That transmission in that war was intercepted and their cipher was decrypted.
「その戦争では会話が盗聴されて暗号がばれたんだって」は英語で「That transmission in that war was intercepted and their cipher was decrypted.」と言います。軍隊の話題は普段と違う単語が使われていますので、「会話」は「conversation」じゃなくて「transmission」、「暗号」は「password」じゃなくて「cipher」なのです。
その戦争では会話が盗聴されて暗号がばれたんだって。
That transmission in that war was intercepted and their cipher was decrypted.