1,473 research outputs found
Hydrodynamic reductions of multi-dimensional dispersionless PDEs: the test for integrability
A (d+1)-dimensional dispersionless PDE is said to be integrable if its
n-component hydrodynamic reductions are locally parametrized by (d-1)n
arbitrary functions of one variable. Given a PDE which does not pass the
integrability test, the method of hydrodynamic reductions allows one to
effectively reconstruct additional differential constraints which, when added
to the equation, make it an integrable system in fewer dimensions (if
consistent).Comment: 16 page
A New Cryptosystem Based On Hidden Order Groups
Let be a cyclic multiplicative group of order . It is known that the
Diffie-Hellman problem is random self-reducible in with respect to a
fixed generator if is known. That is, given and
having oracle access to a `Diffie-Hellman Problem' solver with fixed generator
, it is possible to compute in polynomial time (see
theorem 3.2). On the other hand, it is not known if such a reduction exists
when is unknown (see conjuncture 3.1). We exploit this ``gap'' to
construct a cryptosystem based on hidden order groups and present a practical
implementation of a novel cryptographic primitive called an \emph{Oracle Strong
Associative One-Way Function} (O-SAOWF). O-SAOWFs have applications in
multiparty protocols. We demonstrate this by presenting a key agreement
protocol for dynamic ad-hoc groups.Comment: removed examples for multiparty key agreement and join protocols,
since they are redundan
Algebras, dialgebras, and polynomial identities
This is a survey of some recent developments in the theory of associative and
nonassociative dialgebras, with an emphasis on polynomial identities and
multilinear operations. We discuss associative, Lie, Jordan, and alternative
algebras, and the corresponding dialgebras; the KP algorithm for converting
identities for algebras into identities for dialgebras; the BSO algorithm for
converting operations in algebras into operations in dialgebras; Lie and Jordan
triple systems, and the corresponding disystems; and a noncommutative version
of Lie triple systems based on the trilinear operation abc-bca. The paper
concludes with a conjecture relating the KP and BSO algorithms, and some
suggestions for further research. Most of the original results are joint work
with Raul Felipe, Luiz A. Peresi, and Juana Sanchez-Ortega.Comment: 32 page
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