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Multivariate public-key cryptography (MPKC) is considered as one of the main candidates for post-quantum cryptography (PQC). In MPKC, the MinRank attacks, which try to solve the MinRank problem obtain...ed from a public key, are important since a lot of multivariate schemes are broken by these attacks. Among them, the rectangular MinRank attack was recently proposed for the Rainbow scheme by Beullens, and it tries to solve a new kind of MinRank problem obtained by transforming the public key of Rainbow. Due to this attack, it is known that the security level of Rainbow was reduced. Rainbow is a multi-layered variant of the UOV scheme, and UOV has a resistance to all MinRank attacks since it does not have a structure of MinRank problem. Recently, there have been proposed two new variants of the UOV scheme having a small public key, MAYO and QR-UOV. In this paper, we show that the rectangular MinRank is applicable to new variants MAYO and QR-UOV. Moreover, we estimate the complexity of the attack.続きを見る
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