Cryptology Notes PDF

Cryptology Related to codes on books and grocery items are secret codes. These codes are used to send messages between people, companies, or nations. It is hoped that by devising a code that is difficult to break, the sender can prevent the communication from being read if it is intercepted by an un...

Cryptology Related to codes on books and grocery items are secret codes. These codes are used to send messages between people, companies, or nations. It is hoped that by devising a code that is difficult to break, the sender can prevent the communication from being read if it is intercepted by an unauthorized person. Cryptology is the study of making and breaking secret codes Plaintext is a message before it is coded. Ciphertext is the message after it has been written in code. Example Plain text: LOVE Ciphertext : ORYH The method of changing from plaintext to ciphertext is called encryption. In encrypting the plain text, LOVE, we need a cyclical encrypting code. For example if the cylical encrypting code is 3, each letter of the alphabet is shifted the same number of positions, that is 3 places to the right. Thus A is shifted to D, L is shifted to O, O is shifted to R, V is shifted to Y, and E is shifted to H Therefore, the ciphertext for LOVE is ORYH. The line SHE WALKS IN BEAUTY LIKE THE NIGHT from Lord Byron’s poem “She Walks in Beauty” is in plaintext. Ciphertext is the message after it has been written in code. The line ODA SWHGO EJ XAWQPU HEGA PDA JECDP is the same line of the poem in ciphertext. Can you guess what is the cyclical encrypting code? The line from the poem was encrypted by substituting each letter in plaintext with the letter that is 22 letters after that letter in the alphabet. (Continue from the beginning when the end of the alphabet is reached.) This is called a cyclical coding scheme because each letter of the alphabet is shifted the same number of positions. The original alphabet and the substitute alphabet are shown below.  Formula for Encryption (Encoding) c=(p+m) mod 26 where p = the numerical equivalent of the plain text letter c = the numerical equivalent of the cipher text letter m = cyclical encrypting code Numerical Equivalent for Letters of the English Alphabet  Encoding Catherine the Great c=(p+m) mod 26 Suppose m = 11 (cyclical encrypting code) C corresponds to the number 3, hence p = 3 c = (3 + 11) mod 26 = 14 mod 26 and 14 N. Therefore, C (plaintext) N (ciphertext) A corresponds to the number 1, hence p = 1 c = (1+11)mod 26 = 12 mod 26 and 12 L Therefore, A (plaintext) L (ciphertext) Plaintext: CATHERINE THE GREAT Cipher text: NLESPCTYP ESP RCPLE  Formula for Decryption (Decoding) p = (c+n) mod 26 where p = numerical equivalent of plaintext letter c = numerical equivalent of the ciphertext letter n = may vary depending on the cyclical encrypting code n = 26 - m Once plaintext has been converted to ciphertext, there must be a method by which the person receiving the message can return the message to plaintext. For the cyclical code, the congruence is p = c + n mod 26, where p and c are defined as before and n = 26 - m. The letter N in ciphertext (refer to given example) is decoded below using the congruence p = (c + n) mod 26. Since m = 11, hence n = 26 – 11 = 15; Since N = 14, p = (14 +15) mod 26 p = 29 mod 26 p = 3 mod 26 p = 3. The 3rd letter is C. Thus N is decoded as C. Use m = 7 a. Encode ALPINE SKIING. b. Decode TIFJJ TFLEKIP JBZZEX.