  D\'ech\`ene has proposed generalized Jacobians as a source of groups for
public-key cryptosystems based on the hardness of the Discrete Logarithm
Problem (DLP). Her specific proposal gives rise to a group isomorphic to the
semidirect product of an elliptic curve and a multiplicative group of a finite
field. We explain why her proposal has no advantages over simply taking the
direct product of groups. We then argue that generalized Jacobians offer poorer
security and efficiency than standard Jacobians.
