Do I have to fast as an atonement after I participated in a conversation about a secret that I had sworn not to reveal, even though people were already talking about it and I was not the one who divulged it?

If your intention was not to inform those unaware of the secret, then there is no expiation upon you for not breaking the oath. However, if your intention was not to speak about the matter at all, and you did speak, then expiation is due upon you, which is feeding ten poor persons or clothing them, or freeing a slave. Fasting is only resorted to if one is unable to perform these three acts.