Abstract
We present an original efficient classical attack on MPPK/DS, a proposed multivariate-based post-quantum digital signature scheme. We then use ideas from another recent attack on MPPK/DS by Hao Guo, ultimately producing an attack with efficiency equal to that of the work of an honest verifier.
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Data availability
The code and data use to generate the experimental evidence in this paper are openly available on GitHub at https://github.com/lsmaddison/MPPKDS-Forgery.
Notes
The message space was stated to be \({\mathbb {Z}}_p\) in [2], but evaluating a polynomial in \({\mathbb {Z}}_{p-1}[x_0]\) at a value in \({\mathbb {Z}}_p\) is not well defined. We thus change it to \({\mathbb {Z}}_{p-1}\) and assume that arithmetic is done mod \(p-1\) when evaluating the polynomials. Note that the notation \(GF(p-1)\) was used in [2] to denote \({\mathbb {Z}}_{p-1}\), but we change it here since this ring is not a field.
The signing algorithm in [2] also stipulated that if any of A, B, C, D or E were equal to 1, then the result should be rejected and a new base g should be chosen. We discuss in Section 3.1 why this condition must be removed.
References
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Acknowledgements
This work is part of the first author’s thesis [9]. The second author’s research is partially funded by Natural Sciences and Engineering Research Council Discovery Grant NSERC-RGPIN-2020-05020.
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Maddison, L., Nevins, M. A Classically Efficient Forgery of MPPK/DS Signatures. La Matematica (2024). https://doi.org/10.1007/s44007-024-00095-0
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DOI: https://doi.org/10.1007/s44007-024-00095-0