TY - GEN
T1 - On the Discrete Logarithm Problem on Algebraic Tori
AU - Granger, R
AU - Vercauteren, Frederik R G
N1 - Conference Proceedings/Title of Journal: Advances in Cryptology (CRYPTO 2005)
PY - 2005/8
Y1 - 2005/8
N2 - Using a recent idea of Gaudry and exploiting rational representations
of algebraic tori, we present an index calculus type algorithm for solving
the discrete logarithm problem that works directly in these groups.
Using a prototype implementation, we obtain practical upper bounds for
the difficulty of solving the DLP in the tori $T_2(\F_{p^m})$ and
$T_6(\F_{p^m})$ for various $p$ and $m$.
Our results do not affect the security of the cryptosystems LUC, XTR, or
CEILIDH over prime fields.
However, the practical efficiency of our method against other methods
needs further examining, for certain choices of $p$ and $m$ in regions of
cryptographic interest.
AB - Using a recent idea of Gaudry and exploiting rational representations
of algebraic tori, we present an index calculus type algorithm for solving
the discrete logarithm problem that works directly in these groups.
Using a prototype implementation, we obtain practical upper bounds for
the difficulty of solving the DLP in the tori $T_2(\F_{p^m})$ and
$T_6(\F_{p^m})$ for various $p$ and $m$.
Our results do not affect the security of the cryptosystems LUC, XTR, or
CEILIDH over prime fields.
However, the practical efficiency of our method against other methods
needs further examining, for certain choices of $p$ and $m$ in regions of
cryptographic interest.
M3 - Conference Contribution (Conference Proceeding)
VL - 3621
T3 - Lecture Notes in Computer Science
SP - 66
EP - 85
BT - Advances in Cryptology - CRYPTO 2005
PB - Springer Berlin Heidelberg
ER -