class-group.md

the class group action: why commutativity matters the class group action is the algebraic heart of genies. it is the reason CSIDH can do non-interactive key exchange, verifiable random functions, and threshold protocols — all post-quantum, all without pairings. the key property is commutativity:…

class group the mathematical structure let O = Z[pi] be the endomorphism ring of a supersingular elliptic curve E over F_q, where pi is the Frobenius endomorphism (pi^2 = -q on the curve). the ideal class group cl(O) is a finite abelian group that acts on the set Ell(O, pi) of supersingular curves…