¹Universidad Nacional de Colombia, Medellín, Colombia. Email: jbbaena@unal.edu.co
²Thomas More College, Crestview Hills, United States. Email: crystal.clough@gmail.com
³University of Cincinnati, Cincinnati, United States. Email: jintai.ding@uc.edu

This paper proposes two ways to fix the broken Square-Vinegar signature scheme. We give heuristic arguments as well as experimental evidence to support the security claims. The first variant, Square-Vinegar with Embedding, uses a simple modification that nonetheless changes the nature of the public key polynomials. The second, 2-Square-Vinegar, is a more significant overhaul of the construction, using a bivariate secret map instead of a univariate one.

Key words: Multivariate cryptography, Square-vinegar signature scheme, Odd characteristic.

Este artículo propone dos maneras de arreglar el esquema de firmas Square-Vinegar, el cual ha sido roto. Suministramos argumentos heurísticos, así como evidencia experimental para apoyar nuestras afirmaciones sobre seguridad. La primera variante, Square-Vinegar con inmersión, a pesar de usar una modificación simple, cambia la naturaleza de los polinomios de la clave pública. La segunda, 2-Square-Vinegar, es una revisión más significativa de la construcción, con una función secreta bivariada en lugar de una univariada.

Palabras clave: Criptografía multivariada, esquema de firmas Square-Vinegar, característica impar.

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References

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