Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unification modulo a partial theory of exponentiation   Modular exponentiation is a common mathematical operation in modern
cryptography. This, along with modular multiplication at the base and exponent
levels (to different moduli) plays an important role in a large number of key
agreement protocols. In our earlier work, we gave many decidability as well as
undecidability results for multiple equational theories, involving various
properties of modular exponentiation. Here, we consider a partial subtheory
focussing only on exponentiation and multiplication operators. Two main results
are proved. The first result is positive, namely, that the unification problem
for the above theory (in which no additional property is assumed of the
multiplication operators) is decidable. The second result is negative: if we
assume that the two multiplication operators belong to two different abelian
groups, then the unification problem becomes undecidable.

20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin