Cryptanalysis of Some Self-Synchronous Chaotic Stream Ciphers and Their Improved Schemes

In this paper, a cryptanalysis method that combines a chosen-ciphertext attack with a divide-and-conquer attack by traversing multiple nonzero component initial conditions (DCA-TMNCIC) is proposed. The method is used for security analysis of [Formula: see text]-D ([Formula: see text]) self-synchronous chaotic stream ciphers that employ a product of two chaotic variables and three chaotic variables ([Formula: see text]-D SCSC-2 and [Formula: see text]-D SCSC-3), taking 3-D SCSC-2 as a typical example for cryptanalysis. For resisting the combinational effect of the chosen-ciphertext attack and DCA-TMNCIC, several improved chaotic cipher schemes are designed, including 3-D SCSC based on a nonlinear nominal system (3-D SCSC-NNS) and [Formula: see text]-D SCSC based on sinusoidal modulation ([Formula: see text]-D SCSC-SM ([Formula: see text])). Theoretical security analysis validates the improved schemes.

The genus of graphs associated with vector spaces

Let [Formula: see text] be a k-dimensional vector space over a finite field [Formula: see text] with a basis [Formula: see text]. The nonzero component graph of [Formula: see text], denoted by [Formula: see text], is a simple undirected graph with vertex set as nonzero vectors of [Formula: see text] such that there is an edge between two distinct vertices [Formula: see text] if and only if there exists at least one [Formula: see text] along which both [Formula: see text] and [Formula: see text] have nonzero scalars. In this paper, we find the vertex connectivity and girth of [Formula: see text]. We also characterize all vector spaces [Formula: see text] for which [Formula: see text] has genus either 0 or 1 or 2.

On nonzero component graph of vector spaces over finite fields

In this paper, we study nonzero component graph [Formula: see text] of a finite-dimensional vector space [Formula: see text] over a finite field [Formula: see text]. We show that the graph is Hamiltonian and not Eulerian. We also characterize the maximal cliques in [Formula: see text] and show that there exists two classes of maximal cliques in [Formula: see text]. We also find the exact clique number of [Formula: see text] for some particular cases. Moreover, we provide some results on size, edge-connectivity and chromatic number of [Formula: see text].

THE STANDARD "STATIC" SPHERICALLY SYMMETRIC ANSATZ WITH PERFECT FLUID SOURCE REVISITED

Considering the standard "static" spherically symmetric ansatz ds2 = −B(r) dt2 + A(r) dr2 + r2 dΩ2 for Einstein's equations with perfect fluid source, we ask how we can interpret solutions where A(r)andB(r) are not positive, as they must be for the static matter source interpretation to be valid. Noting that the requirement of Lorentzian signature implies A(r) B(r) > 0, we find two possible interpretations: (i) The nonzero component of the source four-velocity does not have to be u0. This provides a connection from the above ansatz to the Kantowski–Sachs (KS) space–times. (ii) Regions with negative A(r) and B(r) of "static" solutions in the literature must be interpreted corresponding to the tachyonic source. The combinations of source type and four-velocity direction result in four possible cases. One is the standard case, one is identical to the KS case, and two are tachyonic. The dynamic tachyonic case was anticipated in the literature, but the static tachyonic case seems to be new. We derive Oppenheimer–Volkoff-like equations for each case, and find some simple solutions. We conclude that new "simple" black hole solutions of the above form, supported by a perfect fluid, do not exist.

Comment on: Curling rock dynamics - The motion of a curling rock: inertial vs. noninertial reference frames

We examine the approach used and the results presented in a recent publication(Can. J. Phys. 76, 295 (1998))in which (i) a noninertial reference frame is used to examine the motion ofa curling rock, and (ii) the lateral motion of a curling rock isattributed to left-right asymmetry in the force acting on the rock.We point out the important differences between describing the motionin an inertial frame as opposed to a noninertial frame.We show that a force exhibiting left-right asymmetryin an inertial frame cannot explain the lateral motion of a curlingrock. We also examine, as was apparently done in the recent publication,an effective force that has left-right asymmetry in a noninertial, rotating frame. We show that such a force is not left-right asymmetric in an inertial frame, and that anylateral motion of a curling rock attributed to the effective forcein the noninertial frame is actually due to a real force, in aninertial frame, which has a net nonzero component transverse to the velocityof the center of mass. We inquire as to the physical basis for thetransverse component of this real force. We also examine the motion ofa rotating cylinder sliding over a smooth surface for which there isno melting: we show that the motion is easily analyzed in an inertialframe and that there is little to be gained by considering a rotating frame.We relate the results for this simple case to the more involved problemof the motion of a curling rock: we find that the motion of curling rocksis best studied in inertial frames. Perhaps most importantly, we showthat the approach taken and the results presented in the recent publicationlead to predicted motions of curling rocks that are indisagreement with observed motions of real curling rocks.PACS Nos.: 46.00, 01.80+b