Hush-hush and On the sly

Hush-hush adjective - Not known or meant to be known by the general populace.

On the sly and hush-hush are semantically related In some cases you can use "On the sly" instead the phrase "Hush-hush" as an adverb or an adjective.

On the sly adverb - In a furtive manner.

Hush-hush and on the sly are semantically related in secret topic. You can use "Hush-hush" instead the phrase "On the sly" as an adverb or an adjective, if it concerns topics such as sneaky, underground, clandestine, in hidden manner.