SQIsign is blockchain friendly but also very new, I would recommend adding a hash-based backup key in case an attack on SQIsign is found in the future (recall that SIDH broke over the span of a weekend https://eprint.iacr.org/2022/975.pdf).
Backup keys can be added in the form of a Merkle tree where one branch would contain the SQIsign public key and the other the public key of the recovery hash-based scheme. For most transactions it would only add one bit to specify the SQIsign branch.
The hash-based method could be Sphincs+, which is standardized by NIST but requires adding extra code, or Lamport, which is not standardized but can be verified on-chain with OP-CAT.

On Sunday, June 9, 2024 at 12:07:16 p.m. UTC-4 Hunter Beast wrote:
The motivation for this BIP is to provide a concrete proposal for adding quantum resistance to Bitcoin. We will need to pick a signature algorithm, implement it, and have it ready in event of quantum emergency. There will be time to adopt it. Importantly, this first step is a more substantive answer to those with concerns beyond, "quantum computers may pose a threat, but we likely don't have to worry about that for a long time". Bitcoin development and activation is slow, so it's important that those with low time preference start discussing this as a serious possibility sooner rather than later.

This is meant to be the first in a series of BIPs regarding a hypothetical "QuBit" soft fork. The BIP is intended to propose concrete solutions, even if they're early and incomplete, so that Bitcoin developers are aware of the existence of these solutions and their potential.

This is just a rough draft and not the finished BIP. I'd like to validate the approach and hear if I should continue working on it, whether serious changes are needed, or if this truly isn't a worthwhile endeavor right now.

The BIP can be found here:
https://github.com/cryptoquick/bips/blob/p2qrh/bip-p2qrh.mediawiki

Thank you for your time.

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