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Factoring with Elliptic Curve Methods

One of the most interesting things I teaching and research into, is elliptic curve methods. While it is well known how we use elliptic curve methods for key exchange (ECDH) and with signature (ECDSA), it is less well-known that elliptic curve methods can be used to factorize values.

With this we basically compute kP (mod N), and where k is a product of many small numbers, such as Z!, and where we…