Multi proxy signature schemes (MPSS) allow n proxy signers to generate a valid signature on behalf of the original signer. A new efficient self-certified MPSS with message recovery based on the Elliptic Curve Discrete Logarithm Problem (i.e., ECDLP) is proposed in this paper. A rationale for proposing a new scheme is to improve the verification process performance by combining the verification process with message recovery in one single stage (i.e., simultaneously). The security and performance analysis shows, the new scheme has many advantages over the traditional MPS schemes. These benefits include decreasing costs (i.e., certificate sizes, consumption time, and bandwidth requirements) and increasing speed.

We propose a new regularization scheme for stable numerical differentiation of noisy data defined on a bounded domain with . The method generates a sequence of smoothed (regularized) data obtained by solving a perturbed elliptic boundary-value problem. Assuming the measured data are in and the true underlying data are sufficiently smooth, we prove convergence results in the -norm, provided the noisy data converge to true data in the sense. Using the finite element method, we derive error bounds and prove convergence theorems in the case of discrete data. Numerical examples indicate noteworthy results and shed light on some possible applications in image processing and computer vision.

The aim of this paper is to present a new stable method for smoothing and differentiating noisy data defined on a bounded domain Ω ⊂ R N with N ≥ 1 . The proposed method stems from the smoothing properties of the classical diffusion equation; the smoothed data are obtained by solving a diffusion equation with the noisy data imposed as the initial condition. We analyze the stability and convergence of the proposed method and we give optimal convergence rates. One of the main advantages of this method lies in multivariable problems, where some of the other approaches are not easily generalized. Moreover, this approach does not require strong smoothness assumptions on the underlying data, which makes it appealing for detecting data corners or edges. Numerical examples demonstrate the feasibility and robustness of the method even with the presence of a large amounts of noise.