SIKE

SIKE, or Supersingular Isogeny Key Encapsulation, is a post-quantum public-key cryptosystem designed to secure key exchange in a world with quantum computers. It is based on the mathematics of supersingular elliptic curves and isogenies, and is part of the SIDH family.

How it works: The scheme operates over finite fields (often GF(p^2)) and uses the action of isogenies—morphisms between elliptic curves that preserve group structure—to transform public data into a shared secret. Parties generate secret isogenies of small degree, exchange public information derived from those isogenies, and then apply their secret isogenies to obtain a common elliptic-curve parameter from which a symmetric key is derived. The encapsulation mechanism allows one party to transmit a ciphertext that enables the other party to recover the shared key.

Security basis: The hardness assumption is the isogeny-path problem between supersingular elliptic curves, together with related computational problems in the endomorphism rings of such curves. These problems are believed to be resistant to quantum attacks that break many classical public-key schemes, though no known practical quantum algorithm is proven to break SIKE. The field has seen extensive cryptanalytic scrutiny and ongoing evaluation of parameter choices.

History and status: SIKE was introduced by Jao and De Feo in 2011 as a key-encapsulation variant of the SIDH framework. It was submitted to the NIST Post-Quantum Cryptography standardization process as a candidate for isogeny-based cryptography. While it has advanced in evaluation, it did not become a standard, and its practical viability relative to competing schemes remains a topic of discussion.

Parameterization and practicalities: SIKE offers multiple parameter sets that trade key sizes and performance. In practice, public keys and encapsulation capsules are larger than many classical public-key systems, and implementations require optimized elliptic-curve and isogeny arithmetic for efficiency and side-channel resistance.