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56 lines
2.3 KiB
Markdown
56 lines
2.3 KiB
Markdown
# Private keys in Monero
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!!! note
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Author is nowhere close to being a cryptographer. Be sceptical on accuracy.
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In Monero, the root private key is generated [randomly](/cryptography/prng). Other private keys are derived deterministically from the root private key.
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Private key must be kept secret.
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Private key is a **large integer** impossible to guess, like:
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`108555083659983933209597798445644913612440610624038028786991485007418559037440`
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Private key is 256 bits long.
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Private key is a **scalar**, meaning it is a single value.
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In equations scalars are represented by **lowercase letters**.
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## Relation to Ed25519
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Being simply a random integer, private key is not specific to any particular asymmetric cryptography scheme.
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In context of Monero EC cryptography the private key is a number the base point `G` is multiplied by.
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The result of the multiplication is the public key `P` (another point on the curve).
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Multiplication of a point by a number has a very special definition in EC cryptography.
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See this [this guide](https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/) for details.
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### Key strength
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Before deriving Ed25519 public key, the private key is subject to modulo `l`,
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where `l` is the maximum scalar allowed by the [Ed25519 scheme](/cryptography/asymmetric/ed25519).
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The `l` is on the order of 2^252, so the effective key strength is technically 252 bits, not 256 bits.
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This is standard for EC cryptography and is more of a cosmetic nuance than any concern.
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## Encoding
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In user-facing contexts, the private key integer is:
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1. Taken modulo `l` to avoid malleability
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2. Put as array of 32 bytes in a [little-endian](https://en.wikipedia.org/wiki/Endianness#Little) direction (the first byte is the least significant)
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3. Converted to hexadecimal form, like: `b3588a87056fb21dc4d052d59e83b54293882e646b543c29478e4cf45c28a402`
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## Private spend key
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Private spend key is used to spend moneros.
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More specifically, it is used to build one-time private keys which allow to spend related outputs.
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## Private view key
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Private view key is used to recognize your incoming transactions on the otherwise opaque blockchain.
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## One-time private keys
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One-time private key like construct is used in [stealth addresses](https://monero.stackexchange.com/questions/1409/constructing-a-stealth-monero-address).
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