Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Removable Weak Keys for Discrete Logarithm Based Cryptography   We describe a novel type of weak cryptographic private key that can exist in
any discrete logarithm based public-key cryptosystem set in a group of prime
order $p$ where $p-1$ has small divisors. Unlike the weak private keys based on
\textit{numerical size} (such as smaller private keys, or private keys lying in
an interval) that will \textit{always} exist in any DLP cryptosystems, our type
of weak private keys occurs purely due to parameter choice of $p$, and hence,
can be removed with appropriate value of $p$. Using the theory of implicit
group representations, we present algorithms that can determine whether a key
is weak, and if so, recover the private key from the corresponding public key.
We analyze several elliptic curves proposed in the literature and in various
standards, giving counts of the number of keys that can be broken with
relatively small amounts of computation. Our results show that many of these
curves, including some from standards, have a considerable number of such weak
private keys. We also use our methods to show that none of the 14 outstanding
Certicom Challenge problem instances are weak in our sense, up to a certain
weakness bound.

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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an