Subject: [bitcoindev] Double Exponential Hash Rate Growth and Difficulty Adjustment

From: Anders <[email-masked]>
Date: Wed, 18 Dec 2024 17:19:00 -0800 (PST)

Hi,

I've been looking into the long-term implications of the Bitcoin hash rate 
growth for the difficulty adjustment mechanism, and I'd like to discuss a 
potential concern related to double exponential growth.

As we know, the difficulty adjustment mechanism aims to maintain an average 
block time of approximately 10 minutes by adjusting the target value every 
2016 blocks. This target value, when represented in hexadecimal, 
effectively determines the number of leading zeros required for a valid 
block hash.

The Bitcoin hash rate has historically shown a strong exponential growth 
trend, driven by advancements in ASIC technology. However, some 
observations suggest that this growth might be accelerating, potentially 
exhibiting double exponential growth (meaning the rate of exponential 
growth is itself increasing exponentially).

If the hash rate were to continue to grow at a double exponential rate, the 
difficulty would need to increase at an accelerating pace to maintain the 
10-minute block time. This would mean the number of leading zeros in the 
target value would also need to increase at an accelerating rate.

Since the target value is a 256-bit number (64 hexadecimal digits), there's 
a finite limit to the number of leading zeros it can have. With 
approximately 19-20 leading zeros currently observed, there are only about 
44-45 zeros "left" before reaching this limit.

My concern is that with double exponential hash rate growth, we could reach 
this limit much faster than a simple linear projection would suggest, 
potentially within a decade. Once this limit is reached, the current 
difficulty adjustment mechanism would become ineffective, potentially 
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 
assess the likelihood of double exponential growth? Are there any existing 
studies or analyses I should be aware of?

2. If double exponential growth continues, what are the most promising 
approaches to address this potential issue in the long term?

3. What are the trade-offs associated with different solutions, such as 
more frequent difficulty adjustments, changing the difficulty adjustment 
algorithm, or changing the proof-of-work algorithm entirely?

Thanks,

Anders

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