1.How is math used to decipher secret codes?Using your knowledge of coding theory and logic describe how the codes were made and broken.Your response must be 200-300 words in length.
Secret codes are a terrific source of enrichment material for mathematics. The process of encoding and decoding is inherently mathematical, and much sophisticated mathetics has been used and/or developed in connection with cryptography. Cracking codes and unravelling the true meaning of secret messages involves loads of maths, from simple addition and subtraction, to data handling and logical thinking. In fact, some of the most famous code breakers in history have been mathematicians who have been able to use quite simple maths to uncovered plots, identify traitors and influence battles. Warring armies have encrypted their commmunications in an attempt to keep their battle plans a secret from their enemies. Just as one side invented an ingenious new way to encipher its messages, so would its enemies discover a clever way of cracking that code. The result has been that codes and ciphers have become more and more complex and increasingly difficult to crack over time, as, throughout history, an intellectual battle as raged between code makers and code breakers. The most advanced forms of encryption involved simple paper and pencil techniques. But security blunders on both sides during the First World War highlighted a need for a higher level of secrecy, with more advanced methods of enciphering messages. Both the Allies and the Axis countries were looking for a new way to encrypt messages. Secret code is what makes math easier and also it makes the world smarter.
Cracking codes and unraveling the true meaning of secret messages involves loads of math. This can be from simple addition and subtraction, to data handling and logical thinking. In fact, some of the most famous code breakers in history have been mathematicians who have been able to use simple math to uncover plots, identify traitors, and/or influence battles. For example, Julius Caesar was busy taking over the world, invading countries to increase the size of the Roman Empire, so he needed a way of communicating his battle plans and tactics to everyone on his side without the enemy finding out. Caesar then would write messages to his generals in code. Instead of writing the letter 'A', he would write the letter that comes three places further on in the alphabet, the letter 'D'. Instead of a 'B', he would write an 'E', instead of a 'C', he would write an 'F', etc. When he got to the end of the alphabet, however, he would have to go right back to the beginning, so instead of an 'X', he would write an 'A', and instead of a 'Y', he'd write a 'B', etc. This all seems very clever, but so far it's all been letters and no numbers. So how does math come into play? Well, the math comes if you think of the letters as numbers from 0 to 25 with A being 0, B being 1, etc. So, in the code, shifting the alphabet forward three places, is the same as adding three to your starting number. However, you do have to be careful when you get to the end of the alphabet, because there is no letter number 26, so you have to go back to number 0. This is known as 'MOD 26'. If you've got the hang of coding messages by shifting the alphabet forward, then you might have realized that it is actually pretty simple to crack this type of code. It can easily be done just by trail and error. An enemy code breaker would only have to try about 25 different possible shifts before they were able to read your messages, which means that your messages wouldn't be secret for very long. This technique was used much as a “way to stay safe” when trying to communicate information without your enemy knowing. Coding is still being used today!
The tv episode numbers is a great example how math can be used for just about anything and in the movie called breaking the enigma code it talks to us about how the machines were used during the war and how math was a big part of these codes. Letters and numbers are key factors in secret codes. Instead of writing numbers they would be letters and each letter would have a number to it, for example 0 would be A and B would be 1 and so on. Except you can only go to letter 26 since is the highest you can go in the alphabet z, you would go back to 0 or "A" again. This machine was genius and was used alot during the war. Deciphering codes involves basically just numbers and letters except more complext than that. Dont let it fool you though, these codes sometimes took hours to decode and figure out and if you made one mistake while making the code it would be impossible to break the code on the other side. Making these codes and breaking them you would use an enigma machine. To make a code you write your message and it gets scrambled between 3 to 5 notches. To unbreak the code you would need have your rotors in the same exact setting as the machine it was made on then the plugs later on where added to the machine, then the receiver has limited time to decode the message before the enemy did!
