Explicit addition formulae on hyperelliptic curves of genus 2 for isogeny-based cryptography
Copyright policy )Explicit addition formulae on hyperelliptic curves of genus 2 for isogeny-based cryptography
Summary: Some isogeny-based cryptosystems use addition and doubling on the Jacobian over genus-2 sextic and non-monic hyperelliptic curves. In this study, we generalized some formulae for quintic and monic curves to sextic curves using projective coordinates and then compared them. For sextic curves and projective coordinates, the formulae based on \textit{T. Lange}'s [Appl. Algebra Eng. Commun. Comput. 15, No. 5, 295--328 (2005; Zbl 1068.14065)] were faster than those based on \textit{C. Costello} and \textit{K. Lauter}'s [Lect. Notes Comput. Sci. 7118, 92--117 (2012; Zbl 1292.94049)], in contrast to quintic curves. The formulae based on Lange's [loc. cit.] take \(64 M + 6 S\) for addition and \(59M + 9 S\) for doubling, where \(M\) and \(S\) denote the computational costs of multiplication and squaring, respectively.
- University of Tokyo Japan
Computational aspects of algebraic curves, hyperelliptic curves, explicit formulae, Cryptography, Elliptic curves, Applications to coding theory and cryptography of arithmetic geometry, isogeny-based cryptography, Algebraic theory of abelian varieties
Computational aspects of algebraic curves, hyperelliptic curves, explicit formulae, Cryptography, Elliptic curves, Applications to coding theory and cryptography of arithmetic geometry, isogeny-based cryptography, Algebraic theory of abelian varieties
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