silent; not saying a word

to keep mum.

say nothing! be silent! ?

mum's the word

do not reveal what you know (about something); keep silent

Mum's the word, or the surprise party won't be a surprise.

adjective

bashful , buttoned up , clammed up , closemouthed , hushed , mute , muted , nonvocal , not forthcoming , not talkative , quiet , reserved , secretive , shy , soundless , speechless , still , tight-lipped , tongue-tied , uncommunicative , unsociable , unspeaking , voiceless , wordless , zipped , dumb , inarticulate , silent