On Sat, Jul 27, 2013 at 07:49:18PM -0400, Peter Todd wrote:
> Implementation
> ==============
> 
> Savings use P2SH outputs matching the following scriptPubKey form:
> 
> HASH160 <H(nonce_i)> EQUALVERIFY <pubkey> CHECKSIG
> 
> spent with:
> 
> <sig> <nonce_i>

FWIW with some minor scripting language additions such as access to txin
and txout contents, along with merklized abstract syntax tree (MAST)
support, we can even implement a version where scriptPubKey's can be
reused:

    <pubkey> CHECKSIGVERIFY

    // Verify we aren't spending more than the maximum spend amount
    0 GET-TXIN-VALUE      // relative indexing
    0 GET-TXOUT-VALUE
    SUB
    <max-spend-amount>
    LESSTHAN
    VERIFY

    // If the txout is greater than the maximum spend amount force it to
    // also follow these same rules.
    0 GET-TXOUT-VALUE
    <max-spend-amount>
    LESSTHAN
    IFNOT
        GET-THIS-SCRIPT
        MAST-HASH
        <serialized script "MAST-HASH MAST-EVAL">
        CAT
        GET-TXOUT-SCRIPT
        EQUALVERIFY
    ENDIF

    // Hash the provided oracle nonce, saving original for later.
    DUP
    HASH160

    // Use the txid:vout nonce as an index to a table, embedded with MAST
    // script compression.
    0 GET-TXIN-TXID
    0 GET-TXIN-VOUT
    CAT
    HASH160

    // The table, n=64 levels deep, not all levels shown for brevity.
    DUP
    1
    AND
    IF
        1
        RSHIFT
        DUP
        1
        AND
        IF
            1
            RSHIFT
            DUP
            1
            AND
            IF
                <MAST digest, not executed>
            ELSE
                1
                RSHIFT
                DUP
                1
                AND
                IF
                    // Lowest level contains the following pushdata,
                    // with 0 <= i < 2^64
                    <HASH160(HASH160(nonce-secret + i))>
                ELSE
                    <MAST digest, not executed>
                ENDIF
        ELSE
            <MAST digest, not executed>
        ENDIF
    ELSE
        <MAST digest, not executed>
    ENDIF

    // Drop the txid:vout nonce
    SWAP
    DROP

    // Verify that the hash of the nonce and the pre-committed value in
    // the H(nonce) table match.
    EQUALVERIFY

    // Stack now only contains the nonce preceeded by a merkle path linking
    // that nonce to the tip of a merkle tree over all nonces.
    //
    // Verify that path.
    SWAP // Move direction flag to the top
    IF
        SWAP
    ENDIF
    HASH160
    (repeat above five lines 63 more times)

    <nonce-merkle-tree-tip-digest>
    EQUAL

The scriptPubKey is spent by the following scriptSig:

    <nonce-merkle-path-0>...<nonce-merkle-path-63>
    <nonce>
    <signature>
    <serialized-script>

(note that I've left off a number of possible optimizations for clarity)

Now when the user wishes to spend a txout greather than their spending
limit their wallet software will first give them a short 6 word string
calculated from the last 64-bits of H(txid:vout). They simply enter this
string into their phone, ideally via convenient qr-code or voice/thought
recognition, and their phone provides a second short 6 word string to
enter into the wallet software on their computer, authorizing the
payment. If they opt for a paper-based one-time-password table they
simply use the 6 word string as an index to their pre-printed OTP
encyclopedia set.

Like the previously described version the security level is still a
healthy 2^64 - again the attacker needs to find a 64-bit pre-image,
considered to be a highly difficult task for any attacker unable to
count from 0 to 2^64 or store a table containing 2^64 values.

There is the disadvantage of the large storage requirements for both
wallets, however because of the double hashed construction,
H(H(nonce-secret+i)), neither table needs to be kept secret. Thus
without loss of security both tables can be easily stored in a
distributed hash table in the cloud and queried as needed.

-- 
'peter'[:-1]@petertodd.org
0000000000000012199fe3f1f54921e8e11c0b0d318ed6245dee22a4ad55bc65