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Seminar Coding Theory & Cryptography: Thorsten Kleinjung

Thorsten Kleinjung, EPFL

Using Edwards curves in the elliptic curve method

The integer factorisation problem (how to decompose an integer into prime factors) is an interesting mathematical problem. It has gained more attention in recent decades because it plays an important role in the assessment of some cryptographic protocols (e.g. RSA). One of the fastest known algorithms for finding relatively small factors of big numbers is the elliptic curve method (ECM). It has an indirect impact on RSA since the most appropriate algorithm for breaking RSA makes use of ECM.

In recent years a new representation of elliptic curves (Edwards curves) has led to a faster arithmetic on elliptic curves and thus to an acceleration of ECM. After an overview of ECM and Edwards curves I will describe a problem that arises when using Edwards curves for ECM and discuss possible solutions.

Location: Grosser Hörsaal

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