## Cryptology ePrint Archive: Report 2020/1287

Multivariate Cryptographic Primitive based on the product of the roots of a polynomial over a field

Borja Gómez

Abstract: Cryptographic Primitives in Multivariate Public Key Cryptography are of relevant interest, specially in the quadratic case. These primitives classify the families of schemes that we encounter in this field. In this paper, the reader can find a new primitive based on the product of the roots of a polynomial over a field, where the coefficients of this polynomials are the elementary symmetric polynomials on $n$ variables, which guarantees a solution when inverting the scheme. Moreover, a cryptosystem and a digital signature scheme are built on top of this primitive, where distinct parametrizations and criteria that define the schemes are commented, along with applications of attacks available in literature.

Category / Keywords: public-key cryptography / multivariate-cryptography public-key cryptography oil-vinegar quadratic-polynomials finite-fields

Date: received 15 Oct 2020

Contact author: kub0x at elhacker net

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2020/1287

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