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===The Holocaust and “Final Solution”===

===The Holocaust and “Final Solution”===

Adolf Hitler had blamed the Jewish people for Germany’s troubles and as early as 1933 there were Nazi-supported laws prohibiting Jews from holding official positions in government.  Hitler found it useful for his goals to have a scapegoat, and the Nazis made the Jewish people the scapegoats.  Other people, such as gypsies, also became scapegoats.  Nazis claimed to be returning to Germany tradition in part by particularly excluding Jews.  In 1935, Nazis passed Nuremberg Laws that prohibited Jewish people from owning property or even becoming German citizens.  Nazis also forced Jewish people to wear a bright yellow Star of David on their clothing, as a way of ostracizing them.

Adolf Hitler had blamed the Jewish people for Germany’s troubles and as early as 1933 there were Nazi-supported laws prohibiting Jews from holding official positions in government.  Hitler found it useful for his goals to have a scapegoat, and the Nazis made the Jewish people the scapegoats.  Other people, such as gypsies and homosexuals, also became scapegoats.  Nazis claimed to be returning to German tradition in part by particularly excluding Jews.  In 1935, Nazis passed Nuremberg Laws that prohibited Jewish people from owning property or even becoming German citizens.  Nazis also forced Jewish people to wear a bright yellow Star of David on their clothing, as a way of ostracizing them.

Jewish people began to flee Germany, emigrating to other countries such as the United States and safer countries in Europe.  But other countries, including the United States, had limits on immigration.  The pogrom of the Kristallnacht in 1938, described earlier, increased the Jewish emigration from Germany.

Jewish people began to flee Germany, emigrating to other countries such as the United States and safer countries in Europe.  But other countries, including the United States, had limits on immigration.  The pogrom of the Kristallnacht in 1938, described earlier, increased the Jewish emigration from Germany.

The Enigma was a portable cipher machine, roughly the size of a typewriter, which could encrypt and decrypt secret messages.  It used electro-mechanical rotors to convert a message to a secret code, and then another machine could decode that same message and reveal the original message.  This machine was commercially available beginning in the early 1920s.  The Nazi German military version generated codes widely thought to be unbreakable.  

The Enigma was a portable cipher machine, roughly the size of a typewriter, which could encrypt and decrypt secret messages.  It used electro-mechanical rotors to convert a message to a secret code, and then another machine could decode that same message and reveal the original message.  This machine was commercially available beginning in the early 1920s.  The Nazi German military version generated codes widely thought to be unbreakable.  

The Enigma machine was an electromechanical device, equipped with a 26-letter keyboard, with one light per letter of the alphabet. Inside the machine was a set of wired drums for scrambling the input.  To encipher or encrypt a letter, the operator pushed the relevant key and observed which of the lights lit.  The communication between two operators required that each had an Enigma machine set up in the same way as each other.  The large number of possibilities for setting the rotors (and a plugboard that could swap letters) made for an astronomical number of possible configurations, each producing a different cipher.  The Germans changed the settings daily, such that the code had to be re-broken each day in order to decrypt the messages.  

The Enigma machine was equipped with a 26-letter keyboard, with one light per letter of the alphabet. Inside the machine was a set of wired drums for scrambling the input.  To encipher or encrypt a letter, the operator pushed the relevant key and observed which of the lights lit.  The communication between two operators required that each had an Enigma machine set up in the same way as each other.  The large number of possibilities for setting the rotors (and a plugboard that could swap letters) made for an astronomical number of possible configurations, each producing a different cipher.  The Germans changed the settings daily, such that the code had to be re-broken each day in order to decrypt the messages.  

For others to break (decrypt) the code, they had to figure out how the Enigma functioned, the wiring of its rotors and its daily settings (both rotors and plugboard).  

For others to break (decrypt) the code, they had to figure out how the Enigma functioned, the wiring of its rotors and its daily settings (both rotors and plugboard).  

Nazi Germany used the Enigma before and during World War II to send messages about its military maneuvers.  But in 1932 a 27-year-old Polish mathematician (cryptologist) named Marian Rejewski had used advanced mathematics (permutation theory with some group theory) to secretly break (“crack”) the Enigma codes.  He then helped design working “doubles” of the Enigmas that could find the keys necessary for decryption.  By 1938 the Poles were decrypting most of the German messages, and the Poles shared their marvelous discovery with Great Britain and France.  

Nazi Germany used the Enigma before and during World War II to send messages about its military maneuvers.  But in 1932 a 27-year-old Polish mathematician (specifically, a cryptologist) named Marian Rejewski had used advanced mathematics (permutation theory with some group theory) to secretly break (“crack”) the Enigma codes.  He then helped design working “doubles” of the Enigmas that could find the keys necessary for decryption.  By 1938 the Poles were decrypting most of the German messages, and the Poles shared their marvelous discovery with Great Britain and France.  

This breakthrough enabled the Allies to anticipate German military maneuvers, although sometimes the Allies would allow an attack to occur successfully in order to avoid signaling to the Germans that their code had been broken.  The Allied code-breaking effort was known as “Ultra”, as in “ultra-secret”.  

This breakthrough enabled the Allies to anticipate German military maneuvers, although sometimes the Allies would allow an attack to occur successfully in order to avoid signaling to the Germans that their code had been broken.  The Allied code-breaking effort was known as “Ultra”, as in “ultra-secret”.  

At the end of the war, Allied General Dwight Eisenhower said that Ultra was “decisive” to the Allied victory over Germany.  British Prime Minister Winston Churchill also declared, “It was thanks to Ultra that we won the war.”  The breaking of the German codes prevented it from completely blockading Britain with U-boats and enabled the Allied forces to make key strategic decisions throughout the war.  

At the end of the war, Allied General Dwight Eisenhower said that Ultra was “decisive” to the Allied victory over Germany.  British Prime Minister Winston Churchill also declared, “It was thanks to Ultra that we won the war.”  The breaking of the German codes prevented Germany from completely blockading Britain with U-boats and enabled the Allied forces to make key strategic decisions throughout the war.  

===America Enters the War===

===America Enters the War===