The search functionality is under construction.
The search functionality is under construction.

Keyword Search Result

[Keyword] Barreto-Naehrig curve(1hit)

1-1hit
  • Universal Construction of a 12th Degree Extension Field for Asymmetric Pairing

    Masaaki SHIRASE  

     
    PAPER-Mathematics

      Vol:
    E94-A No:1
      Page(s):
    156-164

    It is necessary to perform arithmetic in Fp12 to use an Ate pairing on a Barreto-Naehrig (BN) curve, where p is a prime given by p(z)=36z4+36z3+24z2+6z+1 for some integer z. In many implementations of Ate pairings, Fp12 has been regarded as a 6th degree extension of Fp2, and it has been constructed by Fp12=Fp2[v]/(v6-ξ) for an element ξ ∈ Fp2 such that v6-ξ is irreducible in Fp2[v]. Such a ξ depends on the value of p, and we may use a mathematical software package to find ξ. In this paper it is shown that when z ≡ 7,11 (mod 12), we can universally construct Fp12 as Fp12=Fp2[v]/(v6-u-1), where Fp2=Fp[u]/(u2+1).