A Study of the Hardness of Algebraic Algorithms and Its Applications to Public-Key Cryptography

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We analyzed algebraic algorithms which are computationally intractable. We proposed an improved method for a problem relevant to lattices, an improvement of key-generation algorithm for a homomorphic encryption scheme based on a lattice problem, efficient attacks against some multivariate public-key cryptosystems, and some pairing algorithms. Moreover, based on these analyses, we proposed a multivariate cryptosystem which is expected to be secure against attacks using quantum computers. multivariate public-key cryptosystems, and some pairing algorithms. Moreover, based on these analyses, we proposed a multivariate cryptosystem which is expected to be secure against attacks using quantum computers.