Paper 2006/075

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

Metadata
Available format(s)
PDF PS
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
2006-02-24: received
Short URL
https://ia.cr/2006/075
License
Creative Commons Attribution
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}
}
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