Isogeny-Based Cryptography: A Promising Post-Quantum Technique

Recent advances in quantum computing have made existing public key cryptosystems vulnerable to enormous security threats. Therefore, numerous efforts have been exploring post-quantum cryptographic techniques to address the emergence of quantum computing. We focus on one promising post-quantum cryptography known as isogeny-based cryptography, first by reviewing some concepts of the elliptic curve isogeny, and then, we present three major methods for constructing isogeny-based difficult problems. Then, we present some existing isogeny-based cryptographic primitives, such as signature and key exchange, and analyze their advantages and disadvantages. Finally, we discuss a few major challenges of isogeny research that, we hope, will attract more attention to isogeny-based cryptography.