PIP-0002: Migration from BTC-Style Difficulty Adjustment Algorithm to ASERT

[andrepatta]

PIP-0002: Migration from BTC-Style Difficulty Adjustment Algorithm to ASERT

Author: Andre Patta
Status: Draft
Type: Standards Track
Category: Core
Created: 2025-11-26

Abstract

This proposal introduces a replacement of the original Bitcoin-style Difficulty Adjustment Algorithm (DAA) used in Parallax, which recalculates difficulty once every 2016 blocks, with the ASERT algorithm (Absolutely Scheduled Exponentially Rising Targets). ASERT is the modern, time-aware difficulty algorithm adopted by Bitcoin Cash and provides smooth, continuous, and mathematically stable difficulty adjustment on every block.

The change significantly improves security, hashrate responsiveness, block interval consistency, and resistance to miner manipulation. This document explains the motivation, details the ASERT algorithm, and compares it to the classic DAA, including a discussion of pros and cons for both.

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Motivation

The original Bitcoin DAA compares the actual time elapsed over a 2016 block window with the ideal 2016 * 600 seconds target. This logic made sense in 2009 but introduces several operational weaknesses in 2025 networks, especially new Proof of Work networks such as Parallax.

Problems with the BTC-Style DAA

1. Slow reaction to hashrate changes
   Difficulty remains fixed for approximately two weeks. Large hashrate shifts cause slow blocks or excessively fast blocks until the next retarget.

2. Oscillation attacks and miner gaming
   Miners can raise or drop hashrate strategically near a retarget boundary to exploit lag.

3. Window-based predictability
   Because difficulty is determined by a 2016-block window, miners can observe the current window conditions and predict when difficulty will be low, encouraging chain hopping.

4. Not robust for small to medium networks
   Chains with modest hashrate experience hours of extremely fast or slow blocks, making confirmations unpredictable and harming UX, fee markets, and application-level timing assumptions.

ASERT was designed as a mathematically grounded solution to all of these issues.

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Specification

Let:

• H_ref: anchor height
• t_ref: timestamp of parent of the anchor block
• T_ref: target difficulty of the anchor block
• H_eval: evaluation height
• t_eval: evaluation timestamp
• T_next: computed target

Constants:

• ideal_block_time = 600 seconds
• halflife = 172800 seconds (2 days)
• radix = 65536 (2^16)

Polynomial coefficients:

• A = 195766423245049
• B = 971821376
• C = 5127

1. Compute deltas

heightDelta = H_eval - H_ref
timeDelta = t_eval - t_ref

2. Compute exponent

exponent = ((timeDelta - ideal_block_time * (heightDelta + 1)) * radix) / halflife

3. Separate integer and fractional parts

integerShifts = exponent >> 16
fracPart = exponent - integerShifts * radix

4. Approximate 2^(fracPart / radix)

poly = A*x + B*x^2 + C*x^3 + 2^47
factor = (poly >> 48) + radix

5. Apply multiplier to anchor target

T_temp = T_ref * factor

6. Apply integer shift

if integerShifts > 0:
    T_temp <<= integerShifts
else:
    T_temp >>= -integerShifts

7. Remove fixed point scaling

T_next = T_temp >> 16

8. Enforce bounds

1 <= T_next <= maxTarget

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Rationale

Why Replace the BTC DAA

The BTC DAA works well only under modern Bitcoin-level hashrate conditions. Its design was optimized for slow, stable CPU/GPU mining and large safety margins in block interval variance. In newer networks like Parallax, where hashrate can be extremely dynamic, the original DAA causes severe block interval instability.

ASERT was selected because it is mathematically clean, efficient, predictable, and robust even under extreme hashrate volatility.

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Comparison: BTC DAA vs ASERT

BTC DAA (Original Bitcoin)

Pros

• Simple concept: adjust difficulty based on elapsed time of long windows.
• Extremely stable on very large networks with billions of dollars of mining hardware.
• Resistant to timestamp manipulation due to long averaging window.