When the war broke out many of the countries would send messages by boat but that would take weeks or even months to get the message to the allies or whom ever. Then they came up with another way to commumincate with each other durring the war and they could confuse the enemies.They would do this but sending coded messages. When they sent coded messages only the person with the code or key would be about to crack it nd tell the people what they said or whatever. When they didnt have enough people to do this task they started to teach others how to crack the codes. these people became experts in cracking these codes. but even though they were experts they still took hours to crack them. hen they did they could tell the people that needed the message the message. Durring the war many people made different codes and machines that made it much difficult for them to crack the codes by hand so they tried to build one. ONce they did they found out what those countries were gong to do. So what code basically does for the military and wars is that it helps them tell there allies things without the other people know what they said.
There are many different ways that people use different things such as sounds, numbers, and symbols that are basically meant to represent letters. For example, back in the war people would send things over Morse code, which was basically a dot, and dash system that meant words. A perfect example is the show numbers or also, how there are cases where people in prisons send letters in different languages or such so that they can say things other than what it would say to anyone else. But in the end math can be used to decode all of them. To explain, with math people can do more things such as this other than just the simple facts of adding, and subtracting. I cant really say much more on this subject due to the fact that I haven’t really been taught about this type of thing before, therefore that’s mainly what I have to say about how I feel mathematics and numerals are used to decipher and decode messages such as like I said before secret messages that are obviously put in the form they are so that people such as me nor others can see or know what they mean.
Math can be found just about everywhere in the world. It is the one subject that you cannot go through life without using. Cracking codes and siphers is extrememly important especially in the case of war. These codes are cracked using mathmatical equations and logical reasoning, which is also apart of math. Numbers and symbols or different lettering systems can be used in order to convey secret messages. This is what the movie, 'Breaking the Enigma Code.' During the World Wars, codes were secretly being intercepted and attempted to be cracked in order for opposing countries to learn of their enemies plans. An example of this is the Zimmerman telegram that was sent by Germany but intercepted by the British. They were able to use analysts and mathematicians to crack the German code. This provided them with the information that Germany was going to use submarine warfare and involve Mexico. This was a huge turning point in the war because it enabled America to become apart of the war. If America had not, the British would have lost. The Zimmerman telegram is said to be the most important code ever cracked. The Polish people were also the leaders in cracking foreign codes and enigmas. Math is very much involved in these codes and their deciphering because some machines, like the German enigma machine use a pattern of routers that turn in certain ways and plugs that tell the letters. Reasoning and logical deduction helped the Polish people crack these German codes. Coding is very important to the world and cracking the codes is even more important. Who knows where the world would be if the secret codes of America's enemies were never cracked.
Math is used in code breaking in different ways such as sounds, numbers, and symbols that represent letters. An example would be morse code. This was described in "Breaking the Enigma Code." During World War 1 the british used code breaking to know what the Germans were doing at all times. The zimmerman note was a great example. The zimmerman note was sent to Mexico by Germany, when the code was cracked and it eventually brought the United States into the war. During the 20's and 30's the polish and the french became extremly good at cracking codes. They were always mointoring the Germans. The germans invented a machine that was unbreakable. It was invented by three college students that were geniuses. The machine used routers that turn certain ways and only the germans knew. They would have many different routers that they could use. These codes were eventually cracked by the Polish. Reasoning ans Logical deduction cracked the codes. Coding is very important to wars because it can determine whether or not you win or loose the war. The US at one point even used Navajo Indians so that no one could learn there language.
Math is used to decipher codes in all ways around the world. Some use sound and other tecniques like numbers to send secrete messages to send to other people in the army. The army mainly uses codes to signal to plan attacks against the enemy. The germans were the most skilled at making codes that no one could break. The U.S. could have prevented the bombing on Pearl Harbor if they would have deciphered the codes in faster time. Later in the U.S. history machines took over and were more efficient at deciphering and no longer was the human mind able to crack the codes in a timely manner.
