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93 lines
2.6 KiB
Markdown
93 lines
2.6 KiB
Markdown
# NUT-0 - Notation and Models
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Sending user: `Alice`
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Receiving user: `Carol`
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Mint: `Bob`
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## Bob (mint)
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- `k` private key of mint (one for each amount)
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- `K` public key of mint
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- `Q` promise (blinded signature)
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## Alice (user)
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- `x` random string (secret message), corresponds to point `Y` on curve
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- `r` private key (blinding factor)
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- `T` blinded message
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- `Z` proof (unblinded signature)
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# Blind Diffie-Hellmann key exchange (BDHKE)
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- Mint `Bob` publishes `K = kG`
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- `Alice` picks secret `x` and computes `Y = hash_to_curve(x)`
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- `Alice` sends to `Bob`: `T = Y + rG` with `r` being a random nonce
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- `Bob` sends back to `Alice` blinded key: `Q = kT` (these two steps are the DH key exchange)
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- `Alice` can calculate the unblinded key as `Q - rK = kY + krG - krG = kY = Z`
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- Alice can take the pair `(x, Z)` as a token and can send it to `Carol`.
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- `Carol` can send `(x, Z)` to `Bob` who then checks that `k*hash_to_curve(x) == Z`, and if so treats it as a valid spend of a token, adding `x` to the list of spent secrets.
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## 0.1 - Models
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### `BlindedMessage`
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A encrypted ("blinded") secret and an amount sent from `Alice` to `Bob`.
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```json
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{
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"amount": int,
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"B_": str
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}
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```
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### `BlindedSignature`
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A signature on the `BlindedMessage` sent from `Bob` to `Alice`.
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```json
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{
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"amount": int,
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"C_": str,
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"id": str | None
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}
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```
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### `Proof`
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A `Proof` is also called a `Token` and has the following form:
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```json
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{
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"amount": int,
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"secret": str,
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"C": str,
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"id": None | str,
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"script": P2SHScript | None,
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}
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```
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### `Proofs`
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A list of `Proof`'s. In general, this will be used for most operations instead of a single `Proof`. `Proofs` can be serialized (see Methods/Serialization [TODO: Link Serialization])
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## 0.2 - Methods
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### Serialization of `Proofs`
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To send and receive `Proofs`, wallets serialize them in a `base64_urlsafe` format.
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Example:
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```json
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[
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{
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"id": "DSAl9nvvyfva",
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"amount": 8,
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"secret": "DbRKIya0etdwI5sFAN0AXQ",
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"C": "02df7f2fc29631b71a1db11c163b0b1cb40444aa2b3d253d43b68d77a72ed2d625"
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},
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{
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"id": "DSAl9nvvyfva",
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"amount": 16,
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"secret": "d_PPc5KpuAB2M60WYAW5-Q",
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"C": "0270e0a37f7a0b21eab43af751dd3c03f61f04c626c0448f603f1d1f5ae5a7d7e6"
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}
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```
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becomes
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```
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W3siaWQiOiAiRFNBbDludnZ5ZnZhIiwgImFtb3VudCI6IDgsICJzZWNyZXQiOiAiRGJSS0l5YTBldGR3STVzRkFOMEFYUSIsICJDIjogIjAyZGY3ZjJmYzI5NjMxYjcxYTFkYjExYzE2M2IwYjFjYjQwNDQ0YWEyYjNkMjUzZDQzYjY4ZDc3YTcyZWQyZDYyNSJ9LCB7ImlkIjogIkRTQWw5bnZ2eWZ2YSIsICJhbW91bnQiOiAxNiwgInNlY3JldCI6ICJkX1BQYzVLcHVBQjJNNjBXWUFXNS1RIiwgIkMiOiAiMDI3MGUwYTM3ZjdhMGIyMWVhYjQzYWY3NTFkZDNjMDNmNjFmMDRjNjI2YzA0NDhmNjAzZjFkMWY1YWU1YTdkN2U2In1d
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``` |