Cons

• Adjusts only once every 2016 blocks, causing huge delays in correction.
• Vulnerable to oscillation patterns and difficulty dips.
• Encourages miner opportunism, including chain hopping.
• Poor performance on networks with smaller or inconsistent hashrate.
• Large confirmation time variance makes DApps and wallet UX less predictable.
• Block intervals can become extremely slow for hours or days after sudden hashrate drops.

ASERT

Pros

• Adjusts difficulty on every block, providing immediate reaction to hashrate changes.
• Smooth, monotonic, and non-oscillatory difficulty curve.
• Simple closed-form formula with no need for historical windows.
• Significantly reduces miner manipulation opportunities.
• Improves confirmation predictability for users.
• Better fee market stability due to consistent block production.
• Mathematically proven exponential convergence toward target interval.
• Very lightweight: requires only a single anchor point and current block data.

Cons

• Slightly more complex implementation than BTC DAA.
• Timestamp reliability remains important, since timeDelta is part of the formula.
• Chains must pick a deterministic activation point and anchor.
• Requires careful implementation and testing, especially with big integers in EVM-style PoW chains.

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Backwards Compatibility

This is a consensus breaking change. Nodes that do not implement ASERT at the activation height will diverge from the Parallax network. A specific activation block height must be announced, and the block immediately before it must be used as the deterministic anchor:

• Anchor height = activation height - 1
• Anchor parent time = timestamp of the parent of the anchor block
• Anchor target = target of the anchor block

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Security Considerations

Reorg Resistance

ASERT increases reorg resistance due to tighter coupling between timestamps and expected schedule. Chains that drift behind schedule become progressively harder to extend.

Timestamp Abuse

Short range timestamp manipulation has limited effect due to the exponential damping. Excessive timestamp deviation is constrained by the network’s own median time rules.

Hashrate Volatility

ASERT handles:

• sudden drop-offs
• sudden surges
• miner departures
• miner arrivals

without long periods of unstable block intervals.

Denial of Service

ASERT does not rely on any long historical windows, reducing memory and computational requirements and removing known DAA-window-based DoS vectors.

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References

• BCH ASERT specification
• BCHN test vectors

[andrepatta]

Playing devil's advocate with some arguments in favor of keeping the Bitcoin-style DAA:

As the proposer of this upgrade, I want to explore the other side of the argument and present a case for why Parallax might choose to keep the classic Bitcoin Difficulty Adjustment Algorithm. Although ASERT offers strong theoretical and practical advantages, the traditional 2016-block windowing approach has important strengths that should not be dismissed. Below are the main points that deserve consideration before making a consensus-breaking change.

1. Long-term stability and proven behavior

The Bitcoin DAA has operated reliably through more than a decade of extreme global hashrate volatility, hardware cycles, geopolitical disruptions, and pool migrations. This stability is not accidental. The DAA intentionally reacts slowly so it does not chase short-term fluctuations. For a network that values predictable governance and conservative behavior, this slow adjustment can be a feature rather than a limitation.

Moving Parallax to ASERT creates a more adaptive system, but also one that depends more heavily on real-time conditions being honest and stable. The Bitcoin DAA, by contrast, is relatively indifferent to short-term noise.

2. Strong resistance to timestamp manipulation

A major benefit of the 2016-block averaging window is that timestamp irregularities are largely absorbed into the long-term average. Manipulating timestamps for advantage requires sustained, coordinated effort across many blocks, which is practically impossible without majority control.

ASERT responds to time directly and immediately. Even though protections like MTP exist, a miner with even a small fraction of hashrate can influence the short-term difficulty curve with only minor timestamp games. Under the Bitcoin DAA these same games would have almost no effect.

3. Reduces the impact of short-lived hash spikes or drops

ASERT responds instantly to sharp changes in hashrate. While this is usually positive, it also means that short-term activity from a single large miner can cause sudden difficulty shifts that punish or reward other miners unintentionally. A drop in hashrate can produce an abrupt difficulty collapse, which may re-open the door to opportunistic attacks.

The Bitcoin DAA requires a miner to participate consistently throughout a large window before they have any chance to influence difficulty. This creates a buffer that naturally discourages short-term manipulation and encourages miners to behave consistently over longer periods.

