Isogeny-Based Cryptography and the Rise and Fall of SIKE

Isogeny-based cryptography was once the great hope for post-quantum schemes with tiny keys. Then, in 2022, the leading candidate SIKE was dramatically broken in a single weekend. The story holds important lessons for anyone trusting new cryptography.

What Are Isogenies?

An isogeny is a special map between elliptic curves. Isogeny-based cryptography builds keys by walking through a vast graph of curves connected by these maps. The security rests on the difficulty of finding the path between two curves — a problem with no known efficient classical or quantum solution.

The appeal was enormous: isogeny schemes like SIKE offered public keys of only a few hundred bytes, far smaller than lattice or code-based alternatives.

The SIKE Break

In 2022, a paper by Castryck and Decru showed that SIKE's underlying problem could be solved efficiently using techniques from algebraic geometry. The attack broke SIKE in minutes on a laptop. After fifteen years of study, the scheme fell in a weekend.

This was not a failure of the post-quantum competition — it was the competition working. SIKE was always considered a higher-risk candidate, and NIST had not selected it as a primary standard. But it underscored how quickly new mathematics can overturn assumptions.

Lessons for the Quantum Transition

1. Newer is riskier. Lattice cryptography has more cryptanalysis than isogenies did, but no family is immune to surprise.
2. Use hybrid mode. Pair any new scheme with a classical one so a break does not collapse security entirely.
3. Diversify. Do not bet everything on a single mathematical family.
4. Build crypto-agility. Be able to remove a broken algorithm quickly.

What Survives

Research continues on other isogeny constructions, notably CSIDH and its descendants, which use a different mathematical structure. They remain experimental and are not yet standardised. For production, the safe choice in 2026 is still NIST's lattice-based standards (ML-KEM, ML-DSA) with hash-based SLH-DSA as a conservative backup.

The Takeaway

The SIKE break is a humbling reminder: cryptography advances by breaking things. The post-quantum standards are our best current bet, but they are not certainties. Treat them as such — layer your defences, monitor the research, and stay agile enough to respond when the next surprise arrives.