Complete group law for genus 2 Jacobians on Jacobian coordinates

Abstract

AbstractThis manuscript provides complete, inversion-free, and explicit group law formulas in Jacobian coordinates for the genus 2 hyperelliptic curves of the form $$y^2 = x^5+a_3 x^3+a_2 x^2+a_1 x+a_0$$ y 2 = x 5 + a 3 x 3 + a 2 x 2 + a 1 x + a 0 over a field K with $$\textrm{char}(K) \ne 2$$ char ( K ) ≠ 2 . The formulas do not require the use of polynomial arithmetic operations such as resultant, mod, or gcd computations but only operations in K.