Isogeny-Based Cryptography: SIKE and Lessons Learned

Isogeny-based cryptography once seemed promising, offering tiny key sizes. Then SIKE was broken. The SynX quantum-resistant wallet uses NIST-standardized algorithms that survived this lesson.

SIKE was not the only casualty: which post-quantum algorithms have been broken.

What Were Isogenies?

Isogenies are mappings between elliptic curves:

• Mathematical structures preserving curve properties
• Computing isogenies in one direction is hard
• Promised very compact keys
• Used for SIDH/SIKE key exchange

SIKE's Advantages

SIKE (Supersingular Isogeny Key Encapsulation) offered:

• Smallest key sizes of any PQC candidate (~200 bytes)
• Similar to ECDH key sizes
• Elegant mathematical structure
• Advanced to NIST Round 4

The 2022 Break

The attack used:

• Mathematical structure SIKE relied on
• Techniques from 1990s number theory
• Standard laptop sufficient

Lessons for Cryptography

• Novel mathematical structures carry unknown risks
• Even extensive analysis can miss attacks
• Conservative choices (lattice, hash-based) are safer
• NIST process correctly identified this as "alternate"

Why SynX Chose Conservative Algorithms

The SynX quantum-resistant wallet uses:

• Kyber: Lattice-based, decades of study
• SPHINCS+: Hash-based, minimal assumptions
• Both were selected by NIST in 2022 and standardised in 2024, Kyber as ML-KEM (FIPS 203) and SPHINCS+ as SLH-DSA (FIPS 205)

Ongoing Isogeny Research

Post-SIKE, researchers explore:

• New isogeny-based constructions
• Defenses against the known attack
• Different curve families
• But trust must be rebuilt

Algorithm Selection Philosophy

The SynX quantum-resistant wallet prioritizes:

• Well-studied mathematical foundations
• Conservative security margins
• Primary NIST selections only
• Diversity in cryptographic assumptions

Frequently Asked Questions

Could Kyber be broken like SIKE?

Possible but unlikely. Lattice problems have decades of study without practical attacks. SIKE was newer and less understood.

How does SynX stay safe from future breaks?

Cryptographic agility allows algorithm updates. The SynX quantum-resistant wallet can migrate if needed.