In this paper, we construct super-optimal pairings with efficiently computable endomorphisms. We first consider elliptic curves E/Fq: y2=x3+B and construct super-optimal pairings with automorphisms and Frobenius endomorphisms. In the case of (3,k)=1, these super-optimal pairings can be computed using log2r/φ(3k) Miller iterations, with k the embedding degree. This Miller loop length is only half of that of optimal pairings. Then we consider elliptic curves E'/Fq: y2=x3+u6B and give super-optimal pairings with efficiently computable endomorphisms constructed by Galbraith et al. In the case of (6, k)=1, these super-optimal pairings can be computed by log2r/φ(12k)Miller iterations, with k the embedding degree. This Miller loop length is only 1/4 of that of optimal pairings.
Auto-focus is an important technique for auto reconstruction of digital holograms, and works by focusing criterion function which influences the effect of the autofocus greatly. Aiming at Marine Microorganism holograms, this paper proposes a new focused criterion function established according to characteristics of detail discrete degree in reconstruction image changing with FD. Simulation results illustrate that, the proposed method, compared with several existing methods, has better single peak, higher sensibility and higher signal to noise ratio (SNR). The new method can realize autofocus of reconstruction distance to implement auto reconstruction of holograms.
Based on a new smoothing function of the well-known nonsmooth FB (Fischer-Burmeis-ter) function, a smoothing Newton-type method for second-order cone programming problems is presented in this paper. The features of this method are following: firstly, the starting point can be chosen arbitrarily; secondly, at each iteration, only one system of linear equations and one line search are performed; finally, global, strong convergence and Q-quadratic convergent rate are obtained. The numerical results demonstrate the effectiveness of the algorithm.
A secure electronic protocol, which can be used for electronic voting and electronic bidding, is proposed. The protocol is based on a new cryptographical model called secure multi-party proof that allows any players and a verifier to securely compute a function in the following sense: each of the players learns nothing about other players’ input and nor any information about the value of , and the verifier obtains the value of and its validity but learns nothing about the input of any of the players. In this paper, we firstly define and construct a secure multi-party proof for any polynomial time function with semi-honest participants and verifier, then construct our secure electronic protocol.
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