd) value.

By knowing the X-coordinate and whether the Y-coordinate is Even or Odd, a computer can solve the equation to find the exact Y-coordinate.

3. The 50% Space Saving

• Uncompressed: 65 bytes.

• Compressed: 33 bytes. By dropping the Y-coordinate, we save 32 bytes per public key. In a multisig transaction (e.g., 3-of-5), this saves nearly 160 bytes, significantly reducing transaction fees.

4. Activation in Bitcoin

Most modern wallets (Electrum, BlueWallet, Hardware Wallets) use compressed keys by default. If you see a raw public key starting with 02 or 03, you are looking at a compressed key.

Format	Prefix	Size	Benefit
Uncompressed	04	65 Bytes	None (Legacy)
Compressed	02 / 03	33 Bytes	50% Fee Savings

In the next section, we will explain the Even/Odd Y-Coordinate and how the prefix is chosen.