Overview
Syllabus
Intro
The discrete logarithm problem on elliptic curve Use the group of points of an elliptic curve defined over a finite field
Basic outline of index calculus methods
Transfer of the ECDLP via cover maps Weil de
The GHS construction
Decomposition attack
Nagao's approach for decompositions
Analysis of Nagao's approach
Modified index calculus
A special case: quadratic extensions in odd char
The sieving technique Fact: solutions of the polynomial system only give the polynomial
Second ingredient: the combined attack
The sextic extension case
A concrete attack on a 150-bit curve
Scaling data for our implementation
Taught by
TheIACR