Cryptography the method of applying protocols to information to make it seem like nonsense to hurt those who do not know the protocols. Cryptology is used to encrypt messages and create secure codes; the earliest known use of Cryptographs was in Egyptian times but over time several different types of cryptographs were made today we use it to keep information secure and to create registration numbers.
Focus:
This IA will focus on the math involved in certain ciphers, these ciphers are.
The classic cipher
Substitution cipher
ISBN codes
Public Key
Credit Card codes
Aim
My aim is to understand the ciphers and see if I can make some of my own
Investigation
Transition/Classic Cipher
This was a simple cipher and one of the earliest established. It was said that Julius Caesar used this cipher to protect messages of military importance, it is also known as the Caesar shift. The reason it is simple is because during the time not many people could read.
# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Plain a b c d e f g h i j k l m n o p q r s t u v w x y z cipher C D E F G H I J K L M N O P Q R S T U V W X Y Z A B
In this example each letter is given a corresponding numerical value, add 2 to that number then turn it back into a letter . It can be represented by the mathematical formula f(x)=x+2 and to change it back it would be the inverse of the function (x)^(-1)=x-2 . Using this formula a phrase like “Hello my name is” would become “jgkkqoaqcogku”. It seems like complete nonsense there are also no spaces in between words to make it harder to decrypt, to anyone who saw it and didn’t know that it was would just leave that information alone but knowing the cipher it is easily deciphered so it isn’t used ...
... middle of paper ...
...ple
Choose two distinct prim numbers p and q. p=2 , q =13
Work out n, n= pq n = 26
Work out S, S= (p-1)(p-2) S = (2-1)(13-1) = 1 x 12 = 12
Choose a number A which is smaller than S and has no common factors. A = 5
Find H, HA-1 is a multiple of S 5H-1 is a multiple of 12
H = 5
To encrypt Find N by working out V=NA (mod n) Calculated below
To decrypt Find V by working out N= VS (mod n)
V N
1 15 (mod 26) =1
2 25 (mod 26) = 32 (mod 26) = 6
3 35 (mod 26) = 243 (mod 26) = 9
4 45 (mod 26) = 1024 (mod 26) = 10
Once again the numbers refer to letters in the alphabet. The only number that needs to remain secret is S because only it can decipher the code.
As it can be seen the number for S is 12 which is a very high number to use as an exponent and can be difficult to calculate but using math we can figure it out. Using the formula ab(mod n) = ((a mod n)(b mod n)) mod n
One of Great Britain’s most important naval developments was the founding of the top-secret Office of Naval Intelligence, better known as Room 40. Specializing in cryptography, “the science of writing in secret code” in order to hide sensitive information, Room 40’s cryptanalysts worked around the clock to break the secret code. Decryption is vital in secret transmissions concerning strategic war movements, as the enemy will be looking to intercept information concerning movements and positioning. Great Britain was aided in that the German Navy started the war with three primary codes, and within four months the British Admiralty possessed physical copies of all three of them.
The sender would type the message in plaintext (not encrypted) and the letters would be illuminated on a glass screen. With the press of each typewriter key the rotor would shift 1/26 of a revolution giving each letter a different encryption each time, which made the code so difficult to crack. Due to the complexity of the code the enigma became very useful for the Germans for radioing messages to u-boats. The cipher was finally broken when the British were able to capture some key documents from a German warship.
Cipher can be compared to the prisoner or the Athenian in Ancient Greece who would resist the see to the truth. They felt extremely comfortable
What is encryption? Encryption is a technological technique that protects and secures the transfer of plain text information between two sources through the use of the internet. This is done by rearranging the text using a mathematical algorithm that renovates the message into an indecipherable form, which can only be unlocked and translated with a use of a key. The strength of the encryption key is measured by its length, which is determined by the number of bits and by the type of encryption program.
The code assigned letters in the alphabet and numbers a set of dots (short marks) and dashes (long marks) based on the frequency of use. The code used the English alphabet but they would make the more frequently used letters into the less complex dots and dashes, such as E or A. While the Less frequently used letters such as D or Z got a lot more complex code of dots and dashes. Initially, the code, when transmitted over the telegraph system, was rendered as marks on a piece of paper that the telegraph operator would then translate back into English. Rather quickly. But then the operators became so good at translating the
The RSA encryption is related to the cipher of Julius Caesar (1300s) that shifts three letters to encode messages. The cipher of Julius Caesar was used in war to send messages securely. Here is how Caesar encodes his message using the cipher. First Caesar assigned A through Z to 0 through 25. For instance A is zero. Second, add three to each numbers.
