pay-to-sudoku/README.md

# pay-to-sudoku

```
Author: Sean Bowe
This work was presented at Financial Cryptography 2016 and at <https://bitcoincore.org/en/2016/02/26/zero-knowledge-contingent-payments-announcement/>.
We thank Gregory Maxwell for useful feedback and for participating in our demonstration. We also thank Pieter Wuille, Andrew Poelstra, and Madars Virza for helping with the demonstration.
```

This is an implementation of a zero-knowledge contingent 
payment for paying someone to solve a sudoku puzzle.

```
./get-libsnark
make
cargo run gen 2 # generate circuit for 2^2 x 2^2 puzzle
cargo run test 2 # test the proofs
cargo run serve 2 # run a server on port 25519 for buying solutions
cargo run client 2 # run a client for selling solutions
```

# circuit description for some NxN puzzle:

**primary inputs**: sodoku puzzle `P`, key commitment `C`, encrypted solution `E`

**auxillary inputs**: solution `S`, key `K`

**properties:**

* **puzzle subset**: `S` must be a subset of `P` (the solution must complete the puzzle)
* **solution closure**: `S` must be closed under rows, columns and groups of the solution (the solution must be correct)
* **encryption correctness**: `E` must be `S` encrypted with `K` (using a stream cipher produced from SHA256)
* **solution commitment**: `C` must be `SHA256(K)`

**usage:**

Alice produces puzzle `P` and sends Bob `P` and the zk-SNARK proving key. Bob finds a solution `S` for the puzzle
and constructs `K`, `C`, and `E`. Bob constructs a `Proof`. Bob sends Alice (Proof, `C`, `E`). Alice verifies the
proof. Alice sends a CLTV transaction over the blockchain to Bob with the added constraint that Bob must produce
the preimage of `C` (aka `K`). After Bob redeems the TxOut, Alice uses `K` to decrypt `E`, producing `S`. If Bob
does not redeem the TxOut, Alice recovers her value but does not obtain `S`.