Definition
A Multivariate Public-Key Cryptosystem (MPKC) is a public-key cryptosystem where the public map \(\mathcal{P}\), or trapdoor one-way function, is given as a set of m polynomial equations of a small degree d over n variables in a finite field F. Usually d = 2, hence the alternate name “Multivariate Quadratic” (MQ).
To decrypt, authenticate, or sign digitally, a user must, for a given m-tuple \(\mathbf{z} = ({z}_{1},\ldots, {z}_{m})\), find a solution \(\mathbf{w} = ({w}_{1},\ldots, {w}_{n})\) of the system
For a digital signature, a challenge–response authentication scheme, and an encryption...
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Goubin, L., Patarin, J., Yang, BY. (2011). Multivariate Cryptography. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_421
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