Common use of Trivial Clause in Contracts

Trivial. O Theorem 4.4.1 Let = Z[σ] be an imaginary quadratic order and consider two -oriented elliptic curves (E, ι) and (E′, ι′) that belong to the same orbit under the action of Cl( ), say given in Weierstrass form and connected by an unknown ideal class [a]. Assume that E, E′, ι( ), ι′( ) are all defined over a finite field Fq. Let χ be an assigned character of with modulus m coprime to q. There exists a randomized algorithm for computing χ([a]) that is expected to use ˜ O(m3 log2 q) (4.6) bit operations and O(1) calls to ι(σ), ι′(σ).