Abstract
This chapter gives an overview of the basic concepts of multivariate cryptography. After recalling the basic definitions on (systems of) multivariate polynomials, we present the main construction methods of multivariate public key cryptosystems. We discuss the mathematical problems underlying the security of multivariate cryptography and give an overview of the main attacks against these schemes. Finally, we discuss the advantages and disadvantages of multivariate schemes compared to other (post-quantum) cryptosystems.
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Notes
- 1.
Without loss of generality we assume that each of the polynomials of \(\mathcal P\) contains the same monomials.
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Ding, J., Petzoldt, A., Schmidt, D.S. (2020). Multivariate Cryptography. In: Multivariate Public Key Cryptosystems. Advances in Information Security, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-0716-0987-3_2
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DOI: https://doi.org/10.1007/978-1-0716-0987-3_2
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