We propose a new approach to analyzing dynamical systems that combine hyperbolic and non-hyperbolic (“center”) behavior, e.g. partially hyperbolic diffeomorphisms. A number of applications illustrate its power. We find that any ergodic automorphism of the 4-torus with two eigenvalues in the unit circle is stably Bernoulli among symplectic maps. Indeed, any nearby symplectic map has no zero Lyap...

We show that the recent structure-preserving signature (SPS) scheme of Kiltz, Pan and Wee [CRYPTO 2015], provably secure under the standard bilinear pairings group assumption SXDH, can be improved to have one less group element and one less pairing product equation in the signature verification step. Our improved SPS scheme only requires six group elements (five in one group, and one in the oth...

let $r$ be an associative ring with identity and $z^*(r)$ be its set of non-zero zero divisors.  the zero-divisor graph of $r$, denoted by $gamma(r)$, is the graph whose vertices are the non-zero  zero-divisors of  $r$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$.  in this paper, we bring some results about undirected zero-divisor graph of a monoid ring ov...

0

Abstract We say that a smooth normed space X has property (SL) , if every mapping $$f:X \rightarrow X$$ f : X → preserving the semi-inner product on is linear. It well known Hilbert and same true for finite-dimensional space. In this pa...

Privacy-preserving (PP) applications allow users to perform online daily actions without leaking sensitive information. The PP scalar product (PPSP) is one of the critical algorithms in many private applications. state-of-the-art PPSP schemes use either computationally intensive homomorphic (public-key) encryption techniques, such as Paillier achieve strong security (i.e., 128 b) or random mask...