### ON THE WEIL SUM EVALUATION OF CENTRAL POLYNOMIAL IN MULTIVARIATE QUADRATIC CRYPTOSYSTEM

TOMOHIRO HARAYAMA

##### Abstract

A parity checking-styled Weil sum algorithm is presented for a general class of the univariate polynomials which fully characterize a system of $n$ polynomials in $n$ variables over $F_{2}$. The previously known proof methods of explicit Weil sum evaluation of Dembowski-Ostrom polynomials are extended to general case. The algorithm computes the absolute values of the Weil sums of the generic central polynomials in MQ problem.

Note: This is a resubmission of the previous submission xxxx/129. Please use this paper instead of the previous paper. I slightly modified the abstract. I am sorry for this incovenience. Sincerely, Tomohiro Harayama

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
MQ problemMQ trapdoor functionmultivariate quadratic cryptosystemDembwoski-Ostrom polynomialcentral polynomialcharacter and Weil sum.
Contact author(s)
harayama @ tamu edu
History
Short URL
https://ia.cr/2006/075

CC BY

BibTeX

@misc{cryptoeprint:2006/075,
author = {TOMOHIRO HARAYAMA},
title = {ON THE WEIL SUM EVALUATION OF CENTRAL POLYNOMIAL IN MULTIVARIATE QUADRATIC CRYPTOSYSTEM},
howpublished = {Cryptology ePrint Archive, Paper 2006/075},
year = {2006},
note = {\url{https://eprint.iacr.org/2006/075}},
url = {https://eprint.iacr.org/2006/075}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.