We survey recent work on the elliptic curve discrete logarithm problem. In particular we review index calculus algorithms using summation polynomials, and claims about their complexity. Keywords Elliptic curve discrete logarithm problem (ECDLP) · Summation polynomials · Pollard rho · Index calculus Mathematics Subject Classification (2000) 11Y16 · 11G20 · 14G15 · 13P10 · 14G50 · 11T71 · 14H52
Steven D. Galbraith, Pierrick Gaudry