On Optimizing The Computation Of Isogeny Via Special Points On Elliptic Curves

Supersingular isogeny based cryptography is one candidate of the post-quantum cryptography,which inherits the research achievements of ECC.However,its bottleneck is that the computational efficiency of isogeny operation is relatively low.In order to improve the efficiency,several optimization techniques for faster isogeny computation have been proposed,most of which are relied on the elliptic curve models.Inspired by these work,this thesis extends the 2-torsion point method to Huff curve model and Hessian curve model,as well as the three differential points method to Huff curve model,twisted Jacobi intersection curve model and Edwards curve model,for faster isogenous curve evaluation.In addition,the 3-isogeny computation is also optimized by using the 3-division polynomial on the twisted Jacobi intersection curve model.The above work could enrich the diversity of parameter selection and elliptic curve model selection for isogeny based cryptographic schemes.