challenge vs impugn

challenge is a noun but impugn is not a noun.

Word	Noun	Adjective	Verb	Adverb
challenge	Yes	No	Yes	No
impugn	No	No	Yes	No

As verbs, impugn is a hyponym of challenge; that is, impugn is a word with a more specific, narrower meaning than challenge:

challenge (noun)	impugn (noun)
a call to engage in a contest or fight
questioning a statement and demanding an explanation
a formal objection to the selection of a particular person as a juror
a demand by a sentry for a password or identification
a demanding or stimulating situation

challenge (verb)	impugn (verb)
issue a challenge to	attack as false or wrong
take exception to
raise a formal objection in a court of law
ask for identification