Pairing computation on Edwards curves with high-degree twists

In this paper, we propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a littler faster than that proposed by Arene et.al.. Finally, to improve the efficiency of pairing computation we present twists of degree 4 and 6 on twisted Edwards curves

The Pairing Computation on Edwards Curves

We propose an elaborate geometry approach to explain the group law on twisted Edwards curves which are seen as the intersection of quadric surfaces in place. Using the geometric interpretation of the group law, we obtain the Miller function for Tate pairing computation on twisted Edwards curves. Then we present the explicit formulae for pairing computation on twisted Edwards curves. Our formulae for the doubling step are a little faster than that proposed by Arène et al. Finally, to improve the efficiency of pairing computation, we present twists of degrees 4 and 6 on twisted Edwards curves

Faster Pairing Computation on Jacobi quartic Curves with High-Degree Twists

Abstract. In this paper, we propose an elaborate geometric approach to explain the group law on Jacobi quartic curves which are seen as the intersection of two quadratic surfaces in space. Using the geometry interpretation we construct the Miller function. Then we present explicit formulae for the addition and doubling steps in Miller’s algorithm to compute Tate pairing on Jacobi quartic curves. Both the addition step and doubling step of our formulae for Tate pairing computation on Jacobi curves are faster than previously proposed ones. Finally, we present efficient formulas for Jacobi quartic curves with twists of degree 4 or 6. For twists of degree 4, both the addition steps and doubling steps in our formulas are faster than the fastest result on Weierstrass curves. For twists of degree 6, the addition steps of our formulae are faster than the fastest result on Weierstrass curves

Multi-Modal Haptic Rendering Based on Genetic Algorithm

Multi-modal haptic rendering is an important research direction to improve realism in haptic rendering. It can produce various mechanical stimuli that render multiple perceptions, such as hardness and roughness. This paper proposes a multi-modal haptic rendering method based on a genetic algorithm (GA), which generates force and vibration stimuli of haptic actuators according to the user’s target hardness and roughness. The work utilizes a back propagation (BP) neural network to implement the perception model f that establishes the mapping (I=f(G)) from objective stimuli features G to perception intensities I. We use the perception model to design the fitness function of GA and set physically achievable constraints in fitness calculation. The perception model is transformed into the force/vibration control model by GA. Finally, we conducted realism evaluation experiments between real and virtual samples under single or multi-mode haptic rendering, where subjects scored 0-100. The average score was 70.86 for multi-modal haptic rendering compared with 57.81 for hardness rendering and 50.23 for roughness rendering, which proved that the multi-modal haptic rendering is more realistic than the single mode. Based on the work, our method can be applied to render objects in more perceptual dimensions, not only limited to hardness and roughness. It has significant implications for multi-modal haptic rendering

Improved Exponential-time Algorithms for Inhomogeneous-SIS

The paper is about algorithms for the inhomogeneous short integer solution problem: Given $(A,s)$ to find a short vector $x$ such that $Ax \equiv s \pmod{q}$. We consider algorithms for this problem due to Camion and Patarin; Wagner; Schroeppel and Shamir; Minder and Sinclair; Howgrave-Graham and Joux (HGJ); Becker, Coron and Joux (BCJ). Our main results include: Applying the Hermite normal form (HNF) to get faster algorithms; A heuristic analysis of the HGJ and BCJ algorithms in the case of density greater than one; An improved cryptanalysis of the SWIFFT hash function; A new method that exploits symmetries to speed up algorithms for Ring-SIS in some cases. This paper is published in Journal of Cryptology, Volume 32, Issue 1 (2019) 35--83