Sub Rosa

It’s literally Latin for “under the rose.”

I found a couple reasons why this implies secrecy (from American Heritage):

From the practice of hanging a rose over a meeting as a symbol of confidentiality

And where did this come from? According to Wikipedia:

In Hellenistic and later Roman mythology, roses were associated with secrecy because Cupid gave a rose to Harpocrates (the Hellenistic god of silence) so that he would not reveal the secrets of Venus. Banquet rooms were decorated with rose carvings, reportedly as a reminder that discussions in the rooms should be kept in confidence. This was inherited in later Christian symbolism, where roses were carved on confessionals to signify that the conversations would remain secret.