A New Variant of Unbalanced Oil and Vinegar Using Quotient Ring: QR-UOV

Furue, Hiroki; Ikematsu, Yasuhiko; Kiyomura, Yutaro; Takagi, Tsuyoshi

doi:10.1007/978-3-030-92068-5_7

Cited by 8 publications

(3 citation statements)

References 22 publications

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“…Moreover, 𝑞 is taken as 3, 5, 7, 16, 31 and 256. In particular, 𝑞 = 7, 16, 256 are used in the parameters of UOV [8], MAYO [6] and QR-UOV [19].…”

Section: Additional Experimentsmentioning

confidence: 99%

“…This has led to a renewed interest in the UOV scheme [20] on which Rainbow is based. Recently, there were proposed some variants of UOV such as MAYO [6] and QR-UOV [19] whose ideas are different from using multiple layers of Rainbow. MAYO and QR-UOV have shorter public keys compared to UOV and are planned to be submitted for the additional standardization process of NIST [24].…”

Section: Introductionmentioning

confidence: 99%

“…However, it is not almost known which series appears most frequently among Hilbert series of ideals generated by UOV polynomials for a fixed parameter. By understanding such a series, it might be able to apply to the security analysis of UOV [20] and its variants MAYO [6] and QR-UOV [19].…”

Section: Introductionmentioning

confidence: 99%

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Hilbert Series for Systems of UOV Polynomials

IKEMATSU,

SAITO

2024

IEICE Trans. Fundamentals

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Multivariate public key cryptosystems (MPKC) are constructed based on the problem of solving multivariate quadratic equations (MQ problem). Among various multivariate schemes, UOV is an important signature scheme since it is underlying some signature schemes such as MAYO, QR-UOV, and Rainbow which was a finalist of NIST PQC standardization project. To analyze the security of a multivariate scheme, it is necessary to analyze the first fall degree or solving degree for the system of polynomial equations used in specific attacks. It is known that the first fall degree or solving degree often relates to the Hilbert series of the ideal generated by the system. In this paper, we study the Hilbert series of the UOV scheme, and more specifically, we study the Hilbert series of ideals generated by quadratic polynomials used in the central map of UOV. In particular, we derive a prediction formula of the Hilbert series by using some experimental results. Moreover, we apply it to the analysis of the reconciliation attack for MAYO.

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“…Moreover, 𝑞 is taken as 3, 5, 7, 16, 31 and 256. In particular, 𝑞 = 7, 16, 256 are used in the parameters of UOV [8], MAYO [6] and QR-UOV [19].…”

Section: Additional Experimentsmentioning

confidence: 99%