This question came up listening to Dan Carlin's "Death Throes of the Republic", I was interested in how the ancient Romans (and similar societies) secured their communications.
Two particular aspects come to mind:
Military/Government orders: how did politicians and soldiers in the field ensure orders were authentic? For example When the Senate sent an envoy to relieve Sulla of his command in ~88 BCE, how did Sulla know this was authentic, and not a secret plot by enemies to strip him of his army?
Private correspondence: How was a prominent citizen like Cicero confident enough to include his most private thoughts in some letters, information which would be dangerous in the wrong hands?
A while ago I wrote something about Cicero's experience with the mail, and for your question the answer is he trusted the mail to different extents depending on what he sent and to where. Here is one quote e.g. (my linked comment has ALL the quotes and links to the sources):
I have now received three letters from you—one by the hands of M. Cornelius, which you gave him, I think, at Three Taverns; a second which your host at Canusium delivered to me; a third dated, according to you, from on board your pinnace, when the cable was already slipped. They were all three, to use a phrase from the schools of rhetoric flavoured with the salt of learning, and illumined with the marks of affection. In these letters, indeed, I am urgently pressed by you to send answers, but what renders me rather dilatory in this respect is the difficulty of finding a trustworthy carrier. How few of these gentry are able to convey a letter rather weightier than usual without lightening it by skimming its contents! Besides, I do not always care to send whenever anyone is starting for Epirus: for I suppose that, having offered victims before your Amaltheia, you at once started for the siege of Sicyon. And yet I am not even certain when you start to visit Antonius or how much time you are devoting to Epirus. Accordingly, I don't venture to trust either Achaeans or Epirotes with a letter somewhat more outspoken than usual. Now some events have occurred since you left me worth my writing to you, but they must not be trusted to the risk of a letter being lost, opened, or intercepted.
As for authenticating military orders, Livy says after Claudius Marcellus, a Roman general, was killed, Hannibal used his signet ring to forge orders before Marcellus' death was general knowledge. This is Liv. 27.28:
When the body of Marcellus was discovered, Hannibal took possession of his rings. Fearing that the signet might be used for purposes of forgery, Crispinus sent couriers to all the cities round, warning them that his colleague was killed and his ring in the possession of the enemy, so that they were not to trust any missives sent in the name of Marcellus. Soon after the consul's messenger had arrived at Salapia, a despatch was received from Hannibal purporting to come from Marcellus, and stating that he would come to Salapia the night after they received the letter, and the soldiers of the garrison were to hold themselves in readiness in case their services should be required.