CSIDH and Its Surface Sample Clauses

CSIDH and Its Surface. CSIDH works with the smaller (commutative) subring Endp(E) of End(E), which are rational endomorphisms of a supersingular elliptic curve E. This sub- ring Endp(E) is isomorphic to an order O ⊂ OK. As both [N ] and π are defined C O E O ⊂ ∈ E O ∈ E O O ⊂ O ∈ C O over Fp, we get Z[π] Endp(E). To be more precise, the CSIDH protocol is based on the commutative action of the class group l( ) on the set llp( ) of supersingular elliptic curves E such that Endp(E) is isomorphic to the specific order K. The group action for an ideal class [a] l( ) maps a curve E llp( ) to another curve [a] E llp( ) (see Sect. 2.2). Furthermore, the CSIDH group action is believed to be a hard homogeneous space [13] that allows a Xxxxxx-Xxxxxx-Xxxxxxx-like key agreement protocol with commutative diagram.
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