IACR News item: 25 March 2012
PhD Database
Name: Abdoul Aziz Ciss
Topic: Arithmétique et Extracteurs déterministes sur les courbes elliptiques
Category: public-key cryptography
Description: 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.\r\n\r\nWe 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.\r\n\r\nWe 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.\r\n\r\nWe 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.[...]
Topic: Arithmétique et Extracteurs déterministes sur les courbes elliptiques
Category: public-key cryptography
Description: 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.\r\n\r\nWe 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.\r\n\r\nWe 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.\r\n\r\nWe 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.[...]
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