Algebraic attacks : a survey

Algebraic attacks have recently acquired great importance in the area of cryptography, not only due to the ciphers they have been able to break, but more importantly, because the principle of algebraic attacks is very generic and can be applied to break large classes of ciphers. Several ciphers, previously considered secure and widely used in practice were found to be potentially vulnerable to algebraic attacks. In this survey, we examine algebraic attacks against both public and symmetric key ciphers. We discuss the Boolean functions used in the design of ciphers from the perspective of algebraic attacks, and consider the ”cryptographic” complexity and explicit construction of these functions. We also briefly look at recently discovered methods of solving certain systems of multivariate polynomial equations since algebraic attacks rely on being able to solve such systems of equations efficiently.