Both systems are an example of a hidden Abelian subgroup problem. That is also why Shor's algorithm equally applies to both: https://en.m.wikipedia.org/wiki/Sho

Both systems are an example of a hidden Abelian subgroup problem. That is also why Shor's algorithm equally applies to both: https://en.m.wikipedia.org/wiki/Shor%27s_algorithm#Shor's_algorithm_for_discrete_logarithms https://en.m.wikipedia.org/wiki/Shor%27s_algorithm#Shor's_al... So a hypothetical classic algorithm that breaks the RSA is also highly likely to break the ECDSA.