wickedness, mischief, rudeness
奸 centers on morally twisted behavior: wickedness, mischief, and rudeness all stem from a crooked or devious character.
奸 combines 女 (woman) with 干, which likely contributes a phonetic element. The exact historical development is uncertain, but the character has long been associated with wicked or devious behavior.
A woman 女 beside a shield 干: imagine a devious person hiding behind a shield while plotting mischief.
For カン, picture a can of wickedness being opened: can -> カン, and out spills mischief and rudeness.
cunning and wickedness
someone who curries favor with their master while secretly plotting against him
wiles and cunning; craftiness and treachery
cunning; craft; wiles
evil thief; wicked robber
shrewd (dirty) trick; sinister scheme (design); sly art
disloyal retainer; treacherous subject
evil design; crafty plan; plot
wicked design; vicious plan; plot
villain
wicked person; evil thing
cunning; sly
killing a villain (with a sword, dagger, etc.)
letter explaining the reasons for cutting down an alleged villain; assassin's written vindication of his killing
Chinese traitor (esp. a collaborator with the Japanese)