Paper 2010/516

Key Agreement Protocols Based on Multivariate Polynomials over Fq

Masahiro Yagisawa


In this paper we propose new key agreement protocols based on multivariate polynomials over finite field Fq. We concretely generate the multivariate polynomial F(X)\in Fq[x1,..,xn] such that F(X)=\sum^m_{i=1} ki[Ai(X)^d+ Ai(X)^{d-1}+ ..+ Ai(X)] where Ai(X) =ai1x1+…+ainxn ,coefficients ki , aij\in Fq (i=1,..,m:j=1,..,n) and variables X=(x1,..,xn)^T \in Fq[x1,..,xn]^n. The common key K(X) has the form such that K(X)=\sum^m_{i=1}hi F((bi1x1,...,binxn)^T) where hi ,bij\in Fq (i=1,..,m:j=1,..,n) to be the temporary secret keys of the partner . Our system is immune from the Gröbner bases attacks because obtaining coefficients of F(X) to be secret keys arrives at solving the multivariate algebraic equations, that is, one of NP complete problems .Our protocols are also thought to be immune from the differential attacks because of the equations of high degree.

Note: I revised expression (20).

Available format(s)
Public-key cryptography
Publication info
Published elsewhere. Unknown where it was published
key agreement protocolmultivariate polynomialsGröbner basesNP complete problemsfinite field
Contact author(s)
tfktyagi2 @ c3-net ne jp
2010-10-24: last of 2 revisions
2010-10-12: received
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      author = {Masahiro Yagisawa},
      title = {Key Agreement Protocols Based on Multivariate Polynomials over Fq},
      howpublished = {Cryptology ePrint Archive, Paper 2010/516},
      year = {2010},
      note = {\url{}},
      url = {}
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