Ristenpart et al. showed that the limitation of the indifferentiabilitytheorem of Maurer et al. which does not cover all multi stage security notions

but covers only single stage security notions, defined a new concept (reset

indifferentiability), and proved the reset indifferentiability theorem, which

is an analogy of the indifferentiability theorem covers all security

notions S: if H^U is reset indifferentiable from RO, for any security notion,

a cryptosystem C is at least as secure in the U model as in the RO model.

Unfortunately, they also proved the impossibility of H^U being reset

indifferentiable from a RO where H is a one-pass hash function such as ChopMD

and Sponge constructions.

In this paper, we will propose a new proof of molular approach instead of the

RO methodology, Reset Indifferentiability from Weakened Random Oracle, called

as the WRO methodology, in order to ensure the security of C with H^U,

salvaging ChopMD and Sponge. The concrete proof procedure of the WRO

methodology is as follows:

1. Define a new concept of WRO instead of RO,

2. Prove that H^U is reset indifferentiable from a WRO, (here an example of H

is ChopMD and Sponge), and

3. Prove that C is secure in the WRO model.

As a result we can prove that C with H^U is secure by combining the results of

Steps 2, 3, and the theorem of Ristenpart et al. Moreover, for public-key

encryption (as cryptosystem C) and chosen-distribution attack we will prove

that C(WRO) is secure, which implies the appropriateness of the new concept of

the WRO model.