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Author: Sean Bowe

This work was presented at Financial Cryptography 2016 and at We thank Gregory Maxwell for the idea of ZKCPs, and 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.

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


  • 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)


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.


Pay for the solution to a sudoku puzzle with a zero-knowledge contingent payment




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