In fact, both PAP and CHAP can use unidirectional authentication, so it depends from the authentication type that you use that will define if you need both or just one.
CHAP has three authentication types:
Both, by the peer and by this end.
PAP has two:
Unidirectional and bidirectional
See these links for further reference.
http://www.cisco.com/c/en/us/support/docs/wan/point-to-point-protocol-ppp/25647-understanding-ppp-chap.html
http://www.cisco.com/c/en/us/support/docs/wan/point-to-point-protocol-ppp/25646-ppp-authen-ts-fl.html
http://www.cisco.com/c/en/us/support/docs/wan/point-to-point-protocol-ppp/10313-config-pap.html?referring_site=bodynav
Regards,
Alex Sanchez
CCIE R&S #37454