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Borja Gómez Rodríguez

Borja Gómez Rodríguez

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5
Publications
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Introduction
Amateur and independent researcher focusing in the development of Cryptographic Schemes based in Mathematical branches like: Group Theory, Algebraic Combinatorics, Rings and (Finite) Fields, Linear Algebra, Computational Algebra and more. Currently, I do research in the field of Multivariate Public Key Cryptography.

Publications

Publications (5)
Preprint
Full-text available
In this paper the author introduces methods that represent elements of a Finite Field F q as matrices that linearize certain operations like the product of elements in F q. Since the Central Polynomial Map F(X) coming from the HFE scheme involves multiplication of elements in a Finite Field F q , using a novel method based in Linear Algebra the Qua...
Preprint
Full-text available
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 th...
Preprint
Full-text available
Conventional asymmetric key exchange protocols rely on computing elements in commutative groups, where the employed trapdoor-permutation function is commutative, allowing Alice and Bob to compute the same element in G as changing the orders of the variables or elements doesn't alter the output. The research found in this paper is focused on the ana...
Preprint
Full-text available
This paper introduces a cryptographic commitment using multiple platform groups where the attacker must solve multiple instances of the Discrete Logarithm Problem to break the scheme. The goal is that Al-ice and Bob establish a secret communication after verifying a finite set of values that have been computed using multiple trapdoor-permutation fu...
Preprint
Full-text available
Asymmetric schemes are moving towards a new series of cryptosystems based on known open problems that until the day guarantee security from the point that are not solvable under determined properties. In this paper you can read a novel research done mostly on the field of Multivariate Public Key Cryptography that focus the interest on sharing a pre...