No reduction from AGM to GGM

Unconditional · KZ22

Statement

Under the standard formalizations of the two models, hardness in the AGM does not imply hardness in the GGM, and a generic reduction in the AGM need not yield a corresponding reduction in the GGM — KZ22. This refutes, under those formalizations, the transfer claimed by FKL18.

Notes

• Under the alternative formalization of generic and algebraic computation of JM24, the transfer holds for most algebraic analyses in the literature.