An cryptosystem involving generating an isogeny that maps points from one elliptic curve onto another elliptic curve and publishing a public key corresponding to the isogeny

摘要

Techniques are disclosed to provide public-key encryption systems. More particularly, isogenies of Abelian varieties (e.g., elliptic curves in one dimensional cases) are utilized to provide public-key encryption systems. For example, the isogenies permit the use of multiple curves instead of a single curve to provide more secure encryption. The techniques may be applied to digital signatures and/or identity based encryption (IBE) solutions. The technique of providing public-key encryption includes the method of generating an isogeny that maps a plurality of points from a first elliptic curve onto a second elliptic curve. Composing a plurality of modular isogenies provides the isogeny without revealing any intermediate curves. The public-key corresponding to the isogeny is thus published. A message is encrypted and decrypted using an encryption-key that corresponds to the isogeny, where one of the encryption or decryption keys is a private key that is a dual isogeny of the isogeny.