The Collaborative International Dictionary of English v.0.48:

Befog \Be*fog"\, v. t. [imp. & p. p. Befogged; p. pr. & vb. n.
   Befogging.]
   1. To involve in a fog; -- mostly as a participle or part.
      adj.
      [1913 Webster]

   2. Hence: To confuse; to mystify.
      [1913 Webster]