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From: Tier Nolan <tier.nolan@gmail.com>
Date: Sun, 16 Aug 2020 19:59:25 +0100
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To: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
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Subject: Re: [bitcoin-dev] reviving op_difficulty
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On Sun, Aug 16, 2020 at 4:50 PM Thomas Hartman via bitcoin-dev <
bitcoin-dev@lists.linuxfoundation.org> wrote:

> My understanding is that adding a single op_difficulty operation as
> proposed would enable not true difficulty futures but binary options
> on difficulty.
>
> https://en.wikipedia.org/wiki/Binary_option


Any kind of opcode is a binary option.  Either the output can be spent or
it can't.

You could get a pseudo-continuous future by having lots of outputs with
different thresholds.

Alice and Bob create a transaction with 100 outputs and each having 1% of
the future's value.

Output 0:  Pay Alice if diff < 1.00 trillion else Bob
Output 1:  Pay Alice if diff < 1.01 trillion else Bob
....
Output 98:  Pay Alice if diff < 1.98 trillion else Bob
Output 99:  Pay Alice if diff < 1.99 trillion else Bob

If the difficulty is 1.25 trillion, then Alice gets outputs 0-24 and Bob
gets outputs 25-99.  The future has a tick size of 1%.  It isn't very
efficient though

It would be good to have the option to specify a block height for the
future too.  If it triggered on block time, then miners have an incentive
to give false block times.

I am not clear if there is a way to solve the accounting for the
> payouts, but perhaps there is a way to do this with covenants.
>

I agree you would need covenants or something similar.

There needs to be a way to check the outputs (value and script) of the
spending transaction.  You also need a way for Alice and Bob to create
their spending transaction in sequence.

Output 0: Pay Alice if [output value 0] <= Diff / 1 trillion AND [output
value 1] >= (2 trillion - diff)  / (1 trillion) AND [output 1 pays to Bob]

To spend her output, Alice has to create a transaction which pays Bob and
assigns the coins in the right ratio.  [output value x] means the output
value of the spending transaction for output x.

To get it to work Alice creates a transaction with these restrictions

Output 0:
Script: Anything (Alice gets it to pay herself)
Value: <= Diff / 1 trillion

Output 1:
Script: Must pay to Bob
Value: >= (2 trillion - Diff) / 1 trillion

You also need to handle overflows with the calculations.

Bob can then spend output 1 and get his money.

There is a hold-up risk if Alice doesn't spend her money.  You can make the
output script so either of them can spend their coins to avoid that.

Output 0:
    Pay Alice if [output value 0] <= Diff / 1 trillion AND [output value 1]
>= (2 trillion - diff)  / (1 trillion) AND [output 1 pays to Bob]
      OR
    Pay Bob if [output value 0] <= (2 trillion - Diff) / 1 trillion AND
[output value 1] >= Diff / (1 trillion) AND [output 1 pays to Alice]

You would need a covenant-like instruction to check the output values and
scripts and the diff opcode to get the difficulty.

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<div dir=3D"ltr"><div dir=3D"ltr"><br></div><br><div class=3D"gmail_quote">=
<div dir=3D"ltr" class=3D"gmail_attr">On Sun, Aug 16, 2020 at 4:50 PM Thoma=
s Hartman via bitcoin-dev &lt;<a href=3D"mailto:bitcoin-dev@lists.linuxfoun=
dation.org">bitcoin-dev@lists.linuxfoundation.org</a>&gt; wrote:<br></div><=
blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-l=
eft:1px solid rgb(204,204,204);padding-left:1ex">My understanding is that a=
dding a single op_difficulty operation as<br>
proposed would enable not true difficulty futures but binary options<br>
on difficulty.<br>
<br>
<a href=3D"https://en.wikipedia.org/wiki/Binary_option" rel=3D"noreferrer" =
target=3D"_blank">https://en.wikipedia.org/wiki/Binary_option</a></blockquo=
te><div><br></div><div>Any kind of opcode is a binary option.=C2=A0 Either =
the output can be spent or it can&#39;t.</div><div><br></div><div>You could=
 get a pseudo-continuous future by having lots of outputs with different th=
resholds.</div><div><br></div><div>Alice and Bob create a transaction with =
100 outputs and each having 1% of the future&#39;s value.<br></div><div><br=
></div>
<div class=3D"gmail_quote"><div>Output 0:=C2=A0 Pay Alice if diff &lt; 1.00=
 trillion else Bob<br></div>Output 1:=C2=A0 Pay Alice if diff &lt; 1.01 tri=
llion else Bob</div>


