Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Lever Function with Adequate Indeterminacy   The key transform of the REESSE1+ asymmetrical cryptosystem is Ci = (Ai * W ^
l(i)) ^ d (% M) with l(i) in Omega = {5, 7, ..., 2n + 3} for i = 1, ..., n,
where l(i) is called a lever function. In this paper, the authors give a
simplified key transform Ci = Ai * W ^ l(i) (% M) with a new lever function
l(i) from {1, ..., n} to Omega = {+/-5, +/-6, ..., +/-(n + 4)}, where "+/-"
means the selection of the "+" or "-" sign. Discuss the necessity of the new
l(i), namely that a simplified private key is insecure if the new l(i) is a
constant but not one-to-one function. Further, expound the sufficiency of the
new l(i) from four aspects: (1) indeterminacy of the new l(i), (2) insufficient
conditions for neutralizing the powers of W and W ^-1 even if Omega = {5, 6,
..., n + 4}, (3) verification by examples, and (4) running times of the
continued fraction attack and W-parameter intersection attack which are the two
most efficient of the probabilistic polytime attack algorithms so far. Last,
the authors elaborate the relation between a lever function and a random
oracle.

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The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas