An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme

Historically, multivariate public key cryptography has been less than successful at offering encryption schemes which are both secure and efficient. At PQCRYPTO ’13 in Limoges, Tao, Diene, Tang, and Ding introduced a promising new multivariate encryption algorithm based on a fundamentally new idea: hiding the structure of a large matrix algebra over a finite field. We present an attack based on subspace differential invariants inherent to this methodology. The attack is is a structural key recovery attack which is asymptotically optimal among all known attacks (including algebraic attacks) on the original scheme and its generalizations.