International Association for Cryptologic Research

Ph.D. Database

The aim of the IACR Ph.D. database is twofold. On the first hand, we want to offer an overview of Ph.D. already completed in the domain of cryptology. Where possible, this should also include a subject classification, an abstract, and access to the full text. On the second hand, it deals with Ph.D. subjects currently under investigation. This way, we provide a timely map of contemporary research in cryptology. All entries or changes need to be approved by an editor. You can contact them via phds (at) iacr.org.

Details

Abdoul Aziz Ciss (#768)
Name Abdoul Aziz Ciss
Topic of his/her doctorate. Arithm├ętique et Extracteurs d├ęterministes sur les courbes elliptiques
Category public-key cryptography
Keywords Randomness extractors, elliptic curves, fast arithmetic
Ph.D. Supervisor(s) Djiby Sow
Year of completion 2012
Abstract In this thesis, we present a new deterministic randomness extractor for a finite field $\mathbb{F}_{p^n}$ and a deterministic randomness extractor for an elliptic curve $E$ defined over $\mathbb{F}_{p^n}$. We also introduce a new generalization of the Huff elliptic curves. The extractors we present in this thesis can be used to derive a random secret key at the end of the Diffie-Hellman key exchange.
We have shown under the DDH assumption over $\mathbb{F}_{2^n}$ that the $k$-first coefficients in $\mathbb{F}_{2}$ of a random element of a subgroup of $\mathbb{F}_{2^n}$ are undistinguishable from a random bit-string of the same length.
We also have shown under the DDH assumption over an elliptic curve $E$ defined over $\mathbb{F}_{2^n}$ that the $k$-first coefficients in $\mathbb{F}_{2}$ of a random point of the curve are indistinguishable from a random bit-string of the same length.
We also introduce successfully computation of the Tate pairing on the general Huff curves and we have shown that the Tate pairing on these curves are efficient as in the standard Huff curves.
Your Ph.D. thesis as fulltext 91_AbdoulAzizCiss_ArithmtiqueetExtracteursdt.pdf
E-Mail Address abdoul.ciss (at) ucad.edu.sn
Last Change 2012-03-25 15:10:40
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