The way a shift cipher works is that a letter in plaintext, is replaced by another letter from the alphabet. When using the Standard English alphabet you will have twenty-six different letters that the plaintext can be ciphered to, for example, the plaintext letter “e” could be enciphered to the ciphertext letter “m” meaning the letters would have shifted by eight. The “key” for your enciphered text is now eight, because it takes eight letters from “e” to get to the letter “m”. With this information, it can be seen why a simple shift cipher could easily be decrypted when using only a pair of letters. For example say someone is trying to decrypt a stolen piece of ciphertext, the only way this person will be able to decrypt this piece of text is if they know the way it is encrypted, and the key. The important thing to remember is that the thief may know how it is encrypted but unless he knows the key, he will not be able to decrypt the text. The key is the most important part in any piece of ciphertext, and should only be known to the sender and the receiver of the encrypted text. In this lies the problem with the shift cipher.
Data encryption refers to the process of transforming electronic information into a scrambled form that can only be read by someone who knows how to translate the code. In nowadays business world, it’s the easiest and most practical way to secure the information that we stored and processed, and it’s significant for our sensitive information. For example, as electronic commerce is popular now, the vendors and retailers must protect the customers’ personal information from hackers or competitors. They also have many business files or contracts that need to be strictly protected. Without data encryption, these important information may fall into wrong hands and be misused by others. Besides, data encryption may be used to secure sensitive information that exists on company networks, or create digital signatures, and help to authorize in business. No one should underestimate the importance of encryption. A little mistake in encryption may make sensitive information revealing, or even result in illegal and criminal accuse.
The enigma code was first broken in 1933 by Polish mathematician and cryptologist Marian Rejewski, with the help of his two fellow colleagues Henryk Zygalski and Jerzy Rózyki. While studying at Poznań University in 1929, Rejewski began attending a cryptology course held by the Polish General Staff ’s Cipher Bureau which was only available to the university’s most advanced mathematics students.
Codes have been around for centuries ranging from wax, invisible ink, Morse code, the Enigma used by the Germans during World War II and now steganographic. Steganography is the latest form to insidiously hide information over the Internet without a trace of a file being altered. You are able to hide messages within images, voice or music. Steganography is an ancient method of hiding messages. Today messages are hidden in images and music. Steganography can be traced back to the ancient Greek who would write messages on tablets and cover them in wax. This made the tablets look blank and unsuspicious (Kolata, F4). Citizens of ancient civilizations would tattoo messages on their shaved heads. They would then let their hair grown in and travel across enemy lines to deliver the message (Seper, G1). During World War II the Allies placed a ban on flower deliveries with dates, crossword puzzles and even report cards (Kolata, F4) for fear of a message being hidden with in. Steganographers first alter their data by using encryption and then place the image into a pre-select image. Steganographers look for a piece of code that would be the least significant and look the least altered to the human eye (Kolata, F4), being as inconspicuousness and random as possible. This makes the messages undetectable unless you knew that there is a message hidden and you were able to crack the code.
Computer science is a vast field that includes nearly everything relating to computers. Everyday there is information transmitted all over the Internet. Pictures are uploaded, transactions are made on thousands of online retail websites, and banking transactions take place everyday on the Internet. All of these transactions have created a need for secure communications. People wish to keep things like banking, medical, and political information from the eyes of unwelcome parties. This has created a need for cryptography. Cryptography is the science or study of the techniques of secret writing, especially code and cipher systems, and is used by everyone from the average citizen to the government and military.
Digital Evidence is electronic data, materials, objects, property, documents, or records that are presented in court to prove or disprove allegations made against an arrestee. It takes the form of electronic data or information stored in bits and bytes on magnetic media. The examples of devices that can contain digital evidence include; cellular phones or similar all in one devices, pagers, digital voice recorders.
The internet allows people to communicate sensitive information, and if received in the wrong hands can cause many problems for that person. Cryptography is the study or science of techniques of secret writing and message hiding. Cryptography constitutes any method in which someone attempts to hide a message, or the meaning, in some medium. One specific element of cryptography is encryption, which hides the data or information by transforming it into undecipherable code. Encryption uses a specified key to perform the data transformation.
...ing the first half of 2007 has revealed that the study found the banking industry as soft target for phishing scams in India.
In this era when the Internet provides essential communication between tens of millions of people and is being increasingly used as a tool for security becomes a tremendously important issue to deal with, So it is important to deal with it. There are many aspects to security and many applications, ranging from secure commerce and payments to private communications and protecting passwords. One essential aspect for secure communications is that of cryptography. But it is important to note that while cryptography is necessary for secure communications, it is not by itself sufficient. Cryptography is the science of writing in secret code and is an ancient art; In the old age people use to send encoded message which can be understand by the receiver only who know the symbolic and relative meaning of that encoded message .The first documented use of cryptography in writing dates back to circa 1900 B.C. Egyptian scribe used non-standard hieroglyphs in an inscription. After writing was invented cryptography appeared spontaneously with applications ranging from diplomatic missives to war-time battle plans. It is no surprise, then, that new forms of cryptography came soon after the widespread development of computer communications. In telecommunications and data cryptography is necessary when communicating in any untrusted medium, which includes any network, particularly the Internet [1].Within the context of any application-to-application communication, there are some security requirements, including: