Upvote:4
The Germans certainly tried, and did have some successes, but not on the same scale as the Western Allies. They read British naval ciphers until 1943, which contributed to their successes in the Battle of the Atlantic, and were able to eavesdrop on the scrambled telephone link between the UK and USA.
Their lesser scale of success seems to have been due to the fragmentation and duplication of their efforts. A single large-scale organisation like the British Government Code and Cypher School (GC&CS), based at Bletchley Park, was quite foreign to Nazi ideas of organisation.
They also suffered from "mirror-imaging", assuming that their enemies worked in the same way as them. They found it hard to believe that anyone could assemble the scale of effort required to break their ciphers, which led them to discount the clues that the Enigma was broken.