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An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme



Dustin Moody, Ray A. Perlner, Daniel C. Smith-Tone


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 a structural key recovery attack which is asymptotically optimal among all known attacks (including algebraic attacks) on the original scheme and its generalizations.
Proceedings Title
Post-Quantum Cryptography (Lecture Notes in Computer Science)
Conference Dates
October 1-3, 2014
Conference Location
Conference Title
6th International Conference on Post-Quantum Cryptography (PQCrypto 2014)


differential, encryption, invariant, multivariate public key cryptography


Moody, D. , Perlner, R. and Smith-Tone, D. (2014), An Asymptotically Optimal Structural Attack on the ABC Multivariate Encryption Scheme, Post-Quantum Cryptography (Lecture Notes in Computer Science), Waterloo, -1, [online], (Accessed February 27, 2024)
Created October 3, 2014, Updated November 10, 2018