  The so-called {\em leakage-chain rule} is a very important tool used in many
security proofs. It gives an upper bound on the entropy loss of a random
variable $X$ in case the adversary who having already learned some random
variables $Z_{1},\ldots,Z_{\ell}$ correlated with $X$, obtains some further
information $Z_{\ell+1}$ about $X$. Analogously to the information-theoretic
case, one might expect that also for the \emph{computational} variants of
entropy the loss depends only on the actual leakage, i.e. on $Z_{\ell+1}$.
Surprisingly, Krenn et al.\ have shown recently that for the most commonly used
definitions of computational entropy this holds only if the computational
quality of the entropy deteriorates exponentially in
$|(Z_{1},\ldots,Z_{\ell})|$. This means that the current standard definitions
of computational entropy do not allow to fully capture leakage that occurred
"in the past", which severely limits the applicability of this notion.
  As a remedy for this problem we propose a slightly stronger definition of the
computational entropy, which we call the \emph{modulus computational entropy},
and use it as a technical tool that allows us to prove a desired chain rule
that depends only on the actual leakage and not on its history. Moreover, we
show that the modulus computational entropy unifies other,sometimes seemingly
unrelated, notions already studied in the literature in the context of
information leakage and chain rules. Our results indicate that the modulus
entropy is, up to now, the weakest restriction that guarantees that the chain
rule for the computational entropy works. As an example of application we
demonstrate a few interesting cases where our restricted definition is
fulfilled and the chain rule holds.
