Should one fulfill the request of a person who says, "I ask you by Allah (Amanatuka billah)" or "I adjure you by Allah (Halaftuka billah)" to do something?

A person's statement to his companion: "I entrust you with Allah's name (أمنتك بالله)" or "I adjure you by Allah (حلفتك بالله)," is a confirmation of the secrecy of what has been entrusted. It is not permissible to disclose the secret, because disclosing it is a betrayal of trust and a breach of promise. It is forbidden if it causes harm, and ignoble if it does not cause harm. Disclosing a secret is considered a betrayal, and it is more reprehensible than revealing one's own secret.