Group law on affine conics and applications to cryptography
作者：
Highlights：
• We give an overview of the group’s structure of conics seen as the irreducible component of a projective reducible cubic.
• We explicit group’s operations and parametrizations for conics.
• We focus on conics over finite fields for providing a public-key cryptosystem.
• We perform exponentiation over the Pell’s hyperbola by means of the Réc dei rational functions.
• We improve the More’s algorithm for a fast evaluation of the Réc dei rational functions.
摘要
•We give an overview of the group’s structure of conics seen as the irreducible component of a projective reducible cubic.•We explicit group’s operations and parametrizations for conics.•We focus on conics over finite fields for providing a public-key cryptosystem.•We perform exponentiation over the Pell’s hyperbola by means of the Réc dei rational functions.•We improve the More’s algorithm for a fast evaluation of the Réc dei rational functions.
论文关键词：Algorithms,Rational functions,Finite fields,Public key cryptography,Groups over curves
论文评审过程：Received 13 January 2020, Revised 6 June 2020, Accepted 12 July 2020, Available online 22 July 2020, Version of Record 11 July 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2020.125537
