Suppose that the allies have no luck at breaking Axis encryption in WWII -- either the German Enigma machines and Japanese Purple & Naval codes are tougher, the Axis changes keys far more frequently, and/or the Allies don't have as much help or focus on it.
In any case, the Allies don't break any significant Axis messages throughout the war (or do so at a much lower rate than the Axis does). Please discuss the impact on the course of the war.
The absence of ULTRA intelligence is huge for the European war.
ULTRA was significant for the battle of Britain. While the Luftwaffe was never going to achieve the air supremacy required for
that operation, the BoB could have been much more costly for the RAF.
ULTRA was significant for the Blitz. In the "Battle of the Beams", R. V. Jones correlated the numbers in certain otherwise meaningless Luftwaffe messages with the directions and settings of German radio-guidance beams. IIRC, this was what allowed him to prove that the Germans were using radio-guidance.
ULTRA was colossal for the Battle of the Atlantic. U-boat attacks were devastating in the first half of 1941, until the British broke the German main naval key, HYDRA. Then losses to U-boats dropped by 2/3 immediately, and remained low until February 1942, when the Germans adopted a new, unbroken key for U-boats (TRITON). Losses jumped back to that high level. The Allies "stayed in the game" through 1942 in part because of Enigma they were still reading. HYDRA alerted them to surface navy operations escorting U-boats going on patrol or returning. TETIS was the key of the U-boat training command, which gave the Allies news of U-boats coming into service and deploying to the Atlantic bases.
TRITON was broken in November 1942, and the slaughter was checked. But when the Germans tweaked TRITON in March 1943 and it went dark for three weeks, the losses again spiked.
In middle 1943, the Allies deployed escort carriers, VLR aircraft, and airborne search radar, and broke the U-boats. But even with these technical advantages, ULTRA was still very useful for maneuvering convoys around U-boat patrol lines, and for hunting U-boats in transit to and from the bases in France.
ULTRA was important to the Double-Cross System. The British read lots of traffic between the Abwehr in Germany and its outstations in Spain. Many important XX agents reported to controllers in Spain. ULTRA allowed the British to see exactly how the Germans were reacting to what the British were feeding them.
ULTRA mattered a lot in the North African theater. It gave the Allies the strength and status of Axis forces on a running basis; it enabled Allied air and naval forces to destroy a substantial proportion of Axis supply to Africa.
Many of the results achieved from ULTRA could have been achieved by other means, but later, and at greater cost.
The most obvious damage is in the Battle of the Atlantic: the Allies would lose about 6M to 8M additional tons of shipping, and would have build many additional escorts instead of landing craft, possibly delaying D-Day by months or even a year.
The loss of ships and supplies would handicap Allied operations in the Middle East in 1941 and 1942. This combines with better supply for the Axis forces in North Africa. Would the Axis have been able to conquer Egypt? If Eighth Army is 20% weaker, and Panzer Armee Afrika is 20% stronger... At the very least, the final Allied drive west from Egypt may be delayed by several months.
Perhaps the most important benefit of ULTRA for the Allies was that it gave them continual, reliable information about the strength, deployment, and status of German forces. This information rarely had clear tactical or operational results (on land), but it meant the Alllies could operate with vastly greater confidence. In a few cases,
overconfidence (as in the Battle of the Bulge), but I think those few cases are far more than offset by the continual advantages of the rest of the time. Would Eighth Army have pressed the attack at Second El Alamein after the initial drive stalled if they had not
known what PAA's strength was? Would SHAEF have been as ready to turn loose U.S. First and Third Armies in July 1944 if they had not been
certain there were no unknown large German reserves?
These are merely examples: those particular battles would not take place. But there could be similar battles, and the Allies would face similar challenges.
As to the Pacific: at least one major U.S. tactical success was due to codebreaking: the battle of Midway. Without the decrypts (and the analysis of them, possible only because of previous decrypts), the U.S. would not have anticipated the Japanese attack. They would not have reinforced Midway, they would not have rushed the repair of
Yorktown, and they would not have had the carriers lying in wait. The result would likely be a Japanese victory, and the Pacific War would be longer; except of course it ends when the Bomb goes off.
