Security of Multivariate Signature Scheme Using Non-commutative Rings

Takanori YASUDA  Tsuyoshi TAKAGI  Kouichi SAKURAI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A   No.1   pp.245-252
Publication Date: 2014/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.245
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Foundations
Multivariate Public Key Cryptosystem,  digital signature,  rainbow,  non-commutative ring,  post-quantum cryptography,  

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Multivariate Public Key Cryptosystems (MPKC) are candidates for post-quantum cryptography. Rainbow is a digital signature scheme in MPKC, whose signature generation and verification are relatively efficient. However, the security of MPKC depends on the difficulty in solving a system of multivariate polynomials, and the key length of MPKC becomes substantially large compared with that of RSA cryptosystems for the same level of security. The size of the secret and public keys in MPKC has been reduced in previous research. The NC-Rainbow is a signature scheme in MPKC, which was proposed in order to reduce the size of secret key of Rainbow. So far, several attacks against NC-Rainbow have been proposed. In this paper, we summarize attacks against NC-Rainbow, containing attacks against the original Rainbow, and analyze the total security of NC-Rainbow. Based on the cryptanalysis, we estimate the security parameter of NC-Rainbow at the several security level.