In this paper, we describe a quantum algorithm for computing an isogeny between any two supersingular elliptic curves defined over a given finite field. The complexity of our method is in Õ(p) where p is the characteristic of the base field. Our method is an asymptotic improvement over the previous fastest known method which had complexity Õ(p) (on both classical and quantum computers). We also...

SIDH is a post-quantum key exchange algorithm based on the presumed difficulty of finding isogenies between supersingular elliptic curves. However, and related cryptosystems also reveal additional information: restriction secret isogeny to subgroup curve (torsion-point information). Petit [31] was first demonstrate that torsion-point information could noticeably lower isogenies. In particular, ...

The threat of quantum computers has sparked the development a new kind cryptography to resist their attacks. Isogenies between elliptic curves are one tools used for such cryptosystems. They championed by SIKE (Supersingular isogeny key encapsulation), an alternate candidate third round NIST Post-Quantum Cryptography Standardization Process. While all candidates believed be mathematically secur...

Identity-Based Encryption is a public key cryptosystem that uses the receiver identifier information such as email address, IP name and etc, to compute private in encrypt message. A message can obtain secret corresponding with his privacy from Private Key Generator he decrypt ciphertext. In this paper, we review Boneh-Franklin’s scheme use bilinear map Weil pairing’s properties propose an ident...