Paper 2025/1439

A Note on the Post-Quantum Security of Identity-Based Encryption on Isogenous Pairing Groups

Abstract

The development of cryptographic schemes which remain secure in the post-quantum era is an urgent challenge, particularly in light of the growing ubiquity of low-power devices and the looming threat of quantum computing. Identity-Based Encryption (IBE) offers a compelling alternative to traditional Public Key Infrastructures by simplifying key management, but most classical IBE schemes rely on number-theoretic assumptions that are vulnerable to quantum attacks. In response, Koshiba and Takashima proposed a novel approach based on Isogenous Pairing Groups (IPGs) [ 12 ], claiming partial quantum resistance. In this work, we critically examine their construction and security claims and investigate upon the security in standard security notions. We show that the proposed scheme, despite its theoretical elegance, reduces to the Elliptic Curve Dis- crete Logarithm Problem (ECDLP) on supersingular curves, which can be broken in polynomial time by quantum algorithms in the IND-ID-CPA setting and in subexponential time classically in the authors security models. Our analysis reveals structural weaknesses inherent to the IPG framework, such as the use of explicit group elements in prime-order groups and exploitable isogeny homomorphisms, which undermine the post-quantum security of isogeny based cryptography. These findings suggest that IPG-based constructions, which use more than a single point per pairing group, are unlikely to provide robust post-quantum security. In Koshiba and Takashima’s proposed IBE system, we can directly observe this, when paying regards to not only the IBE’s Master Secret Key but also Users’ Secret Keys.