Elementary Cryptography  Concepts of encryption  Symmetric (secret key) Encryption (DES & AES)(DES & AES)  Asymmetric (public key) Encryption (RSA)(RSA)  Key exchange protocols and certificates  Digital Signatures  Cryptographic hash functions

Elementary Cryptography Terminology & Background  Sender (A), Recipient (B), Transmission media (T)  Interceptor / intruder (C) (availability)  C might block message from reaching R  C might intercept message (confidentiality)  C might modify message (integrity)  C might fabricate an authentic-looking message (integrity)

Terminology & Background  Encryption – process of encoding a message  Decryption – transforming encoded message back to normal  Encrypt – encode, encipher  Decrypt – decode, decipher  Cryptosystem – system for encryption and decryption  Plaintext – original form of message  Ciphertext – encoded form of message

Terminology & Background  Algorithms – rules for encryption and decryption  Key – value used to encrypt message  C = E(K, P) where P=plaintext, K = key, E = encryption algorithms, and C = ciphertext  Symmetric encryption P = D(K, E(K,P))  Asymmetric encryption P = D(K D, E(K E,P))  Keyless cipher  Cryptography (hidden writing) – uses encryption to hide message  Cryptanalysis – attempts to find meanings in encrypted messages  Cryptology – study of encryption and decryption

Types of Encryption  Substitution – one or more characters are replaced with another  Transpositions (permutations) – order of characters is rearranged  Hybrid – combinations of the two types

Substitution Ciphers  Caesar Cipher Each letter is translated a fixed number of positions in the alphabetEach letter is translated a fixed number of positions in the alphabet C i = E(p i ) = p i + 3C i = E(p i ) = p i + 3 Plaintext A B C D E F G H I J K L …Plaintext A B C D E F G H I J K L … Ciphertext d e f g h i j k l m n o …Ciphertext d e f g h i j k l m n o … Easy to perform; easy to breakEasy to perform; easy to break Look for double letters and then use common words with double lettersLook for double letters and then use common words with double letters

Other Substitution Ciphers  Use a key to scramble the letters  A B C D E F G H I J K L M N O …  c i p h e r s a b d f g j k l …  Rearrange using a fixed distance between letters (e.g. every 3 rd )  A B C D E F G H I J K L M N O …  a d g j m p s v y b e h k n r …

Complexity of Substitution Encryption and Decryption  Substitution encryption algorithms can be performed by direct lookup in tables and are O(n) algorithms

One-Time Pads  The pad consists of a large number of pages where each page contains a non- repeating key  The sender would write the keys above the message (e.g. a 300 character message would require 30 pages of 10 character keys)  The message is scrambled using a Vigenere tableau built from the message and key  Problem is synchronizing the receiver’s pad with the senders pad

Vernum Cipher  One-time pad consists of an arbitrary long non-repeating sequence of numbers that are combined with the plaintext  Each plaintext character is represented by its numeric equivalent and is added to one of the random numbers. The ciphertext character is computed from the sum mod 26  Repeated characters are typically represented by different ciphertext characters

Book Ciphers  Uses a passage from a book to form the letters at the top of a Vigenere Tableau  Computes ciphertext character by taking the intersection of the plaintext character and corresponding character at that position from the book passage  Relatively easy to break using frequency distributions

Transpositions (Permutations)  Columnar Transposition rearranging plaintext message into columns and then reading it row by row  “YES COMPUTER SECURITY IS FUN” would be written  Y M R R S  E P S I F  S U E T U  C T C Y N  O E U I X is encrypted as “ymrrs epsif suetu ctcyn oeuix” where the X is just filler. is encrypted as “ymrrs epsif suetu ctcyn oeuix” where the X is just filler.  Transposition algorithms require a constant amount of time per character and are O(n) algorithms, but space required to store results and delay in waiting for all characters to be read are dependent on the size of the plaintext

Cryptanalysis  Attempt to break a single message  Attempt to recognize patterns in encrypted messages  Attempt to infer some meaning without breaking the encryption  Attempt to deduce the key  Attempt to find weaknesses in the implementation or environment of use of encryption  Attempt to find general weaknesses in an encryption algorithm

Breakable Encryption  An encryption algorithm is called breakable when, given enough time and data, an analyst can determine the algorithm  May be impractical  A 25-character message of just uppercase letters has (10 35 ) possible decipherments. A computer performing operations/sec would take years

Cryptoanalysis of Substitution Ciphers  Brute force would require trying checking 26! permutations which at one permutation per microsecond would take over a thousand years  Look for short words, words with repeated patterns, common first and last letters  Look at frequency distributions  Could reduce time to hours

Cryptoanalysis of Transposition Algorithms  Compute letter frequencies of ciphertext; if appear with normal frequency, then assume a transposition algorithm was used  By shifting text, look for common digrams (e.g EN)and trigrams (e.g. ENT)