Optimization of isogeny computation algorithms for post-quantum cryptography
Mohammed El Baraka, Siham Ezzouak · Scientific African · 2025
Isogeny-based cryptography has emerged as a strong candidate for post-quantum security due to the believed hardness of finding isogenies between supersingular elliptic curves. However, an ongoing challenge is the efficient computation of isogenies in practical cryptographic protocols such as SIDH or SIKE. In this work, we present new algorithmic optimizations for isogeny computation, notably by leveraging Fast Fourier Transform (FFT) techniques for polynomial arithmetic and by exploiting endomorphisms inherent to supersingular curves. We provide detailed mathematical derivations, analyze theoretical complexities, and validate the performance gains through experimental results. Our findings indicate a substantial efficiency improvement, making isogeny-based systems more feasible for real-world post-quantum applications.