# implications of shor's algorithm on $F_{2^m}$ elliptic curves and GHASH

The security of elliptic curves depends on the difficulty of the discrete logarithm problem. Should Shor's Algorithm ever prove viable then elliptic curves would cease to offer any useful security properties, hence the need for post quantum crypto algorithms.

Most discussions of Shor's algorithm are for integers but how applicable is it for polynomials?

This is relevant because SEC2 defines a bunch of elliptic curves over $$F_{2^m}$$ instead of $$F_P$$.

I'm also curious about how Shor's Algorithm would impact GCM / GHASH, which operates in $$F_{2^m}$$.

• Please sperate this question into ECC and GCM/GHash – kelalaka May 19 at 16:09

I'm also curious about how Shor's Algorithm would impact GCM / GHASH, which operates in $$F_{2^m}$$.