# The Cashu Protocol

Cashu is an open source ecash protocol built for Bitcoin. It is an open protocol which means that everyone can write their own software to interact with other Cashu apps. Applications that follow the specifications will be compatible with the rest of the ecosystem.

## BDHKE

The Blind Diffie-Hellmann Key Exchange (BDHKE) is the basic cryptographic scheme used in the Cashu protocol to sign and redeem ecash tokens. There are three actors in this model:

- Sending user:
`Alice`

- Receiving user:
`Carol`

- Mint:
`Bob`

### Bob (mint)

`k`

private key of mint (one for each amount)`K`

public key of mint`Q`

promise (blinded signature)

### Alice (user)

`x`

random string (secret message), corresponds to point`Y`

on curve`r`

private key (blinding factor)`T`

blinded message`Z`

proof (unblinded signature)

### Blind Diffie-Hellmann key exchange (BDHKE)

- Mint
`Bob`

publishes public key`K = kG`

`Alice`

picks secret`x`

and computes`Y = hash_to_curve(x)`

`Alice`

sends to`Bob`

:`B_ = Y + rG`

with`r`

being a random blindind factor (**blinding**)`Bob`

sends back to`Alice`

blinded key:`C_ = kB_`

(these two steps are the DH key exchange) (**signing**)`Alice`

can calculate the unblinded key as`C_ - rK = kY + krG - krG = kY = C`

(**unblinding**)- Alice can take the pair
`(x, C)`

as a token and can send it to`Carol`

. `Carol`

can send`(x, C)`

to`Bob`

who then checks that`k*hash_to_curve(x) == C`

(**verification**), and if so treats it as a valid spend of a token, adding`x`

to the list of spent secrets.

## NUTs

Cashu NUTs (Notation, Usage, and Terminology) specify the Cashu protocol and can be found here.