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Multivariate public key cryptography is one of the main approaches to guarantee the security of communication in a post-quantum world. One of the most promising candidates in this area is the Rainbow signature scheme, which was first proposed by J. Ding and D. Schmidt in 2005. In this paper the authors develop a model of security for the Rainbow signature scheme. They use this model to find parameters for Rainbow over GF(16), GF(31) and GF(256) which, under certain assumptions, guarantee the security of the scheme for now and the near future.
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