In the movie it has become obvious that cracking codes and ciphers involves alot of mathematical concepts. If math was not involved in creating these codes then it would make it a lot easier for the enemy to decode them. That is why we use mathematical codes using numbers, letter, and or symbols with secret messages with in them. Once decoding the messages by the own human mind got increasingly easier a machine called the "Enigma" was created. This machine allowed a mathematical equation using numbers and letters to create and hide a code. The machine would make it increasingly harder for the human mind to crack such codes. Math and the alphabet are both used together when creating a hidden message. For example the letter A would be 0 and so on and so forth. During war times this way of communication was vital to an armies plans and tactics. Also an army would try and retrieve enemy codes and decode them before they would have time to execute their plans. Yet once the machine was created it became a lot harder for both armies to decode one another's hidden messages. To crack the codes even with the machine you would need a specific part that would able the machine to go back and retrace the mathematical equation and provide you with the embedded messages. Over time many mathematical equations were created to make codes harder to solve. Math is a huge aspect of creating a embedded code. With out the use of math in creating a code, it would be a lot easier for the enemy to decode. That is why mathematical equations and science are both needed in creating and decoding these secret messages.
during world war one code making and code breaking became more relevent to the outcome of the war. infact the decodation of the zimmerman note by british code breakers helped turn the tide of the war. it brought theunited states into the war on the allied side which was vital to a allied victory. with the invention of wireless telegraph it was quiet easy for the british to recieve the german codes especcially after they cut the german landline leaving them with no other choice but to use wireless. it was deciphering the code that was the problem. the british put together a special unite dedicated to crypt analisi. the members in this unite were all highly intellegent and understood advanced mathmatics becouse to decipher codes and ciphers quiet a bit of arithmatic must be used. one of these codebreakers had recieved a message in high grade german cipher suggesting it was important. using bits and pieces of old messages that other codebreakers had broke they were able to put the message into readable german which they then translated and discovered the zimmerman note and thus turned the tide of the great war
in world war 2 codes and ciphers andvanced along with the technology. in the pursuit of a unbreakable codethe germans made a machine that feild troops could use to trype messages in with out having to go back to hq or have theenemy decode them. the machine was quiet complicated but put simply when u push a letter such as H a message would be sent via wires to a large disc that would code the letter H that u typed in into another letter and then send that letter to a seond wheel and the processes would be repeated up to 8 times near the end of the war. the downside is that the reciever of the messages had to have the disc in exactly the same as the sender. a code breaker with nothing more then a calculator would have had to take years to decipher this code luckily the allies had developed a machine that would take the message and spit out all possible options in mere hours leaving one that would actually be coherent. the americans were actually more succesful on the code making front. they used navajo and their distinct native american dilect to make a code. it was not cracked by the japanese who it was used against and was inmesurably useful in the war effort
The significance of math and code breaking is very similar. You need math to figure out the patterns for the message to figure out what it said. For example back in the Caesar Augustus time period he would send messages with different letters than what the message states. He sent instead of an A he’d write a C, every letter was 3 letters forward in the alphabet than what the letter actually was. If the enemy was trying to decode it then they would have to use mathematical equations to figure it out, granted for Caesar’s code it wouldn’t be too hard it would only take 25 attempts to figure it out but the point is that it would take math to figure it out. Later they realized it really wasn’t that hard to figure out so they started changing letters for symbols making it extremely hard and millions of different processes to figure out the message. Once you get into those harder messages that have a lot of things that it could be, then you obviously have to start going into more complex mathematical equations due to the vast number of attempts that will need to be done. There are many ways that math helps in cracking codes and it is obvious that without it, it would be extremely hard and nearly impossible to figure out.
The use of math was highly effective during the war. Numbers, symbols and letters were used as a code to deliver information to someone without the enemy deciphering the codes. However, many people were trained to read morse code and read the codes that were being sent by a special machine. With this machine, you could type a certain letter and another letter on a separate keyboard would light up to indicate what that letter represented. As easy as this seems, it was actually a complex process. Both the receiver of the code and the sender must have the wheels and settings of their machine match exactly or it won't decipher properly. Every letter either represented a totally different letter to make code breaking more difficult. More secret codes would have a letter be represented as a complex number that would take much too long to figure out. A certain code would would be a pattern of numbers representing letters. The letter A would represent 0; B, 1; C, 2 etc. But once you got to the number nine, it would start back at 0 and it became much more difficult to break the codes. Specific codes would transfer information about specific warfare, tactics and maneuvers that would be used against the enemies.
