# Impact of algorithms for factoring using elliptic curves over $\mathbb{Q}$

Recently a few papers have appeared that describe a new approach to factoring, using elliptic curves over $\mathbb{Q}$. See, e.g.,

However, these papers don't seem to describe the complexity of these novel methods. What is the running time of these methods? Are these methods faster than the standard known algorithms for factoring? What is the impact of these new ideas on the security of RSA and other factoring-based cryptosystems? Should we be concerned?

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