Browsing Mathematics (Faculty of) by Subject "elliptic curves"
Now showing items 1-5 of 5
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Elliptic Curves over Finite Fields and their l-Torsion Galois Representations
(University of Waterloo, 2015-09-08)Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2-dimensional Galois representation of $\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong ... -
Evaluating Large Degree Isogenies between Elliptic Curves
(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 ... -
Machine-Level Software Optimization of Cryptographic Protocols
(University of Waterloo, 2014-04-30)This work explores two methods for practical cryptography on mobile devices. The first method is a quantum-resistant key-exchange protocol proposed by Jao et al.. As the use of mobile devices increases, the deployment of ... -
On Pairing-Based Signature and Aggregate Signature Schemes
(University of Waterloo, 2009-01-21)In 2001, Boneh, Lynn, and Shacham presented a pairing-based signature scheme known as the BLS signature scheme. In 2003, Boneh, Gentry, Lynn, and Shacham presented the first aggregate signature scheme called the BGLS ... -
On Prime-Order Elliptic Curves with Embedding Degrees 3, 4 and 6
(University of Waterloo, 2007-01-22)Bilinear pairings on elliptic curves have many cryptographic applications such as identity based encryption, one-round three-party key agreement protocols, and short signature schemes. The elliptic curves which are ...