A new perturbed matsumoto-imai signature scheme

Two new modification methods, triangular perturbation and dual perturbation, are proposed for multivariate signature schemes to enhance the security with almost no loss of efficiency. A new multivariate signature scheme is then constructed by applying the two new methods together to the well-known Matsumoto-Imai cryptosystem. This new signature scheme has a specially designed structure making it have several competitive advantages: 1) the public map remains surjective (this property is important for a signature scheme), 2) it is almost as efficient as the original scheme and 3) it can resist all current known structure-based attacks to MPKC and behave like a random system against direct attacks. A new efficient and effective modification method is thus provided for multivariate signature schemes.