Secret codes are a terrific source of enrichment material for mathematics. The process of encoding and decoding is inherently mathematical, and much sophisticated mathetics has been used and/or developed in connection with cryptography. Cracking codes and unravelling the true meaning of secret messages involves loads of maths, from simple addition and subtraction, to data handling and logical thinking. In fact, some of the most famous code breakers in history have been mathematicians who have been able to use quite simple maths to uncovered plots, identify traitors and influence battles. Warring armies have encrypted their commmunications in an attempt to keep their battle plans a secret from their enemies. Just as one side invented an ingenious new way to encipher its messages, so would its enemies discover a clever way of cracking that code. The result has been that codes and ciphers have become more and more complex and increasingly difficult to crack over time, as, throughout history, an intellectual battle as raged between code makers and code breakers. The most advanced forms of encryption involved simple paper and pencil techniques. But security blunders on both sides during the First World War highlighted a need for a higher level of secrecy, with more advanced methods of enciphering messages. Both the Allies and the Axis countries were looking for a new way to encrypt messages. Secret code is what makes math easier and also it makes the world smarter.
ReplyDeleteCracking codes and unraveling the true meaning of secret messages involves loads of math. This can be from simple addition and subtraction, to data handling and logical thinking. In fact, some of the most famous code breakers in history have been mathematicians who have been able to use simple math to uncover plots, identify traitors, and/or influence battles.
ReplyDeleteFor example, Julius Caesar was busy taking over the world, invading countries to increase the size of the Roman Empire, so he needed a way of communicating his battle plans and tactics to everyone on his side without the enemy finding out. Caesar then would write messages to his generals in code. Instead of writing the letter 'A', he would write the letter that comes three places further on in the alphabet, the letter 'D'. Instead of a 'B', he would write an 'E', instead of a 'C', he would write an 'F', etc. When he got to the end of the alphabet, however, he would have to go right back to the beginning, so instead of an 'X', he would write an 'A', and instead of a 'Y', he'd write a 'B', etc.
This all seems very clever, but so far it's all been letters and no numbers. So how does math come into play? Well, the math comes if you think of the letters as numbers from 0 to 25 with A being 0, B being 1, etc. So, in the code, shifting the alphabet forward three places, is the same as adding three to your starting number. However, you do have to be careful when you get to the end of the alphabet, because there is no letter number 26, so you have to go back to number 0. This is known as 'MOD 26'.
If you've got the hang of coding messages by shifting the alphabet forward, then you might have realized that it is actually pretty simple to crack this type of code. It can easily be done just by trail and error. An enemy code breaker would only have to try about 25 different possible shifts before they were able to read your messages, which means that your messages wouldn't be secret for very long. This technique was used much as a “way to stay safe” when trying to communicate information without your enemy knowing. Coding is still being used today!
The tv episode numbers is a great example how math can be used for just about anything and in the movie called breaking the enigma code it talks to us about how the machines were used during the war and how math was a big part of these codes. Letters and numbers are key factors in secret codes. Instead of writing numbers they would be letters and each letter would have a number to it, for example 0 would be A and B would be 1 and so on. Except you can only go to letter 26 since is the highest you can go in the alphabet z, you would go back to 0 or "A" again. This machine was genius and was used alot during the war. Deciphering codes involves basically just numbers and letters except more complext than that. Dont let it fool you though, these codes sometimes took hours to decode and figure out and if you made one mistake while making the code it would be impossible to break the code on the other side. Making these codes and breaking them you would use an enigma machine. To make a code you write your message and it gets scrambled between 3 to 5 notches. To unbreak the code you would need have your rotors in the same exact setting as the machine it was made on then the plugs later on where added to the machine, then the receiver has limited time to decode the message before the enemy did!
ReplyDeleteWhen the war broke out many of the countries would send messages by boat but that would take weeks or even months to get the message to the allies or whom ever. Then they came up with another way to commumincate with each other durring the war and they could confuse the enemies.They would do this but sending coded messages. When they sent coded messages only the person with the code or key would be about to crack it nd tell the people what they said or whatever. When they didnt have enough people to do this task they started to teach others how to crack the codes. these people became experts in cracking these codes. but even though they were experts they still took hours to crack them. hen they did they could tell the people that needed the message the message. Durring the war many people made different codes and machines that made it much difficult for them to crack the codes by hand so they tried to build one. ONce they did they found out what those countries were gong to do. So what code basically does for the military and wars is that it helps them tell there allies things without the other people know what they said.
