I see, so your suggestion is that a sequence of OP_IF ... OP_ENDIF can be
replaced by a Merklized Script tree of that depth in practice.

I'm concerned that at script creation time it takes exponential time to
complete a Merkle root of depth 'n'.  Can anyone provide benchmarks or
estimates of how long it takes to compute a Merkle root of a full tree of
various depths on typical consumer hardware?  I would guess things stop
becoming practical at a depth of 20-30.

On Thu, Nov 22, 2018 at 9:28 AM Johnson Lau <jl2012@xbt.hk> wrote:

> With MAST in taproot, OP_IF etc become mostly redundant, with worse
> privacy. To maximise fungibility, we should encourage people to use MAST,
> instead of improve the functionality of OP_IF and further complicate the
> protocol.
>
>
> On 22 Nov 2018, at 1:07 AM, Russell O'Connor via bitcoin-dev <
> bitcoin-dev@lists.linuxfoundation.org> wrote:
>
> On Mon, Nov 19, 2018 at 10:22 PM Pieter Wuille via bitcoin-dev <
> bitcoin-dev@lists.linuxfoundation.org> wrote:
>
>> So my question is whether anyone can see ways in which this introduces
>> redundant flexibility, or misses obvious use cases?
>>
>
> Hopefully my comment is on-topic for this thread:
>
> Given that we want to move away from OP_CODESEPARATOR, because each call
> to this operation effectively takes O(script-size) time, we need a
> replacement for the functionality it currently provides.  While perhaps the
> original motivation for OP_CODESEPARTOR is surrounded in mystery, it
> currently can be used (or perhaps abused) for the task of creating
> signature that covers, not only which input is being signed, but which
> specific branch within that input Script code is being signed for.
>
> For example, one can place an OP_CODESEPARATOR within each branch of an IF
> block, or by placing an OP_CODESEPARATOR before each OP_CHECKSIG
> operation.  By doing so, signatures created for one clause cannot be used
> as signatures for another clause.  Since different clauses in Bitcoin
> Script may be enforcing different conditions (such as different time-locks,
> hash-locks, etc), it is useful to be able to sign in such a way that your
> signature is only valid when the conditions for a particular branch are
> satisfied.  In complex Scripts, it may not be practical or possible to use
> different public keys for every different clause. (In practice, you will be
> able to get away with fewer OP_CODESEPARATORS than one in every IF block).
>
> One suggestion I heard (I think I heard it from Pieter) to achieve the
> above is to add an internal counter that increments on every control flow
> operator, OP_IF, OP_NOTIF, OP_ELSE, OP_ENDIF, and have the signature cover
> the value of this counter.  Equivalently we divide every Bitcoin Script
> program into blocks deliminated by these control flow operator and have the
> signature cover the index of the block that the OP_CHECKSIG occurs within.
> More specifically, we will want a SigHash flag to enables/disable the
> signature covering this counter.
>
> There are many different ways one might go about replacing the remaining
> useful behaviour of OP_CODESEPARATOR than the one I gave above. I would be
> happy with any solution.
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>