2-Isogenies Between Elliptic Curves in Hesse Model

  • João Paulo da Silva
  • Ricardo Dahab
  • Julio López

Resumo


Cryptosystems based on the problem of calculating isogenies between supersingular elliptic curves were recently proposed as strong candidates in the area of Post-Quantum Cryptography. In order to evaluate isogenies applied in cryptography constructions we use the Vèlu formula. However, this formula only applies to elliptic curves in the Weierstrass model. This paper presents morphisms that can be used to construct 2-isogeny formulas for curves in the Hesse model.
Publicado
25/10/2018
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SILVA, João Paulo da; DAHAB, Ricardo; LÓPEZ, Julio. 2-Isogenies Between Elliptic Curves in Hesse Model. In: SIMPÓSIO BRASILEIRO EM SEGURANÇA DA INFORMAÇÃO E DE SISTEMAS COMPUTACIONAIS (SBSEG) , 2018 Anais do XVIII Simpósio Brasileiro em Segurança da Informação e de Sistemas Computacionais. Porto Alegre: Sociedade Brasileira de Computação, oct. 2018 . p. 57 - 64.