Invention Grant
US08666066B2 Encoding points of an elliptic curve 有权
编码椭圆曲线的点

  • Patent Title: Encoding points of an elliptic curve
  • Patent Title (中): 编码椭圆曲线的点
  • Application No.: US13144477
    Application Date: 2010-01-08
  • Publication No.: US08666066B2
    Publication Date: 2014-03-04
  • Inventor: Thomas Icart
  • Applicant: Thomas Icart
  • Applicant Address: FR Issy-les-Moulineaux
  • Assignee: Morpho
  • Current Assignee: Morpho
  • Current Assignee Address: FR Issy-les-Moulineaux
  • Priority: FR0950189 20090114
  • International Application: PCT/FR2010/050023 WO 20100108
  • International Announcement: WO2010/081980 WO 20100722
  • Main IPC: H04L29/00
  • IPC: H04L29/00
Encoding points of an elliptic curve
Abstract:
The method comprises, in an electronic component, carrying out a cryptographic calculation that includes the step of obtaining points P on an elliptic curve following the equation Y2+a1XY+a3Y=X3+a2X2+a4+X+a6 (1) where a1, a2, a3, a4 et a6 are elements of a set A of elements; where A is a ring of modular integers Z/qZ where q is a positive integer resulting from a number I of different prime numbers strictly higher than 3, I being an integer higher than or equal to 2, where A is a finite body Fq with q the power of a prime integer; where X and Y are the coordinates of the points P and are elements of A. The method comprises determining a diameter (11), and obtaining the coordinates X and Y of a point P (13) by applying a function (12) to said parameter. The Euler function φ of A corresponds to the equation φ(A) mod 3=1. The function is a reversible and deterministic function expressed by a rational fraction in a1, a2, a3, a4 and a6 and in said parameter in A, and reaches at least a number q/41 of points P, with I being equal to 1 for a finite body Pq. The method further comprises using the point P in a cryptographic application for ciphering or hashing or signature or authentication or identification.
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