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Multivariate Public Key Cryptosystems (MPKC) can be potentially applied to post-quantum cryptography. Rainbow is a digital signature scheme in MPKC that affords relatively efficient encryption and dec...ryption. However, the security of MPKC depends on the difficulty in solving a system of multivariate polynomials, and a substantial number of their coefficients is required to attain a reasonable level of security. For a public key cryptosystem, it is important to study the reduction of key size. In the case of RSA with a small key size, the lattice attack works efficiently [7, 2], whereas in the case of cryptosystems based on discrete logarithm, Pollard’s λ-method [6, 4] works efficiently [3]. Moreover, the key size of the McEliece cryptosystem, which is another candidate for post-quantum cryptography, has been reduced by Berger et al. [1]. In the case of Rainbow, it is known that CyclicRainbow [5] reduces the size of the public key while maintaining the security of the original Rainbow. In this paper, we reduce the secret key size of Rainbow by using non-commutative rings. The proposed scheme is constructed by replacing a definition field with a non-commutative ring in the original Rainbow scheme. Non-commutative rings are a well-established topic in mathematics; for examples, quaternion algebras and group rings have been studied in depth.続きを見る
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Mendeley出力
