Cryptography Basics

• Plaintext refers to an original message.
• Ciphertext refers to the coded message.
• Enciphering/encryption is the process of converting from plaintext to ciphertext.
• Deciphering/decryption is restoring the plaintext from the ciphertext.
• Cryptography is the area of study of the many schemes used for encryption.
• A cryptographic system/cipher is a scheme.
• Cryptanalysis involves techniques used for deciphering a message without any knowledge of the enciphering details.
• Cryptology includes the areas of cryptography and cryptanalysis.
• Cryptographic systems are characterized along three independent axes: the type of encryption techniques used, the number of keys used, and how the plaintext is processed.

Encryption Techniques

• Substitution techniques map plaintext elements (bits, letters, or groups) into other elements.
• Transposition rearranges elements in the plaintext.
• Product systems involve multiple stages of substitutions and transpositions.

Number of Keys Used

• Symmetric, single-key, or secret-key encryption involves one key.
• Asymmetric, key-pair, or public-key encryption uses two keys.

Processing Method

• Block ciphers process one block of input elements at a time.
• Stream ciphers process one input element at a time.
• Secure use of conventional (symmetric) encryption has two requirements: a strong encryption algorithm and secure exchange and safeguarding of the secret key.
• In cryptanalysis and brute-force attacks, there are two types of attacks on conventional encryption schemes.
• One attack relies on the nature of the algorithm and general characteristics of the plaintext.
• The other exploits the algorithm's characteristics to deduce a specific plaintext or the key being used, while in brute-force attack the attacker tries every possible key on a piece of ciphertext until an intelligible translation into plaintext is obtained. On average, half of all possible keys must be tried to achieve success.
• Unconditionally secure encryption means that no matter how much time an opponent has, it's impossible to decrypt the ciphertext.
• Computationally secure encryption is achieved if the cost of breaking the cipher exceeds the value of the encrypted information or if the time required exceeds the useful lifetime of the information.

Substitution Technique

• Involves replacing plaintext letters with other letters, numbers, or symbols.
• If the plaintext is viewed as a sequence of bits, substitution involves replacing bit patterns with ciphertext bit patterns.

Caesar Cipher

• A substitution technique that replaces each letter by the 3rd letter to the right, wrapping around the alphabet so that the letter following Z is A.
• Encryption formula is C = E(p) = (p + k) mod (26), where C is the cipher, E is encryption, p is the number of the letter, and k is the shift (any amount from 1 to 25).
• Decryption formula is P = D(C) = (C - k) mod (26).
• For added security with telegraph messages, cryptographers would omit word length and punctuation and block messages into four/five letter groups.
• To decrypt a Caesar cipher by brute force, the ciphertext is written with shifts, and the result column is scanned for readable text, from which the key is deducted.

Mono-alphabetic Cipher

• Each symbol in the plain text is randomly mapped to a fixed symbol in cipher text using a fixed key of 26 letters.
• The cipher line can be any permutation (shuffling) of the 26 alphabet characters, for a total of 26! permutations.
• The user and sender agree on a key, and the same letter will be replaced by the same cipher.
• If the text is longer than the key, the key is continued with the rest of the alphabet in order.

Mono-alphabetic Cipher VS Caesar Cipher

• Mono-alphabetic uses has shifting, caesar shift uses shifting
• Mono-alphabetic uses key difference plain text and the cipher is not the same
• Mono-alphabetic has a key Size of 26!, Caesar shift has 25
• Mono-alphabetic is more powerful than Caesar Cipher
• Mono-alphabetic Frequency Analysis is used to cryptanalysis, Caesar Cipher Brute Force will find the key easily
• Natural English text has a very distinct distribution allowing for codes to be deciphered.
• Human languages are redundant; E is the most common letter, followed by T, R, N, I, O, A, S; other letters are rare; and tables exist for letter frequencies.

Cryptanalysis

• It is best to calculate the frequency distribution of the letters in the cipher text and compare to English frequencies.
• Monoalphabetic ciphers are easy to break because they reflect the frequency data of the original alphabet.
• This can be overcome with providing multiple substitutes (homophones) for a single letter
• Digrams, or two letter combinations, and trigrams three letter combinations like the and th, can influence deciphering

Playfair Cipher

• A multiple-letter encryption cipher that treats digrams (2 letters) in the plaintext as single units and translates these units into cipher text digrams.
• Stages included are: Creating Playfair Key Matrix, Preparing Plain Text, and Applying Playfair rules to map every 2 letters to its corresponding cipher ones.
• To encode a message, the sender and receiver select a particular key and create a 5x5 matrix based on a keyword, filling in letters of keyword lacking duplicates filling remaining slots with the remaining alphabet letters.
• Preparing plain text involves breaking text into two-letter chunks(LX for single letter word), repeated letters in the same chunk being separated by X (balxloon), and an extra X to fill the last letter when the number of letter os odd.

Playfair Encryption Rules:

• If both letters fall in the same row, replace each with the letter to the right (wrapping back to start from the end).
• If both letters fall in the same column, replace each with the letter below it (wrapping to top from bottom).
• Otherwise, form a rectangle with the two letters and take the letters on the horizontal opposite corner of the rectangle.
• Security is much improved over monoalphabetic ciphers with need to analyze a 676 entry frequency.
• It can be broken, given a few hundred letters and still has much of plaintext structure