<div class=3D"gmail_quote"><div>....<br></div><div>Output 98:=C2=A0 Pay Ali=
ce if diff &lt; 1.98 trillion else Bob<br></div>Output 99:=C2=A0 Pay Alice =
if diff &lt; 1.99 trillion else Bob</div><div class=3D"gmail_quote"><br></d=
iv><div class=3D"gmail_quote">If the difficulty is 1.25 trillion, then Alic=
e gets outputs 0-24 and Bob gets outputs 25-99.=C2=A0 The future has a tick=
 size of 1%.=C2=A0 It isn&#39;t very efficient though</div><div class=3D"gm=
ail_quote"><br></div><div class=3D"gmail_quote">It would be good to have th=
e option to specify a block height for the future too.=C2=A0 If it triggere=
d on block time, then miners have an incentive to give false block times.<b=
r></div><br><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0=
.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
I am not clear if there is a way to solve the accounting for the<br>
payouts, but perhaps there is a way to do this with covenants.<br></blockqu=
ote><div><br></div><div>I agree you would need covenants or something simil=
ar.</div><div><br></div><div>There needs to be a way to check the outputs (=
value and script) of the spending transaction.=C2=A0 You also need a way fo=
r Alice and Bob to create their spending transaction in sequence.</div><div=
><br></div><div>Output 0:=20
 Pay Alice if [output value 0] &lt;=3D Diff / 1 trillion AND [output value =
1] &gt;=3D (2 trillion - diff)=C2=A0 / (1 trillion) AND [output 1 pays to B=
ob]</div><div><br></div><div>To spend her output, Alice has to create a tra=
nsaction which pays Bob and assigns the coins in the right ratio.=C2=A0 [ou=
tput value x] means the output value of the spending transaction for output=
 x.</div><div><br></div><div>To get it to work Alice creates a transaction =
with these restrictions</div><div><br></div><div>Output 0:</div><div>Script=
: Anything (Alice gets it to pay herself)</div><div>Value:=20
 &lt;=3D Diff / 1 trillion <br></div><div><br></div><div>Output 1:</div><di=
v>Script: Must pay to Bob</div><div>Value: &gt;=3D (2 trillion - Diff) / 1 =
trillion<br></div><div><br></div><div>You also need to handle overflows wit=
h the calculations.</div><div><br></div><div>Bob can then spend output 1 an=
d get his money.</div><div><br></div><div>There is a hold-up risk if Alice =
doesn&#39;t spend her money.=C2=A0 You can make the output script so either=
 of them can spend their coins to avoid that.</div><div><br></div><div>
Output 0: <br></div><div>=C2=A0=C2=A0=C2=A0 Pay Alice if [output value 0] &=
lt;=3D Diff / 1 trillion AND [output value 1] &gt;=3D (2 trillion - diff)=
=C2=A0 / (1 trillion) AND [output 1 pays to Bob]

</div><div>=C2=A0=C2=A0=C2=A0=C2=A0=C2=A0 OR</div><div>=C2=A0=C2=A0=C2=A0 P=
ay Bob if [output value 0] &lt;=3D (2 trillion - Diff) / 1 trillion AND [ou=
tput value 1] &gt;=3D Diff / (1 trillion) AND [output 1 pays to Alice] <br>=
</div><div><br></div><div>You would need a covenant-like instruction to che=
ck the output values and scripts and the diff opcode to get the difficulty.=
<br></div></div></div>

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