CRYPTOGRAPHY G REEK WORD MEANING “ SECRET WRITING ”

CRYPTOGRAPHY: Cryptography is the study of secret (crypto-) writing (-graphy). It is concerned with developing algorithms which may be used to: It conceals the context of some message from all except the sender and recipient (privacy or secrecy). It verifies the correctness of a message to the recipient (authentication or integrity). It is the basis of many technological solutions to computer and communications security problems.

BASIC TERMINOLOGY: Cryptography: The art or science encompassing the principles and methods of transforming message an intelligible into one that is unintelligible, and then retransforming that message back to its original form. Plaintext : The original intelligible message. Cipher text: The transformed message. Cipher: It is an algorithm for transforming an intelligible message into one that is unintelligible by transposition and/or substitution methods. Key: Some critical information used by the cipher, known only to the sender & receiver.

Encipher (encode): The process of converting plaintext to cipher text using a cipher and a key. Decipher (decode): The process of converting cipher text back into plaintext using a cipher and a key. Cryptanalysis (code breaking): The study of principles and methods of transforming an unintelligible message back into an intelligible message without knowledge of the key. Cryptology: The field encompassing both cryptography and cryptanalysis. CONT’D…

Encryption: The mathematical function mapping plaintext to cipher text using the specified key: Y = E K (X) Decryption: The mathematical function mapping cipher text to plaintext using the specified key: X = D K (Y) = E K -1 (Y) Cryptographic system: The family of transformations from which the cipher function E K is chosen. CONT’D…

B ASIC E LEMENTS : Plaintext: The original message with no transformation. Cipher text: The plaintext message after modification to obscure it from normal usage and readability. encryption converts plaintext into cipher text. decryption converts cipher text into plaintext. Cryptographic algorithm: The mathematical operation used to convert plain text into cipher text. Key: The secret key used to encrypt or decrypt the message.

S TREAM AND B LOCK C IPHERS : Stream Cipher: It encrypts a digital data stream one byte at a time. Block Cipher: It encrypts blocks of plaintext, treated as a whole and used to produce a cipher text block of equal length.

CRYPTOSYSTEM: Quintuple ( E, D, M, K, C ) M set of plaintexts. K set of keys. C set of ciphertexts. E set of encryption functions e: M  K  C. D set of decryption functions d: C  K  M.

S IMPLIFIED C ONVENTIONAL E NCRYPTION M ODEL : Not secret

CLASSICAL ENCRYPTION TECHNIQUES: Substitution Ciphers: Monoalphabetic Ciphers Additive Cipher/ Shift Cipher/ Caesar Cipher Multiplicative Ciphers Affine Cipher Polyalphabetic Ciphers Autokey Cipher Playfair Cipher Vignere Cipher Hill Cipher

SUBSTITUTION CIPHERS: It replaces one symbol with another. If the symbols in the plain text are alphabetic characters, we replace one character with another. For example, we can replace 3 with 7, and 2 with 6. Categorized as either monoalphabetic ciphers or polyalphabetic ciphers.

MONOALPHABETIC CIPHERS: In monoalphabetic substitution, a character (or a symbol) in the plaintext is always changed to the same character (or symbol) in the ciphertext regardless of its position in the text. For example, if the algorithm says that letter A in the plaintext is changed to letter D, every letter A is changed to letter D. The relationship between letters in the plaintext and the ciphertext is always one-to-one.

ADDITIVE CIPHER / SHIFT CIPHER / CAESAR CIPHER: It is the simplest monoalphabetic cipher. It was developed 2000 years ago, by Julius Caesar. Additive Ciphers are sometimes referred to as Shift Ciphers or Caesar Cipher. Replace each letter with the letter standing 3 places further down the alphabet. C i = E(P i )=(P i +3) mod 26. P i =D(C i )=(C i -3) mod 26. Plain Text: ABCDEFGHIJKLMNOPQRSTUVWXYZ Cipher Text: DEFGHIJKLMNOPQRSTUVWXYZABC

G ENERALIZED C AESAR C IPHER : It can use any shift from 1 to 25, i.e., replace each letter by a letter a fixed distance away. C i =E(P i )=(P i +k) mod 26. P i =D(C i )=(C i -k) mod 26.

MULTIPLICATIVE CIPHERS: The encryption algorithm specifies multiplication of the plaintext by the key and the decryption algorithm specifies division of the ciphertext by the key. Decryption, would be multiplying by the multiplicative inverse of the key.

AFFINE CIPHER: Combining the additive and multiplicative ciphers to get what is called the affine cipher – a combination of both ciphers with a pair of keys. The first key is used with the multiplicative cipher, and the second key is used with the additive cipher.

POLYALPHABETIC CIPHERS: Each occurrence of a character may have a different substitute. The relationship between a character in the plaintext to a character in the ciphertext is one-to-many. For example: “a” could be enciphered as “D” in the beginning of the text, but as “N” at the middle.

AUTOKEY CIPHER: It is a simple polyalphabetic cipher called the autokey cipher. In this cipher, the key is a stream of subkeys, in which each subkey is used to encrypt the corresponding character in the plaintext. The first subkey is a predetremined value secretly agreed upon by Alice and Bob. The second subkey is the value of the first plaintext character (between 0 and 25). The third subkey is the value of the second plaintext. And so on. The name of the cipher, autokey, implies that the subkeys are automatically created from the plaintext cipher characters during the encryption process.

PLAYFAIR CIPHER: Best-known multiple-letter substitution cipher. Digram cipher (diagram to digram, i.e., E(p i p i+1 )=c i c i+1 through key-based 5x5 transformation table). Still leaves much of the structure of the plaintext language  relatively easy to break. Keyword = monarchy Plaintext: H S E A A R M U Ciphertext: B P I M R M C M MONAR CHYBD EFGI/JK LPQST UVWXZ

V IGENÈRE CIPHER : Best-known polyalphabetic ciphers. Each key letter determines one of 26 Caesar (shift) ciphers. c i = E(p i ) = p i + k i mod(key length). Example: Keyword is repeated to make a key as long as the plaintext. Key: deceptivedeceptivedeceptive Plaintext: wearediscoveredsaveyourself Cipheretxt: ZICVTWQNGRZGVTWAVZHCQYGLMGJ

V IGENÈRE CIPHER :

TRANSPOSITION CIPHERS: It does not substitute one symbol for another, instead it changes the location of the symbols. A symbol in the first position of the plaintext may appear in the tenth position of the ciphertext. A symbol in the eight position in the plaintext may appear in the first position of the ciphertext. A transposition cipher reorders (transposes) the symbols.

KEYLESS TRANSPOSITION CIPHERS: Simple transposition ciphers, which were used in the past, are keyless. There are two methods for permutation of characters. In the first method, the text is written into a table column by column and then transmitted row by row. In the second method, the text is written into a table row by row and then transmitted column by column.

KEYED TRANSPOSITION CIPHERS: The permutation is done on the whole plaintext to create the whole ciphertext. Another method is to divide the plaintext into groups of predetermined size, called blocks, and then use a key too permute the characters in each block separately.