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26 lines
1.0 KiB
Markdown
26 lines
1.0 KiB
Markdown
# Notation
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Sending user: `Alice`<br>
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Receiving user: `Carol`<br>
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Mint: `Bob`
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## Bob (mint)
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- `k` private key of mint (one for each supported 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-Hellman key exchange (BDH)
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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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