Against Allowing Quantum Recovery of Bitcoin

In a recent discussion on the Bitcoin Development Mailing List, an intriguing point was raised concerning the implications of an Elliptic Curve Discrete Logarithm Problem (ECDLP) breaker on a modified version of Taproot that mandates script-path spending while disallowing key-path spending. The conversation delves into a hypothetical scenario where an ECDLP breaker exists, positing its impact on Taproot's security model.

The essence of the debate revolves around how an honest keyholder constructs a public key (Q = P_N + H(P_N||S)G), where (P_N) represents a Nothing-Up-My-Sleeve (NUMS) internal key, and the combined operation involves a hash function and elliptic curve group generator (G). The concern is whether an adversary equipped with an ECDLP breaker could undermine the security by deducing the discrete logarithm of (Q), albeit the requirement to unveil a hash commitment complicates direct exploitation of this vulnerability.

The discourse further explores the necessity for the attacker to generate a new public key (Q = P_2 +H(P_2||S_2)G) under the constraint of revealing a hash commitment to a tweak, which adheres to conventional Taproot rules. This nuance underscores the potential resilience of such a system against attacks, given the pre-requisite for the attacker to predetermine (P_2) prior to hashing. An alternative suggestion mooted in the discussion includes disabling NUMS, which might present a viable mitigation strategy in this outlined scenario.

Additionally, the conversation briefly touches upon the broader implications for cryptographic security in the advent of quantum computing advancements, particularly concerning the robustness of SHA2 against potential quantum algorithm breakthroughs capable of efficiently finding preimages. This speculative inquiry hints at the need for the cryptographic community to contemplate extreme adversarial capabilities and their ramifications on established security paradigms.

The exchange encapsulates a detailed technical analysis aimed at scrutinizing the security implications of hypothetical alterations to the Taproot protocol in the face of advanced cryptographic attack vectors, emphasizing the ongoing effort within the Bitcoin development community to anticipate and fortify against emergent threats.