Paper 2025/1458

INKE: Isogeny-Based PKE Using Intermediate Curves

Won Kim, Korea University

Changmin Lee, Korea University

Suhri Kim, Sungshin Women's University

Seokhie Hong, SmartM2M

Sangjin Lee, Korea University

Abstract

POKE (POint-based Key Exchange), proposed by Basso and Maino at Eurocrypt 2025, is currently the fastest known isogeny-based public-key encryption scheme. Although POKE is secure against currently known key-recovery attacks, there is no known reduction from key-recovery security to IND-CPA security. In this work, we propose INKE, a variant of POKE that replaces torsion points in the encryption process with intermediate elliptic curves. This modification enables a quantum reduction from key-recovery security to IND-CPA security in the algebraic isogeny model (AIM), while maintaining the practical performance. Although INKE is overall slower than POKE and has larger public-key and ciphertext sizes, it remains more efficient than other group-action-based key exchange protocols such as CSIDH and CORAL that admit reductions from key-recovery security to shared-secret security in algebraic group action model (AGAM). To illustrate the practical overhead of INKE compared to POKE, we provide an optimized C implementation together with detailed benchmark comparisons at each security level.

@misc{cryptoeprint:2025/1458,
      author = {Hyeonhak Kim and Won Kim and Changmin Lee and Suhri Kim and Seokhie Hong and Sangjin Lee},
      title = {{INKE}: Isogeny-Based {PKE} Using Intermediate Curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1458},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1458}
}