Towards Minimizing Memory Requirement for Implementation of Hyperelliptic Curve Cryptosystems

Author(s):  
Pradeep Kumar Mishra ◽  
Pinakpani Pal ◽  
Palash Sarkar
2020 ◽  
pp. 1-23
Author(s):  
MICHELE BOLOGNESI ◽  
NÉSTOR FERNÁNDEZ VARGAS

Abstract Let C be a hyperelliptic curve of genus $g \geq 3$ . In this paper, we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on C with trivial determinant. In order to do this, we describe a fibration of (a birational model of) the moduli space, whose fibers are GIT quotients $(\mathbb {P}^1)^{2g}//\text {PGL(2)}$ . Then, we identify the restriction of the theta map to these GIT quotients with some explicit degree 2 osculating projection. As a corollary of this construction, we obtain a birational inclusion of a fibration in Kummer $(g-1)$ -varieties over $\mathbb {P}^g$ inside the ramification locus of the theta map.


1981 ◽  
Vol 82 ◽  
pp. 1-26
Author(s):  
Daniel Comenetz

Let X be a nonsingular algebraic K3 surface carrying a nonsingular hyperelliptic curve of genus 3 and no rational curves. Our purpose is to study two algebraic deformations of X, viz. one specialization and one generalization. We assume the characteristic ≠ 2. The generalization of X is a nonsingular quartic surface Q in P3 : we wish to show in § 1 that there is an irreducible algebraic family of surfaces over the affine line, in which X is a member and in which Q is a general member. The specialization of X is a surface Y having a birational model which is a ramified double cover of a quadric cone in P3.


2010 ◽  
Vol 19 (08) ◽  
pp. 1665-1687 ◽  
Author(s):  
MOHAMMAD REZA HOSSEINY FATEMI ◽  
HASAN F. ATES ◽  
ROSLI SALLEH

The sub-pixel motion estimation (SME), together with the interpolation of reference frames, is a computationally extensive part of the H.264 encoder that increases the memory requirement 16-times for each reference frame. Due to the huge computational complexity and memory requirement of the H.264 SME, its hardware architecture design is an important issue especially in high resolution or low power applications. To solve the above difficulties, we propose several optimization techniques in both algorithm and architecture levels. In the algorithm level, we propose a parabolic based algorithm for SME with quarter-pixel accuracy which reduces the computational budget by 94.35% and the memory access requirement by 98.5% in comparison to the standard interpolate and search method. In addition, a fast version of the proposed algorithm is presented that reduces the computational budget 46.28% further while maintaining the video quality. In the architecture level, we propose a novel bit-serial architecture for our algorithm. Due to advantages of the bit-serial architecture, it has a low gate count, high speed operation frequency, low density interconnection, and a reduced number of I/O pins. Also, several optimization techniques including the sum of absolute differences truncation, source sharing exploiting and power saving techniques are applied to the proposed architecture which reduce power consumption and area. Our design can save between 57.71–90.01% of area cost and improves the macroblock (MB) processing speed between 1.7–8.44 times when compared to previous designs. Implementation results show that our design can support real time HD1080 format with 20.3 k gate counts at the operation frequency of 144.9 MHz.


2016 ◽  
Vol 102 (3) ◽  
pp. 316-330 ◽  
Author(s):  
MAJID HADIAN ◽  
MATTHEW WEIDNER

In this paper we study the variation of the $p$-Selmer rank parities of $p$-twists of a principally polarized Abelian variety over an arbitrary number field $K$ and show, under certain assumptions, that this parity is periodic with an explicit period. Our result applies in particular to principally polarized Abelian varieties with full $K$-rational $p$-torsion subgroup, arbitrary elliptic curves, and Jacobians of hyperelliptic curves. Assuming the Shafarevich–Tate conjecture, our result allows one to classify the rank parities of all quadratic twists of an elliptic or hyperelliptic curve after a finite calculation.


2018 ◽  
Vol 36 (1) ◽  
pp. 334-355
Author(s):  
Yuan Li ◽  
J. Zhang ◽  
Yudong Zhong ◽  
Xiaomin Shu ◽  
Yunqiao Dong

Purpose The Convolution Quadrature Method (CQM) has been widely applied to solve transient elastodynamic problems because of its stability and generality. However, the CQM suffers from the problems of huge memory requirement in case of direct implementation in time domain or CPU time in case of its reformulation in Laplace domain. The purpose of this paper is to combine the CQM with the pseudo-initial condition method (PICM) to achieve a good balance between memory requirement and CPU time. Design/methodology/approach The combined methods first subdivide the whole analysis into a few sub-analyses, which is dealt with the PICM, namely, the results obtained by previous sub-analysis are used as the initial conditions for the next sub-analysis. In each sub-analysis, the time interval is further discretized into a number of sub-steps and dealt with the CQM. For non-zero initial conditions, the pseudo-force method is used to transform them into equivalent body forces. The boundary face method is employed in the numerical implementation. Three examples are analyzed. Results are compared with analytical solutions or FEM results and the results of reformulated CQM. Findings Results demonstrate that the computation time and the storage requirement can be reduced significantly as compared to the CQM, by using the combined approach. Originality/value The combined methods can be successfully applied to the problems of long-time dynamic response, which requires a large amount of computer memory when CQM is applied, while preserving the CQM stability. If the number of time steps is high, then the accuracy of the proposed approach can be deteriorated because of the pseudo-force method.


Sign in / Sign up

Export Citation Format

Share Document