Bitcoin Devs Should Be Learning Isogeny Cryptography

Isogeny-based cryptography (IBC) is presented as the most promising post-quantum replacement for classical elliptic curve cryptography in Bitcoin. Unlike hash-based signatures (the current leading PQC candidate), isogenies preserve algebraic structure that enables key-tweaking, BIP32 HD wallet derivation, and silent payments — features that most PQC schemes forfeit. SQIsign offers the smallest pubkey+signature sizes of any NIST PQC candidate (213 bytes at NIST-I), while the newer PRISM scheme offers simpler implementation at comparable sizes. The 2022 SIDH attack is contextualized: it did not break most IBC systems and actually accelerated the field by rediscovering Kani's Lemma. Isogeny rerandomization is shown to generalize taproot key tweaking, BIP32 derivation, and silent payments into a single quantum-safe primitive. Drawbacks include slow verification (>1ms per signature), malleable signatures in SQIsign, lack of compact multisig schemes, difficulty generating NUMS curves, and a steep mathematical learning curve. Bitcoin developers, businesses, custodians, and investors are urged to invest in IBC research now.