© G. Dhillon, IS Department Virginia Commonwealth University Principles of IS Security Cryptography and Technical IS Security

© G. Dhillon, IS Department Virginia Commonwealth University The process

© G. Dhillon, IS Department Virginia Commonwealth University Time required for key search Key size in bitsNo of alternative keys Time required to decrypt 1 key per microsecondDecryption rate: 1 million keys per microsecond minutes2.15 milliseconds years10 hours x years5.4 x years x years5.9 x years

© G. Dhillon, IS Department Virginia Commonwealth University Basics of cryptanalysis A 0 B 1 C 2 D 3 E 4 F 5 G 6 H 7 I 8 J 9 K 10 L 11 M 12 N 13 O 14 P 15 Q 16 R 17 S 18 T 19 U 20 V 21 W 22 X 23 Y 24 Z 25

© G. Dhillon, IS Department Virginia Commonwealth University Modular Arithmetic Representation of a letter by a number code allows for performing arithmetic to the operation. This form of arithmetic is called modular, where instances such as P + 2 would equal R or Z + 1 equals A would occur. Since the addition wraps around from one end to the other, every result would be between 0 and 25. This form of modular arithmetic is written as mod n. And n is a number in the range 0≤result<n. In net effect the result is the remainder by n.

© G. Dhillon, IS Department Virginia Commonwealth University Example As an example, 53 mod 26 and alternative ways of arriving at the result: 53 mod 26 would be 53 divided by 26, with the remainder being the result, which in this case would be 26 time 2 equals 52 and remainder 1 or Count 53 ahead of A or 0 in the above representation and each time after crossing Z or 25 return to position A or 0. This will result in arriving at B or 1, which is the result. (Note: in the first count begin at 0).

© G. Dhillon, IS Department Virginia Commonwealth University Substitution Caesar Cipher, each letter is translated to a letter that appears after a fixed number of letters in the text. It is said that Caesar used to shift 3 letters. Thus a plaintext A would be d in ciphertext (Note: capital letters are generally used to depict plaintext and ciphertext is in lower text). Based on the Caesar Cipher, a plaintext word such as LONDON would become orqgrq.

© G. Dhillon, IS Department Virginia Commonwealth University Example using richmond 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 r i c h m o n d a b c e f g j k l p q s t u v w x y

© G. Dhillon, IS Department Virginia Commonwealth University Vigenère Cipher cont. The modern Vigenère tableau

© G. Dhillon, IS Department Virginia Commonwealth University Exercise Encrypt: IT WAS THE BEST OF TIMES IT WAS THE WORST OF TIMES And the key word used is KEYWORD.

© G. Dhillon, IS Department Virginia Commonwealth University Cryptanalysis Finding patterns. In order to use this method, one needs to identify all repeated patterns in the ciphertext. Clearly for plaintext to be enciphered twice, the key needs to go through a number of rotations. Any patterns over three characters is certainly not accidental. Factoring distances between repeated bigrams. Kasaki method suggests that the distance between the repeated patterns must be a multiple of the keyword length. For each instance, we write down starting positions and then compute the distance between successive position Bigram Location Distance Factors wg =17 1, 17 co =28 1, 2, 7 qp =7 1, 7 Interpretation. By factoring distances between bigrams helps in interpreting or narrowing down the search for a keyword, which can then be used to decrypt the plaintext message. In our example above the common factors are 1 and 7. Clearly there is less likelihood of a 1 character keyword. This narrows down our task of figuring out the keyword (Note: the keyword used in the above example is 7 characters long KEYWORD).

© G. Dhillon, IS Department Virginia Commonwealth University Transpositions In this case characters of plaintext are rearranged into columns In this case characters of plaintext are rearranged into columns. As an example, the message IT WAS THE BEST OF TIMES IT WAS THE WORST OF TIMES would be written as: I T W A S T H E B E S T O F T I M E S I T W A S T H E W O R S T O F T I M E S X The ciphertext for this message would be: itsi this thtm wetm weoe awoe seti trtx

© G. Dhillon, IS Department Virginia Commonwealth University Digrams In any language there are certain letters that have a high frequency of appearing together. These are referred to as digrams. For example, the ten most common digrams in English language are: EN, RE, ER, NT, TH, ON, IN, TF, AN and OR. The ten most common trigrams are: ENT, ION, AND, ING, IVE, TIO, FOR, OUR, THI, ONE.

© G. Dhillon, IS Department Virginia Commonwealth University

© G. Dhillon, IS Department Virginia Commonwealth University DES

© G. Dhillon, IS Department Virginia Commonwealth University Details of the cycle