## Journals

- Advances in Mathematics of Communications
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### Open Access Journals

AMC

Starting with Shoup's seminal paper [24], the generic group model has been an important tool in reductionist security arguments. After an informal explanation of this model and Shoup's theorem, we discuss the danger of flaws in proofs. We next describe an ontological difference between the generic
group assumption and the random oracle model for hash unctions. We then examine some criticisms that have been leveled at the generic group model and raise some questions of our own.

AMC

We take a critical look at security models that
are often used to give "provable security"
guarantees. We pay particular attention to
digital signatures, symmetric-key encryption, and
leakage resilience. We find that there has been
a surprising amount of uncertainty about what
the "right" definitions might be. Even
when definitions have an appealing
logical elegance and nicely reflect certain
notions of security, they fail to take into
account many types of attacks and do not provide a comprehensive
model of adversarial behavior.

AMC

For symmetric pairings $e : \mathbb{G} \times \mathbb{G} \rightarrow \mathbb{G}_T$, Verheul proved
that the existence of an efficiently-computable isomorphism $\phi : \mathbb{G}_T
\rightarrow \mathbb{G}$ implies that the Diffie-Hellman problems in $\mathbb{G}$ and $\mathbb{G}_T$
can be efficiently solved. In this paper, we explore the implications of
the existence of efficiently-computable isomorphisms $\phi_1 : \mathbb{G}_T
\rightarrow \mathbb{G}_1$ and $\phi_2 : \mathbb{G}_T \rightarrow \mathbb{G}_2$ for asymmetric
pairings $e : \mathbb{G}_1 \times \mathbb{G}_2 \rightarrow \mathbb{G}_T$. We also give a simplified
proof of Verheul's theorem.

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