A Novel Post-Quantum Approach: "Proof-Of-Decay" (Cryptographic Half-Life) for Unmigrated Dormant UTXOs

Protecting the Bitcoin network from potential quantum computing attacks presents a critical challenge, particularly for coins with exposed keys, such as those stored in early Pay-to-PubKey (P2PK) outputs or long-dormant wallets. Historically, two primary solutions have been discussed. The first involves implementing a hard freeze, declaring unmigrated coins permanently inaccessible after a certain deadline, which raises concerns about violating property rights and punishing legitimate owners who may have lost their keys. The second option is to take no action, leaving these coins susceptible to being stolen en masse if an attacker with quantum capabilities emerges, resulting in an abrupt and potentially catastrophic increase in market supply.

A novel solution proposes introducing a cryptographic decay function tied to block height, designed to address the shortcomings of the previous approaches. Under this system, any unspent transaction output (UTXO) that remains in a vulnerable state past a designated post-quantum transition deadline would begin to lose value gradually according to a mathematical schedule, similar to radioactive decay. The process begins after a multi-year grace period during which wallet holders are encouraged to upgrade their addresses to quantum-secure formats. Once the deadline passes, affected UTXOs automatically start decaying, with a small percentage of their balance deducted at regular intervals, such as every 50,000 blocks (approximately once per year).

The satoshis "lost" through this decay can be handled in one of two ways: either burned, effectively reducing the total supply, or recycled into the coinbase reward pool, thus supporting Proof-of-Work miners and maintaining network security. This mechanism alters the game theory around quantum attacks: the reward for cracking an old key diminishes with time, undermining the economic incentive for hackers. Furthermore, the gradual nature of this decay prevents sudden shocks to market supply, fostering greater stability in the ecosystem.

For those who eventually recover access to dormant or inherited wallets, this approach offers a fairer outcome compared to a total freeze. Although the recovered balance would be reduced over time, legitimate claimants would not be deprived of their entire holdings, preserving some value even after years of inactivity.

Several technical and philosophical questions arise regarding the feasibility of this proposal. One concern is whether such a decay function could be efficiently implemented at the consensus script level without causing excessive expansion of the UTXO set. Another consideration is whether shifting from an absolute notion of ownership towards a model of time-based economic decay truly provides stronger defense against quantum threats from a game-theoretic perspective than existing alternatives. Further discussion and analysis are required to assess whether this decay or half-life concept represents a viable and innovative compromise for future-proofing Bitcoin's security.