4. More consistent monetary issuance over long horizons

Bitcoin’s difficulty scheme produces a very smooth issuance curve at the macro level. Because adjustments are so gradual, the emission rate never deviates dramatically from the expected schedule. Even if blocks speed up or slow down temporarily, the impact on long-term supply is minimal.

ASERT converges more aggressively toward the 600 second schedule, but this can create more short-term variance in the number of blocks per day. At the scale of years this evens out, but on shorter horizons such as halving epochs or periods of market sensitivity, the Bitcoin DAA may provide a calmer monetary environment.

5. Simplicity and social auditability

The 2016-block retarget rule is easy to explain and easy for both technical and non-technical participants to verify:

"Every 2016 blocks, the network checks how long that period took and adjusts difficulty accordingly."

This simplicity allows a wide range of users to independently reason about the system without needing to understand polynomial approximations, fixed point arithmetic, or exponential correction formulas. ASERT is not overly complex for developers, but it does introduce a steeper conceptual barrier for the broader community.

6. Sensitivity to unreliable timestamps on young networks

Parallax relies on median time past rules to limit timestamp abuse, but ASERT's dependence on accurate timestamps means that even small irregularities in miner clocks or node configurations can influence difficulty. On a young network where miners are still geographically distributed and infrastructure is immature, this sensitivity may become an operational concern.

The Bitcoin DAA mostly ignores this category of risk by smoothing timing irregularities across very large windows.

7. Avoiding unnecessary consensus churn

Any migration to ASERT involves the selection of an anchor, new consensus rules, careful code review, test vector validation, and coordination across the ecosystem. The classic DAA is extremely simple to implement and has a very small consensus surface area. ASERT is more complex and therefore introduces extra opportunities for subtle edge-case bugs or implementation divergence.

Given that Parallax is still early in its lifecycle, it may be safer to postpone consensus complexity until the network matures.

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Conclusion

The classic Bitcoin DAA is not obsolete. It is intentionally conservative and prioritizes stability, simplicity, long-term consistency, and resistance to manipulation. ASERT provides clear benefits, especially for networks with volatile hashrates, but it also introduces new sensitivities and implementation risks. The Parallax community should carefully weigh whether the benefits of rapid responsiveness outweigh the operational and conceptual stability that the Bitcoin DAA still provides.

[andrepatta]

Over the last few days Parallax has experienced a sharp drop in total computing power. Difficulty is currently anchored around a 605 GH/s proxy while the network hash rate has fallen to roughly 140 GH/s, which is why we are seeing block times drift toward 2000 to 2400 seconds. Miners have also continued to leave the network, so it is possible this mismatch becomes even more pronounced.

I want to share my current view on how we should approach this situation and how it relates to PIP-0002.

First, I am still personally in favor of keeping the Bitcoin-style DAA. It is conservative, predictable, simple, and battle-tested. Even though it reacts slowly, the slow reaction is part of its design philosophy. Difficulty will correct itself at the next 2016-block retarget at height 18144, and that will bring block times back toward the expected schedule as long as we can reach that window.

Second, I do not believe we should rush a protocol-level change unless the chain becomes genuinely stuck. Right now the chain is moving, just very slowly. Slow blocks are painful, but they are not the same thing as a stalled chain. A consensus change like replacing the DAA is a serious decision and should only be considered if the network cannot naturally progress to the next retarget.

Third, if the chain stops progressing entirely and it becomes clear that we will never reach block 18144 under current difficulty, then I agree that we should consider migrating to ASERT with an MTP-based activation. In that scenario ASERT would act as a recovery mechanism rather than a performance upgrade. It would prevent the network from being permanently frozen if miners exit to the point where blocks can no longer be found in any reasonable timeframe.

But as long as blocks are still being mined, even slowly, my position is to let the Bitcoin-style DAA do what it was designed to do. Once we hit block 18144 difficulty will drop dramatically and block production will normalize again.

So the short version is:

• I prefer keeping the BTC-style DAA.
• If we cannot reach the next difficulty window and the chain freezes, then ASERT with MTP activation becomes a practical fallback.
• But while the chain is still progressing, even at a crawl, I do not support making a protocol change.

This keeps the network aligned with the conservative and stable philosophy that Parallax was built on, while still acknowledging a clear emergency path if the chain were ever to become completely stuck.