Recent work at Eurocrypt 2025 by Basso and Maino introduced POKÉ, an isogeny-based public key encryption (PKE) scheme. POKÉ shows how two parties can derive a shared secret on a higher-dimensional, SIDH-like commutative diagram via basis evaluations, giving the fastest isogeny-based PKE to date with performance comparable to the original SIDH. In this paper we present PIKE, a new isogeny-based PKE obtained by tweaking the POKÉ design. Our key change is to use pairings to derive the shared secret while preserving post-quantum security. This brings two benefits: (i) decryption is directly faster, and (ii) by relaxing the required prime form, we can choose smaller primes, further improving overall runtime. We provide a proof-of-concept implementation in SageMath. Under the NIST I setting, our benchmarks show speedups of \(1.30\times \) (key generation), \(1.24\times \) (encryption), and \(1.47\times \) (decryption) over POKÉ, while maintaining competitive public key and ciphertext sizes.

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PIKE: Faster Isogeny-Based Public Key Encryption with Pairing-Assisted Decryption

  • Shiping Cai,
  • Mingjie Chen,
  • Yi-Fu Lai,
  • Kaizhan Lin

摘要

Recent work at Eurocrypt 2025 by Basso and Maino introduced POKÉ, an isogeny-based public key encryption (PKE) scheme. POKÉ shows how two parties can derive a shared secret on a higher-dimensional, SIDH-like commutative diagram via basis evaluations, giving the fastest isogeny-based PKE to date with performance comparable to the original SIDH. In this paper we present PIKE, a new isogeny-based PKE obtained by tweaking the POKÉ design. Our key change is to use pairings to derive the shared secret while preserving post-quantum security. This brings two benefits: (i) decryption is directly faster, and (ii) by relaxing the required prime form, we can choose smaller primes, further improving overall runtime. We provide a proof-of-concept implementation in SageMath. Under the NIST I setting, our benchmarks show speedups of \(1.30\times \) (key generation), \(1.24\times \) (encryption), and \(1.47\times \) (decryption) over POKÉ, while maintaining competitive public key and ciphertext sizes.