Question: Let F = Z 5 [ x ] / x 2 + x + 1 be a finite field. Is x 1 is a primitive

Let F=Z5[x]/x2+x+1 be a finite field.

  • Is x1 is a primitive root of F ?
  • Find a cyclic subgroup of order 6 in F .
  • Compute logx1(3(x+1)) .
  • Suppose the Diffie-Hellman method is used with group G=F, g=x1and secret exponents a=5 , b=7 . What is the common secret key K that is exchanged?

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