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The Generating Series of Support Minors MinRank Ideals



Daniel Smith-Tone


The support minors method has become indispensable to cryptanalysts in attacking various post-quantum cryptosystems in the areas of multivariate cryptography and rank-based cryptography. The complexity analysis for support minors minrank calculations is a bit messy, with no closed form for the Hilbert series of the ideal generated by the support minors equations (or, more correctly, for the quotient of the polynomial ring by this ideal). In this article, we provide a generating series whose coefficients are the Hilbert Series of related MinRank ideals. This simple series therefore reflects and relates the structure of all support minors ideals. Its simplicity also makes it practically useful in computing the complexity of support minors instances.
Cryptology Eprint Archive


Multivariate Cryptography, Rank-Based Cryptography, Hilbert Series, MinRank.


Smith-Tone, D. (2023), The Generating Series of Support Minors MinRank Ideals, Cryptology Eprint Archive, [online],, (Accessed July 12, 2024)


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Created September 24, 2023, Updated January 4, 2024