Browsing Theses by Author "Soukharev, Vladimir"

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Evaluating Large Degree Isogenies between Elliptic Curves

Soukharev, Vladimir (University of Waterloo, 2010-12-20)

An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between elliptic curves efficiently. For ordinary curves ...
Post-Quantum Elliptic Curve Cryptography

Soukharev, Vladimir (University of Waterloo, 2016-05-16)

We propose and develop new schemes for post-quantum cryptography based on isogenies over elliptic curves. First we show that ordinary elliptic curves are have less than exponential security against quantum computers. These ...