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Date: Thu, 19 Dec 2024 12:00:55 -0800 (PST)
From: Anders <blabline@gmail.com>
To: Bitcoin Development Mailing List <bitcoindev@googlegroups.com>
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 <CAAg3Je1hVqcR_DGZEXhaeO7CEU1k-SLx_1QX=XmnS2Bn11joXw@mail.gmail.com>
Subject: Re: [bitcoindev] Double Exponential Hash Rate Growth and Difficulty Adjustment
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Okay, that sounds like a simple and clever approach without the need for a=
=20
hard fork.

On Thursday, December 19, 2024 at 8:48:10=E2=80=AFPM UTC+1 Michael Cassano =
wrote:

> Hi Anders,
>
> Thank you for the question.
>
> A solution is to keep miners on SHA256 (instead of switching to a hash=20
> that allows for a larger range of difficulty targets) but to require them=
=20
> to hash again to achieve a secondary difficulty target.
>
> At max target difficulty miners would publish blocks when SHA256(header)=
=20
> =3D=3D 1 and when SHA256(SHA256(header)) <=3D secondary_target where=20
> secondary_target adjusts up and down if primary_target is 1 (where=20
> primary_target represents today's target difficulty).
>
> Nodes then verify blocks by checking that SHA256(header) is =3D=3D 1 and =
that=20
> SHA256(SHA256(header) is less than secondary_target.
>
> Best regards,
> Mike
>
> On Wed, Dec 18, 2024 at 6:21=E2=80=AFPM Anders <blab...@gmail.com> wrote:
>
>> Hi,
>>
>> I've been looking into the long-term implications of the Bitcoin hash=20
>> rate growth for the difficulty adjustment mechanism, and I'd like to=20
>> discuss a potential concern related to double exponential growth.
>>
>> As we know, the difficulty adjustment mechanism aims to maintain an=20
>> average block time of approximately 10 minutes by adjusting the target=
=20
>> value every 2016 blocks. This target value, when represented in=20
>> hexadecimal, effectively determines the number of leading zeros required=
=20
>> for a valid block hash.
>>
>> The Bitcoin hash rate has historically shown a strong exponential growth=
=20
>> trend, driven by advancements in ASIC technology. However, some=20
>> observations suggest that this growth might be accelerating, potentially=
=20
>> exhibiting double exponential growth (meaning the rate of exponential=20
>> growth is itself increasing exponentially).
>>
>> If the hash rate were to continue to grow at a double exponential rate,=
=20
>> the difficulty would need to increase at an accelerating pace to maintai=
n=20
>> the 10-minute block time. This would mean the number of leading zeros in=
=20
>> the target value would also need to increase at an accelerating rate.
>>
>> Since the target value is a 256-bit number (64 hexadecimal digits),=20
>> there's a finite limit to the number of leading zeros it can have. With=
=20
>> approximately 19-20 leading zeros currently observed, there are only abo=
ut=20
>> 44-45 zeros "left" before reaching this limit.
>>
>> My concern is that with double exponential hash rate growth, we could=20
>> reach this limit much faster than a simple linear projection would sugge=
st,=20
>> potentially within a decade. Once this limit is reached, the current=20
>> difficulty adjustment mechanism would become ineffective, potentially=20
>> leading to unstable block times and network instability.
>>
>> My questions for the list are:
>>
>> 1. Has there been more formal analysis of the Bitcoin hash rate trend to=
=20
>> assess the likelihood of double exponential growth? Are there any existi=
ng=20
>> studies or analyses I should be aware of?
>>
>> 2. If double exponential growth continues, what are the most promising=
=20
>> approaches to address this potential issue in the long term?
>>
>> 3. What are the trade-offs associated with different solutions, such as=
=20
>> more frequent difficulty adjustments, changing the difficulty adjustment=
=20
>> algorithm, or changing the proof-of-work algorithm entirely?
>>
>> Thanks,
>>
>> Anders
>>
>> --=20
>> You received this message because you are subscribed to the Google Group=
s=20
>> "Bitcoin Development Mailing List" group.
>> To unsubscribe from this group and stop receiving emails from it, send a=
n=20
>> email to bitcoindev+...@googlegroups.com.
>> To view this discussion visit=20
>> https://groups.google.com/d/msgid/bitcoindev/e86753f2-1c79-484d-8f61-47a=
5dd148b45n%40googlegroups.com=20
>> <https://groups.google.com/d/msgid/bitcoindev/e86753f2-1c79-484d-8f61-47=
a5dd148b45n%40googlegroups.com?utm_medium=3Demail&utm_source=3Dfooter>
>> .
>>
>