ReplyDeletemy blog post got deleted after i wrote it sorry...-paige carterrrrrr
ReplyDeleteThere are many different ways that people use different things such as sounds, numbers, and symbols that are basically meant to represent letters. For example, back in the war people would send things over Morse code, which was basically a dot, and dash system that meant words. A perfect example is the show numbers or also, how there are cases where people in prisons send letters in different languages or such so that they can say things other than what it would say to anyone else. But in the end math can be used to decode all of them. To explain, with math people can do more things such as this other than just the simple facts of adding, and subtracting. I cant really say much more on this subject due to the fact that I haven’t really been taught about this type of thing before, therefore that’s mainly what I have to say about how I feel mathematics and numerals are used to decipher and decode messages such as like I said before secret messages that are obviously put in the form they are so that people such as me nor others can see or know what they mean.
ReplyDeleteMath can be found just about everywhere in the world. It is the one subject that you cannot go through life without using. Cracking codes and siphers is extrememly important especially in the case of war. These codes are cracked using mathmatical equations and logical reasoning, which is also apart of math. Numbers and symbols or different lettering systems can be used in order to convey secret messages. This is what the movie, 'Breaking the Enigma Code.' During the World Wars, codes were secretly being intercepted and attempted to be cracked in order for opposing countries to learn of their enemies plans. An example of this is the Zimmerman telegram that was sent by Germany but intercepted by the British. They were able to use analysts and mathematicians to crack the German code. This provided them with the information that Germany was going to use submarine warfare and involve Mexico. This was a huge turning point in the war because it enabled America to become apart of the war. If America had not, the British would have lost. The Zimmerman telegram is said to be the most important code ever cracked. The Polish people were also the leaders in cracking foreign codes and enigmas. Math is very much involved in these codes and their deciphering because some machines, like the German enigma machine use a pattern of routers that turn in certain ways and plugs that tell the letters. Reasoning and logical deduction helped the Polish people crack these German codes. Coding is very important to the world and cracking the codes is even more important. Who knows where the world would be if the secret codes of America's enemies were never cracked.
ReplyDeleteThat Anonymous above was mine: Carly Edwards
ReplyDeleteMath is used in code breaking in different ways such as sounds, numbers, and symbols that represent letters. An example would be morse code. This was described in "Breaking the Enigma Code." During World War 1 the british used code breaking to know what the Germans were doing at all times. The zimmerman note was a great example. The zimmerman note was sent to Mexico by Germany, when the code was cracked and it eventually brought the United States into the war. During the 20's and 30's the polish and the french became extremly good at cracking codes. They were always mointoring the Germans. The germans invented a machine that was unbreakable. It was invented by three college students that were geniuses. The machine used routers that turn certain ways and only the germans knew. They would have many different routers that they could use. These codes were eventually cracked by the Polish. Reasoning ans Logical deduction cracked the codes. Coding is very important to wars because it can determine whether or not you win or loose the war. The US at one point even used Navajo Indians so that no one could learn there language.
ReplyDeletethat last comment was bobby burns
ReplyDeleteMath is used to decipher codes in all ways around the world. Some use sound and other tecniques like numbers to send secrete messages to send to other people in the army. The army mainly uses codes to signal to plan attacks against the enemy. The germans were the most skilled at making codes that no one could break. The U.S. could have prevented the bombing on Pearl Harbor if they would have deciphered the codes in faster time. Later in the U.S. history machines took over and were more efficient at deciphering and no longer was the human mind able to crack the codes in a timely manner.
