Although advances in SHA-1 cryptanalysis have been made since the 2005 announcement of a 2 attack by Wang et al., the details of the attack have not yet been presented or verified. This note does just that. Working from Adi Shamir’s 2005 CRYPTO rump session presentation of Wang et al.’s work, this note verifies and presents the differential path and associated conditions. Although the error ana...

Not long ago it was reported m the press that Adi Shamir, from the Weizmann Institute of Science m Israel, had broken one of the first public key cryptosystems, the Merkle-Hellman knapsack System Saentific American (August 1982, p 79) reported maccurately that He did so by provmg that a mathematical problem called the knap sack problem, which had been considered e^ceedmgly dtfficult, am be solv...

The Poisson-Boltzmann (PB) equation has been extensively used to analyze the energetics and structure of proteins and other significant biomolecules immersed in electrolyte media. A new highly efficient approach for solving PB-type equations that allows for the modeling of many-atoms structures such as encountered in cell biology, virology, and nanotechnology is presented. We accomplish these e...

Image inpainting in wavelet domain refers to the recovery of an image from incomplete and/or inaccurate wavelet coefficients. To reconstruct the image, total variation (TV) models have been widely used in the literature and they produce high-quality reconstructed images. In this paper, we consider an unconstrained TV-regularized, l2-data-fitting model to recover the image. The model is solved b...

In this paper we propose an iterative method using alternating direction method of multipliers (ADMM) strategy to solve linear inverse problems in Hilbert spaces with a general convex penalty term. When the data is given exactly, we give a convergence analysis of our ADMM algorithm without assuming the existence of a Lagrange multiplier. In case the data contains noise, we show that our method ...

In this paper, we apply the alternating direction method (ADM) to solve a constrained linear least-squares problem where the objective function is a sum of two least-squares terms and the constraints are box constraints. Using ADM, we decompose the original problem into two easier least-squares subproblems at each iteration. To speed up the inner iteration, we linearize the subproblems whenever...

Image inpainting in wavelet domains refers to the recovery of an image from incomplete and/or inaccurate wavelet coefficients. To reconstruct the image, total variation (TV) models have been widely used in the literature, and they produce high-quality reconstructed images. In this paper, we consider an unconstrained, TV-regularized, 2-data-fitting model to recover the image. The model is solved...

The Alternating Direction Method of Multipliers (ADMM) has been proved to be effective for solving separable convex optimization subject to linear constraints. In this paper, we propose a Generalized Symmetric ADMM (GS-ADMM), which updates the Lagrange multiplier twice with suitable stepsizes, to solve the multi-block separable convex programming. This GS-ADMM partitions the data into two group...

A. Derivation of the proximal operation for the smoothed hinge loss By the definition of the smoothed hinge loss, we have that, for −1 ≤ y i v ≤ 0, f * i (v) = sup u∈R {uv − f i (u)} = sup u∈R uv − 1 2 (1 − y i u)