Key Pair Generation

Generate an ECDSA key pair:

d is the private key (a 256-bit integer in [1, n-1]). Q = dG is the public key (a point on the curve).

CRITICAL: use a CSPRNG. Not random.random(). Not the time. secrets.randbits (Python's CSPRNG) or os.urandom.

The private key must NEVER leak. Anyone with d can sign as you.

Storage:

• Hardware: HSM, secure enclave (iPhone), Trezor, Ledger.
• Software: encrypted file, sealed with a passphrase.
• Memory: zero out as soon as possible after use.

Public key formats:

• Uncompressed: 04 || x (32B) || y (32B) → 65 bytes.
• Compressed: 02/03 || x → 33 bytes.

Bitcoin addresses:

• Hash160(pubkey) = RIPEMD160(SHA256(pubkey))
• Base58Check encode = address.

Address derivation hides the public key until you spend (the spend reveals it). Defense-in-depth if ECDSA is ever broken — addresses with no spends remain unbroken.

Address derivation is hash-based, but the underlying ownership is ECC.