Chosen Message Attack Against Goldreich-Goldwasser-Halevi's Signature Scheme from Crypto'97

The Goldreich-Goldwasser-Halevi(GGH)’s signature scheme from Crypto ’99 is cryptanalyzed, which is based on the well-known lattice problem. We mount a chosen message attack on the signature scheme, and show the signature scheme is vulnerable to the attack. We collects n lattice points that are linearly independent each other, and constructs a new basis that generates a sub-lattice of the original lattice. The sub-lattice is shown to be sufficient to generate a valid signature. Empirical results are presented to show the effectiveness of the attack. Finally, we show that the cube-like parameter used for the private-key generation is harmful to the security of the scheme.