ReplyDeleteIn the movie it has become obvious that cracking codes and ciphers involves alot of mathematical concepts. If math was not involved in creating these codes then it would make it a lot easier for the enemy to decode them. That is why we use mathematical codes using numbers, letter, and or symbols with secret messages with in them. Once decoding the messages by the own human mind got increasingly easier a machine called the "Enigma" was created. This machine allowed a mathematical equation using numbers and letters to create and hide a code. The machine would make it increasingly harder for the human mind to crack such codes. Math and the alphabet are both used together when creating a hidden message. For example the letter A would be 0 and so on and so forth. During war times this way of communication was vital to an armies plans and tactics. Also an army would try and retrieve enemy codes and decode them before they would have time to execute their plans. Yet once the machine was created it became a lot harder for both armies to decode one another's hidden messages. To crack the codes even with the machine you would need a specific part that would able the machine to go back and retrace the mathematical equation and provide you with the embedded messages. Over time many mathematical equations were created to make codes harder to solve. Math is a huge aspect of creating a embedded code. With out the use of math in creating a code, it would be a lot easier for the enemy to decode. That is why mathematical equations and science are both needed in creating and decoding these secret messages.
ReplyDeleteduring world war one code making and code breaking became more relevent to the outcome of the war. infact the decodation of the zimmerman note by british code breakers helped turn the tide of the war. it brought theunited states into the war on the allied side which was vital to a allied victory. with the invention of wireless telegraph it was quiet easy for the british to recieve the german codes especcially after they cut the german landline leaving them with no other choice but to use wireless. it was deciphering the code that was the problem. the british put together a special unite dedicated to crypt analisi. the members in this unite were all highly intellegent and understood advanced mathmatics becouse to decipher codes and ciphers quiet a bit of arithmatic must be used. one of these codebreakers had recieved a message in high grade german cipher suggesting it was important. using bits and pieces of old messages that other codebreakers had broke they were able to put the message into readable german which they then translated and discovered the zimmerman note and thus turned the tide of the great war
ReplyDeletein world war 2 codes and ciphers andvanced along with the technology. in the pursuit of a unbreakable codethe germans made a machine that feild troops could use to trype messages in with out having to go back to hq or have theenemy decode them. the machine was quiet complicated but put simply when u push a letter such as H a message would be sent via wires to a large disc that would code the letter H that u typed in into another letter and then send that letter to a seond wheel and the processes would be repeated up to 8 times near the end of the war. the downside is that the reciever of the messages had to have the disc in exactly the same as the sender. a code breaker with nothing more then a calculator would have had to take years to decipher this code luckily the allies had developed a machine that would take the message and spit out all possible options in mere hours leaving one that would actually be coherent. the americans were actually more succesful on the code making front. they used navajo and their distinct native american dilect to make a code. it was not cracked by the japanese who it was used against and was inmesurably useful in the war effort
ReplyDeleteThe significance of math and code breaking is very similar. You need math to figure out the patterns for the message to figure out what it said. For example back in the Caesar Augustus time period he would send messages with different letters than what the message states. He sent instead of an A he’d write a C, every letter was 3 letters forward in the alphabet than what the letter actually was. If the enemy was trying to decode it then they would have to use mathematical equations to figure it out, granted for Caesar’s code it wouldn’t be too hard it would only take 25 attempts to figure it out but the point is that it would take math to figure it out. Later they realized it really wasn’t that hard to figure out so they started changing letters for symbols making it extremely hard and millions of different processes to figure out the message. Once you get into those harder messages that have a lot of things that it could be, then you obviously have to start going into more complex mathematical equations due to the vast number of attempts that will need to be done. There are many ways that math helps in cracking codes and it is obvious that without it, it would be extremely hard and nearly impossible to figure out.
ReplyDeleteThe use of math was highly effective during the war. Numbers, symbols and letters were used as a code to deliver information to someone without the enemy deciphering the codes. However, many people were trained to read morse code and read the codes that were being sent by a special machine. With this machine, you could type a certain letter and another letter on a separate keyboard would light up to indicate what that letter represented. As easy as this seems, it was actually a complex process. Both the receiver of the code and the sender must have the wheels and settings of their machine match exactly or it won't decipher properly. Every letter either represented a totally different letter to make code breaking more difficult. More secret codes would have a letter be represented as a complex number that would take much too long to figure out. A certain code would would be a pattern of numbers representing letters. The letter A would represent 0; B, 1; C, 2 etc. But once you got to the number nine, it would start back at 0 and it became much more difficult to break the codes. Specific codes would transfer information about specific warfare, tactics and maneuvers that would be used against the enemies.
ReplyDelete