Isoga: An Isogeny-Based Quantum-Resist Searchable Encryption Scheme Against Keyword Guessing Attacks

Abstract

Driven by cloud computing technologies, public-key encryption with keyword search (PEKS) is becoming a common practice from aspects of the Industrial Internet of Things, smart healthcare, vehicular social networks, and so on. However, a dozen years of PEKS development is accompanied by some security and privacy issues in the encrypted data search and access processes. The keyword guessing attack is a typical user privacy threat model, that is, an adversary could guess the user’s retrieval keyword given a search trapdoor. On the other hand, the emergence of quantum computers make traditional PEKS schemes no longer secure. Although scholars put forward some postquantum secure PEKS schemes, these schemes are based on lattice cryptography with a larger key size. To the best of our knowledge, there is no quantum-resist PEKS scheme established on elliptic curve cryptography. This article utilizes PEKS with designated tester primitive and quantum resistance of isogeny. Then, we put forward a postquantum searchable encryption scheme named Isoga, which fights against keyword guessing attacks. We prove Isoga’s searchable ciphertext security and trapdoor indistinguishability under isogeny-related difficult assumptions. Performance evaluation indicates that the Isoga scheme is more practical in the quantum environment, considering seven schemes’ security properties, communication cost, and computing overload among.