(as original)

This paper concerns the possibility of developing a coherent
theory of security when feasibility is associated
with expected probabilistic polynomial-time (expected PPT).
The source of difficulty is that
the known definitions of expected PPT strategies
(i.e., expected PPT interactive machines)
do not support natural results of the type presented below.

To overcome this difficulty,
we suggest new definitions of expected PPT strategies,
which are more restrictive than the known definitions
(but nevertheless
extend the notion of expected PPT non-interactive algorithms).
We advocate the conceptual adequacy of these definitions,
and point out their technical advantages.
Specifically, identifying a natural subclass of black-box simulators,
called normal, we prove the following two results:

(1) Security proofs that refer to all strict PPT adversaries
(and are proven via normal black-box simulators), extend to
provide security with respect to all adversaries that satisfy
the restricted definitions of expected PPT.

(2) Security composition theorems of the type known for strict PPT
hold for these restricted definitions of expected PPT,
where security means simulation by normal black-box simulators.

Specifically, a normal black-box simulator is required
to make an expected polynomial number of steps,
when given oracle access to any strategy,
where each oracle call is counted as a single step.
This natural property is satisfies by most known simulators
and is easy to verify.