Transforming the POKE  public key  Protocol into a Key Encapsulation Mechanism

Nouhou Abdou Idris; Yunusa Abdulsalam; Mustapha Hedabou

Paper 2025/1616

Transforming the POKE public key Protocol into a Key Encapsulation Mechanism

Nouhou Abdou Idris

, Mohammed VI polytechnic University

Yunusa Abdulsalam

Mustapha Hedabou

Abstract

The inherent presence of large-scale quantum computers is deemed to threaten the traditional public-key cryptographic systems. As a result, NIST has necessitated the development of post-quantum cryptography (PQC) algorithms. Isogeny-based schemes have compact key sizes; however, there have been some fundamental vulnerabilities in the smooth-degree isogeny systems. Therefore, the literature has concentrated its efforts on higher-dimensional isogenies of non-smooth degrees. In this work, we present POKE-KEM, a key encapsulation mechanism (KEM) derived from the POKE public-key encryption (PKE) scheme via a Fujisaki-Okamoto (FO) transformation with its corresponding optimized security levels during transformation. Despite POKE’s efficiency advantages, its current formulation provides only IND-CPA security, limiting practical deployment where adaptive chosen-ciphertext security is essential. The resulting POKE-KEM construction achieves IND-CCA security under the computational hardness of the C-POKE problem in both the random oracle model (ROM) and quantum random oracle model (QROM). Our implementation demonstrates significant practical advantages across all NIST security levels (128, 192, and 256 bits), supporting the practical viability of POKE-KEM for post-quantum cryptographic deployments. We provide a comprehensive security analysis including formal proofs of correctness, rigidity, and IND-CCA security. Our underlying construction leverages the difficulty of recovering isogenies with unknown, non-smooth degrees, resistant to known quantum attacks

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Post-quantum cryptography Isogeny-based cryptography Key encapsulation mechanism Fujisaki-Okamoto transform.
Contact author(s): abdou idris-nouhou @ um6p ma
History: 2025-09-11: approved; 2025-09-08: received; See all versions
Short URL: https://ia.cr/2025/1616
License: CC BY

BibTeX

@misc{cryptoeprint:2025/1616,
      author = {Nouhou Abdou Idris and Yunusa Abdulsalam and Mustapha Hedabou},
      title = {Transforming the {POKE}  public key  Protocol into a Key Encapsulation Mechanism},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1616},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1616}
}