--=20
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To unsubscribe from this group and stop receiving emails from it, send an e=
mail to bitcoindev+unsubscribe@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/bitcoindev/=
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Okay, that sounds like a simple and clever approach without the need for a =
hard fork.<br /><br /><div class=3D"gmail_quote"><div dir=3D"auto" class=3D=
"gmail_attr">On Thursday, December 19, 2024 at 8:48:10=E2=80=AFPM UTC+1 Mic=
hael Cassano wrote:<br/></div><blockquote class=3D"gmail_quote" style=3D"ma=
rgin: 0 0 0 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left:=
 1ex;"><div dir=3D"ltr">Hi Anders,<div><br></div><div>Thank you for the que=
stion.</div><div><br></div><div>A solution is to keep miners on SHA256 (ins=
tead of switching to a hash that allows for a larger range of difficulty ta=
rgets) but to require them to hash again to achieve a secondary difficulty =
target.</div><div><br></div><div>At max target difficulty miners would publ=
ish blocks when SHA256(header) =3D=3D 1 and when SHA256(SHA256(header)) &lt=
;=3D secondary_target where secondary_target adjusts up and down if primary=
_target is 1 (where primary_target represents today&#39;s target difficulty=
).</div><div><br></div><div>Nodes then verify blocks by checking that SHA25=
6(header) is =3D=3D 1 and that SHA256(SHA256(header) is less than secondary=
_target.</div><div><br></div><div>Best regards,</div><div>Mike</div></div><=
br><div class=3D"gmail_quote"></div><div class=3D"gmail_quote"><div dir=3D"=
ltr" class=3D"gmail_attr">On Wed, Dec 18, 2024 at 6:21=E2=80=AFPM Anders &l=
t;<a href data-email-masked rel=3D"nofollow">blab...@gmail.com</a>&gt; wrot=
e:<br></div></div><div class=3D"gmail_quote"><blockquote class=3D"gmail_quo=
te" style=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-sty=
le:solid;border-left-color:rgb(204,204,204);padding-left:1ex">Hi,<br><br>I&=
#39;ve been looking into the long-term implications of the Bitcoin hash rat=
e growth for the difficulty adjustment mechanism, and I&#39;d like to discu=
ss a potential concern related to double exponential growth.<br><br>As we k=
now, the difficulty adjustment mechanism aims to maintain an average block =
time of approximately 10 minutes by adjusting the target value every 2016 b=
locks. This target value, when represented in hexadecimal, effectively dete=
rmines the number of leading zeros required for a valid block hash.<br><br>=
The Bitcoin hash rate has historically shown a strong exponential growth tr=
end, driven by advancements in ASIC technology. However, some observations =
suggest that this growth might be accelerating, potentially exhibiting doub=
le exponential growth (meaning the rate of exponential growth is itself inc=
reasing exponentially).<br><br>If the hash rate were to continue to grow at=
 a double exponential rate, the difficulty would need to increase at an acc=
elerating pace to maintain the 10-minute block time. This would mean the nu=
mber of leading zeros in the target value would also need to increase at an=
 accelerating rate.<br><br>Since the target value is a 256-bit number (64 h=
exadecimal digits), there&#39;s a finite limit to the number of leading zer=
os it can have. With approximately 19-20 leading zeros currently observed, =
there are only about 44-45 zeros &quot;left&quot; before reaching this limi=
t.<br><br>My concern is that with double exponential hash rate growth, we c=
ould reach this limit much faster than a simple linear projection would sug=
gest, potentially within a decade. Once this limit is reached, the current =
difficulty adjustment mechanism would become ineffective, potentially leadi=
ng to unstable block times and network instability.<br><br>My questions for=
 the list are:<br><br>1. Has there been more formal analysis of the Bitcoin=
 hash rate trend to assess the likelihood of double exponential growth? Are=
 there any existing studies or analyses I should be aware of?<div><br>2. If=
 double exponential growth continues, what are the most promising approache=
s to address this potential issue in the long term?</div><div><br>3. What a=
re the trade-offs associated with different solutions, such as more frequen=
t difficulty adjustments, changing the difficulty adjustment algorithm, or =
changing the proof-of-work algorithm entirely?</div><div><br>Thanks,<br><di=
v><br></div><div>Anders</div></div>

<p></p></blockquote></div><div class=3D"gmail_quote"><blockquote class=3D"g=
mail_quote" style=3D"margin:0px 0px 0px 0.8ex;border-left-width:1px;border-=
left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">

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</blockquote></div>
</blockquote></div>

<p></p>

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