Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations

The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NP-hard over any field. When the number of equations m is the same as the number of unknowns n the best known algorithms are exhaustive search for small fields, and a Gr

• Type: Conference
• Year: 2000
• Where: EUROCRYPT
• Authors: Nicolas Courtois, Alexander Klimov, Jacques Patarin, Adi Shamir
• Keywords: Algorithm, Cryptology, EUROCRYPT 2000, Gr¨obner Base Algorithms, Polynomial Equations