Popping "R-propping": breaking hardness assumptions for matrix groups over GF(2^8)

Abstract

A recent series of works propose to build post-quantum public-key encapsulation, digital signatures, group key agreement and oblivious transfer from ``R-propped'' variants of the Symmetric Decomposition and Discrete Logarithm problems for matrix groups over $\FF_{2^8}$.
We break all four proposals by presenting a linearisation attack on the Symmetric Decomposition platform, a forgery attack on the signature scheme, and a demonstration of the insecurity of the instances of the Discrete Logarithm Problem used for signatures, group key agreement and oblivious transfer, showing that none of the schemes provides adequate security.