In 1997, Goldreich, Goldwasser and Halevi presented the GGH cryptosystem, which is based on hard lattice problems. Only two years later, Nguyen pointed out major flaws on the scheme. From that point on, the system was considered officially dead. However, in 2012, Yoshino and Kunihiro proposed some improvements on the GGH cryptosystem, claiming to have fixed the flaws pointed out by Nguyen. In this paper, we make a thorough analysis of this tweaked GGH scheme, showing that, in practice, it behaves mostly in the same way as the original scheme. We also propose some modifications that can effectively make the new GGH different from the original one.
In this paper, we propose a zero-knowledge proof for a special case of the hidden subset sum problem. This problem was presented by [Boyko et al. 1998] as the underlying problem of methods for generating random pairs of the form (x, gx (mod p)) using precomputations. The proof we propose is an adaptation of a zero-knowledge protocol for the subset sum problem presented by [Blocki 2009].
In this paper, we propose a new type of construction for a secure and efficient public-key cryptosystem, which is based on a new problem from the theory of lattices.
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