Introduction to algebraic approaches for solving isogeny path-finding problems (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties)

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Description

The isogeny path-finding is a computational problem that finds an isogeny connecting two given isogenous elliptic curves. The hardness of the isogeny path-finding problem supports the fundamental security of isogeny-based cryptosystems. In this paper, we introduce an algebraic approach for solving the isogeny path-finding problem. The basic idea is to reduce the isogeny problem to a system of algebraic equations using modular polynomials, and to solve the system by Gröbner basis computation. We report running time of the algebraic approach for solving the isogeny path-finding problem of 3-power isogeny degrees on supersingular elliptic curves. This is a brief summary of [16] with implementation codes.

Journal

  • RIMS Kokyuroku Bessatsu

    RIMS Kokyuroku Bessatsu B90 169-184, 2022-06

    Research Institute for Mathematical Sciences, Kyoto University

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Details 詳細情報について

  • CRID
    1050012003719916288
  • NII Book ID
    AA12196120
  • HANDLE
    2433/276280
  • ISSN
    18816193
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB

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