Isogeny-based cryptosystems (problem 3)

Solve Decisional Diffie-Hellman (DDH) in the context of CSIDH: Let E0E_0 be a supersingular elliptic curve defined over Fp\mathbb F_p with endomorphism ring Z[π]\mathbb Z[\pi]. Distinguish between triples (a∗E0,b∗E0,c∗E0)(\mathfrak a * E_0, \mathfrak b* E_0,\mathfrak c* E_0) and triples (a∗E0,b∗E0,ab∗E0)(\mathfrak a * E_0, \mathfrak b* E_0,\mathfrak a\mathfrak b * E_0) where a,b,c\mathfrak a, \mathfrak b, \mathfrak c are ideals in Z[π]\mathbb Z[\pi] of odd norm.

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