Private Keys in Monero

Author is nowhere close to being a cryptographer. Be sceptical on accuracy.

In Monero, the root private key is generated randomly. Other private keys are derived deterministically from the root private key.

Private key must be kept secret.

Private key is a large integer impossible to guess, like: 108555083659983933209597798445644913612440610624038028786991485007418559037440

Private key is 256 bits long.

Private key is a scalar, meaning it is a single value.

In equations scalars are represented by lowercase letters.

Relation to Ed25519

Being simply a random integer, private key is not specific to any particular asymmetric cryptography scheme.

In context of Monero EC cryptography the private key is a number the base point G is multiplied by. The result of the multiplication is the public key P (another point on the curve). Multiplication of a point by a number has a very special definition in EC cryptography. See this this guide for details.

Key strength

Before deriving the public key, private key is subject to modulo l, where l is the maximum scalar allowed by the edwards25519 curve.

The l is on the order of 2^252, so the effective key strength is technically 252 bits, not 256 bits. This is standard for EC cryptography and is more of a cosmetic nuance than any concern.

Encoding

In user-facing contexts, the private key integer is:

1. Taken modulo l to avoid malleability
2. Put as array of 32 bytes in a little-endian direction (the first byte is the least significant)
3. Converted to hexadecimal form, like: b3588a87056fb21dc4d052d59e83b54293882e646b543c29478e4cf45c28a402

Private spend key

Private spend key is used to spend moneros.

More specifically, it is used to build one-time private keys which allow to spend related outputs.

Private view key

Private view key is used to recognize your incoming transactions on the otherwise opaque blockchain.

One-time private keys

One-time private key like construct is used in stealth addresses.