Algebraic Cryptanalysis of Hidden Field Equation (HFE) Cryptosystems Using Gröbner Bases

By Jean-Charles Faugère, Antoine Joux. Annual International Cryptology Conference, 2003

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Fast and robust numerical solutions to minimal problems for cameras with radial distortion (2008, methodology): “The state-of-the-art method for solving polynomial equations is based on calculations with Gr¨obner bases [16] and has many applications in computer vision, but also in other ﬁelds such as cryptology [7] and robotics[1].”
On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations (2004, methodology): “This results in an efficient algorithm that has been used to break a cryptographic challenge [ FJ03 ].”