Algebraic Cryptanalysis
Algebraic cryptanalysis describes a cipher as a system of multivariate polynomial equations over GF(2) and recovers the key by solving the system (e.g., with XL or Gröbner-basis methods).
Purpose
It offers a potential attack avenue against ciphers with highly algebraic structure (e.g., AES, reduced-round Keccak) and is a focus of the post-quantum era.
Mechanism
The S-box, linear layer, and key addition are expressed as multivariate equations; plaintext, ciphertext, and key variables are linked, and the system is solved with SAT solvers or Gröbner-basis algorithms. Practical efficiency depends on the sparsity and degree of the equations.
Use cases
- Algebraic attack research on AES
- Cryptanalysis of MQ schemes
- Equation-solving attacks