Public Key Cryptography by Batten Lynn Margaret

Author:Batten, Lynn Margaret
Language: eng
Format: epub
Publisher: Wiley
Published: 2013-01-06T16:00:00+00:00

5.3 The Elliptic Curve Factoring Scheme

In this section, we describe how elliptic curves can be used to factor numbers suspected of being composite. We saw in Section 2.2 that Fermat's Little Theorem can be used to check if a number is prime or not. In fact, it cannot definitively prove that a number is prime, as some composite numbers pass the FLT test.

We can also use elliptic curve cryptography to test if a number is prime. This is because when adding points, we need to compute an inverse for the slope. If we add enough points together and the modulus is in fact composite, there is a high probability that along the way we will be unable to compute an inverse because we found a factor of the modulus. Again, if all point additions are correctly computed, this is no guarantee that the modulus is a prime.

This method of factoring was first described formally in [24], but we give a brief algorithm here for the method.

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