Breaking the Symmetry: a Way to Resist the New Differential Attack

sflash had recently been broken by Dubois, Stern, Shamir, etc., using a differential attack on the public key. The C∗− signature schemes are hence no longer practical. In this paper, we will study the new attack from the point view of symmetry, then (1) present a simple concept (projection) to modify several multivariate schemes to resist the new attacks; (2) demonstrate with practical examples that this simple method could work well; and (3) show that the same discussion of attack-and-defence applies to other big-field multivariates. The speed of encryption schemes is not affected, and we can still have a big-field multivariate signatures resisting the new differential attacks with speeds comparable to sflash.