Improved supersingularity testing of elliptic curves

抄録

In protocols of isogeny-based cryptosystems, we send data of elliptic curves. Then it is necessary to identify supersingularity of the elliptic curves to guarantee the correctness of protocol. Among deterministic algorithms for the purpose, Sutherland proposed an efficient algorithm that utilizes sequences of $2$-isogenies computed by using modular polynomials. In this paper, we improve the efficiency of the algorithm by using some properties of $x$-coordinates of $2$-torsion points instead of modular polynomials. Our experimental result shows that our algorithm succeeded in reducing the computation time by 14 to 32 percent compared to Sutherland's algorithm.