Section: Overall Objectives

Highlights of the Year

• Mohab Safey El Din was invited speaker in the International Symposium on Symbolic and Algebraic Computation (ISSAC), held in Boston, June 26-29, 2013.

• In [6] we investigate the security of HFE and Multi-HFE schemes. Our attacks are based on solving the MinRank problem. We prove that they are polynomial in the degree of the extension field for all possible practical settings used in HFE and Multi-HFE.

• In [11] we consider an algorithm to solve the DLP problem on Edwards curves, which are a well-known family of elliptic curves. We exploit the symmetries and the structure of twisted Edwards and twisted Jacobi intersections curves to gain an exponential factor $2^{\omega (n-1)}$ in the complexity bound where $\omega$ is the exponent of matrix multiplication.

• In [17] we give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is not zero and is attained.