Measuring Algorithmic Complexity in Chaotic Lasers

Thanks to the simplicity and robustness of its calculation methods, algorithmic (or Kolmogorov) complexity appears as a useful tool to reveal chaotic dynamics when experimental time series are too short and noisy to apply Takens’ reconstruction theorem. We measure the complexity in chaotic regimes, with and without extreme events (sometimes called optical rogue waves), of three different all-solid-state lasers: Kerr lens mode locking femtosecond Ti:Sapphire (“fast” saturable absorber), Nd:YVO4 [Formula: see text] Cr:YAG (“slow” saturable absorber) and Nd:YVO4 with modulated losses. We discuss how complexity characterizes the dynamics in an understandable way in all cases, and how it provides a correction factor of predictability given by Lyapunov exponents. This approach may be especially convenient to implement schemes of chaos control in real time.

Projective Reconstruction in Algebraic Vision

We discuss the geometry of rational maps from a projective space of an arbitrary dimension to the product of projective spaces of lower dimensions induced by linear projections. In particular, we give an algebro-geometric variant of the projective reconstruction theorem by Hartley and Schaffalitzky.

Asynchronous Group Authentication Based on Geometric Approach

Individual authentication in air warfare is used to check whether a single participant is a legal member of the predefined group but not determine all participants at one time. An asynchronous (m, t, n) group authentication protocol is proposed based on multidimensional sphere reconstruction theorem of space analytic geometry without making any computational assumption, where m is the number of participants, t is threshold value, and n is the number of members. The proposed protocol can determine whether all participants belong to the predefined group at one time, which is applicable to batch verification prior to individual authentication. The center’s coordinate of (t-1)-dimensional sphere is treated as the shared secret and the coordinate of the point on the surface of the sphere, multiplied by a random blind factor, is issued to all members as their tokens. If m participants can reconstruct the shared secret by utilizing their tokens, indicate that there is not any invalid participant, otherwise perform individual authentication. Analyses show the proposed scheme can not only rule out the illegal outsider but also resist up to t-1 group member conspiring to forge a valid token for an outsider. In addition, compared with other schemes the proposed scheme is more applicable for air warfare network, with light-weight computation, flexible distribution, and high information rate.