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- Shi Bai, Steven D Galbraith, Liangze Li, Daniel Sheffield, Patarin Wagner, Schroeppel +4 others
- 2014

The paper is about algorithms for the inhomogeneous short integer solution problem: Given (A, s) to find a short vector x such that Ax ≡ s (mod q). We consider algorithms for this problem due (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… (More)

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… (More)

- Liangze Li, Fan Zhang
- WISA
- 2012

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… (More)

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