Multiparty Hash Puzzles

In a hash puzzle contract, the spender has to provide a preimage x that hashes to a predefined value y to unlock a UTXO. It can be extended to multiple parties so that multiple preimages have to be provided such that y1 = H(x1), y2 = H(x2), …, yN = H(xN) [1]. Below shows an examples of three parties.

contract MultiPartyHashPuzzles {
    Sha256 hash1;   // hash1 = b'136523B9FEA2B7321817B28E254A81A683D319D715CEE2360D051360A272DD4C'
    Sha256 hash2;   // hash2 = b'E222E30CF5C982E5F6251D755B0B16F608ACE631EB3BA9BDAF624FF1651ABF98'
    Sha256 hash3;   // hash3 = b'2A79F5D9F8B3770A59F91E0E9B4C379F7C7A32353AA6450065E43A8616EF5722'

    // preimage1: e.g., "bsv" -> b'627376'
    // preimage2: e.g., "sCrypt" -> b'734372797074'
    // preimage3: e.g., "IDE" -> b'494445'
    public function unlock(bytes preimage1, bytes preimage2, bytes preimage3) {
        require(sha256(preimage1) == this.hash1);
        require(sha256(preimage2) == this.hash2);
        require(sha256(preimage3) == this.hash3);
    }
}

The above solution is problematic when N is large since all N hashes have to be included in the locking script, bloating the transaction. Instead, we can combine all y’s into a single y such that y = H(H(y1 || y2) || y3) [2] as shown below.

contract MultiPartyHashPuzzlesCompact {
    // only 1 hash needs to go into the locking script, saving space
    Sha256 combinedHash; // combinedHash = b'C9392767AB23CEFF09D207B9223C0C26F01A7F81F8C187A821A4266F8020064D'

    // preimage1: e.g., "bsv" -> b'627376'
    // preimage2: e.g., "sCrypt" -> b'734372797074'
    // preimage3: e.g., "IDE" -> b'494445'
    public function unlock(bytes preimage1, bytes preimage2, bytes preimage3) {
        Sha256 hash1 = sha256(preimage1);
        Sha256 hash2 = sha256(preimage2);
        Sha256 hash3 = sha256(preimage3);
        Sha256 hash12 = sha256(hash1 + hash2);
        Sha256 hash123 = sha256(hash12 + hash3);

        require(hash123 == this.combinedHash);
    }
}
[1]H is a hash function. An online hash calculator can be found here.
[2]|| is concatenation.