Paper 2026/896

CORAL Faster Isogeny Group Action for Post-Quantum NIKE

Giacomo Borin, IBM Research - Zurich, University of Zurich

Ryan Rueger, IBM Research - Zurich, Technical University of Munich

Sina Schaeffler, IBM Research - Zurich, ETH Zurich

Abstract

There are two kinds of cryptographic group actions: restricted and unrestricted. While unrestricted actions like (qt-)PEGASIS are needed for more advanced constructions, restricted ones like dCTIDH are sufficient for instantiating a NIKE and usually much more efficient. In this work, we propose CORAL, a significantly faster algorithm to evaluate the same action as (qt-)PEGASIS, but in a restricted fashion; CORAL only computes two-dimensional $2$-isogenies to evaluate the action and outperforms both recent unrestricted (KLaPoTi, (qt-)PEGASIS) and (restricted) CSIDH-based approaches (SQALE, dCTIDH). In essence, CORAL trades off unrestrictedness for efficiency. Our unoptimised C implementation evaluates a group-action in 240 ms with a 2032-bit prime. When used to construct a non-interactive key exchange, CORAL yields an actively secure post-quantum NIKE with compact public keys (e.g. 256 bytes for 2032-bit primes).

@misc{cryptoeprint:2026/896,
      author = {Andrea Basso and Giacomo Borin and Ryan Rueger and Sina Schaeffler},
      title = {{CORAL} Faster Isogeny Group Action for Post-Quantum {NIKE}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/896},
      year = {2026},
      url = {https://eprint.iacr.org/2026/896}
}