Breaking `128-bit Secure' Supersingular Binary Curves (or how to solve discrete logarithms in ${\mathbb{F}}_{2^{4\cdot 1223}}$ and ${\mathbb{F}}_{2^{12\cdot 367}}$)

Robert Granger, Thorsten Kleinjung, Jens Zumbrägel

In late 2012 and early 2013 the discrete logarithm problem (DLP) in finite fields of small characteristic underwent a dramatic series of breakthroughs, culminating in a heuristic q…