### New candidates for multivariate trapdoor functions

Jaiberth Porras, John B. Baena, and Jintai Ding

##### Abstract

We present a new method for building pairs of HFE polynomials of high degree, such that the map constructed with such a pair is easy to invert. The inversion is accomplished using a low degree polynomial of Hamming weight three, which is derived from a special reduction via Hamming weight three polynomials produced by these two HFE polynomials. This allows us to build new candidates for multivariate trapdoor functions in which we use the pair of HFE polynomials to fabricate the core map. We performed the security analysis for the case where the base field is $GF(2)$ and showed that these new trapdoor functions have high degrees of regularity, and therefore they are secure against the direct algebraic attack. We also give theoretical arguments to show that these new trapdoor functions over $GF(2)$ are secure against the MinRank attack as well.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Multivariate cryptographyHFE polynomialsHFE cryptosystemtrapdoor functionsZhuang-zi algorithm
Contact author(s)
jbbaena @ unal edu co
History
Short URL
https://ia.cr/2014/387

CC BY

BibTeX

@misc{cryptoeprint:2014/387,
author = {Jaiberth Porras and John B.  Baena and Jintai Ding},
title = {New candidates for multivariate trapdoor functions},
howpublished = {Cryptology ePrint Archive, Paper 2014/387},
year = {2014},
note = {\url{https://eprint.iacr.org/2014/387}},
url = {https://eprint.iacr.org/2014/387}
}

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