Security in Computing Cryptography (Traditional Ciphers)

I.Substitution Ciphers A. Monoalphabetic Substitution Ciphers 1.An improvement over the Caesar cipher 2.Change/replace one symbol with another - 3.Obscures the meaning of a symbol (confusion) 4.P { a b c d e f g ……. z } C { Q W E R T Y U ……. M } 5.Each symbol in the plain alphabet P maps onto some other symbol in the cipher alphabet C

6.Effectively, we are using a 26-character key (26-letter string) corresponding to the alphabet 7.In how many ways can all the 26-character be rearranged (permutation)? B. Brute force attack 1.Not feasible: 26! (4 x ) – Enormous the key space; 2.At 1 nsec (billionth of a second) per solution, a computer would take ~10 billion years (10 10 ) to try all the keys I.Substitution Ciphers

4 x Incomprehensible!

B. Cryptanalysis Attack 1.Basic attack takes advantage of statistical properties of English: 2.In English, e (most common letter) followed by t, o, a, n, i, etc. 3.Common two-letter combinations (digrams): th, in, er, re, an 4.Common three-letter combinations (trigrams): the, ing, and, ion I.Substitution Ciphers

1.First, count relative frequencies of all letters in the ciphertext 2.Second, tentatively assign most common letter to e, next common one to t and so on 3.Third, find common trigrams of the form [t ? e], strongly suggesting that ? is h 4.Fourth, check if [t h ? t] occurs frequently, suggesting that ? stands for a I.Substitution Ciphers

C. Multiple substitutions 1.Two or more substitution ciphers used in series 2.Letters 1, 3, 5.. encrypted under cipher (or key) 1 ; letter 2, 4, 6 encrypted cipher (or key) 2 etc. I.Substitution Ciphers

3.Example a)I THINK THAT I SHALL NEVER SEE b)Under cipher 1 : I H N T A I H L N V R E c)Under cipher 2: T I K H T S A L E E S E d)Cipher 1 = n + 3; cipher 2 = n + 5 e)Ciphertext 1 : L K Q W D L K O Q Y U H f)Ciphertext 2 : Y N P M Y X F Q J J X J g)Result: LYKNQPWMDYLXKFOQQJYJUXHJ I.Substitution Ciphers

II.Transposition Ciphers A. Various Types 1.Plaintext symbols are simply reordered and not replaced like substitution cipher (diffusion) 2.Each letter represents itself keeping the frequency distribution intact 3.Simple Example a)Plaintext : CAT b)Possible Ciphertext: { CTA, ACT, ATC, TCA, TAC }

II.Transposition Ciphers B. Columnar Transposition Simple Example 1.Plaintext written in fixed-length rows, read off by columns 2.Example: SAM PLE becomes SPALME C. Other more complex Examples 1.Use of a key to number the columns....

III.One-Time Pad 1.The only unbreakable cipher (Theoretically) 2.Example 1.First, convert the plaintext message into a bit string (7-bit ASCII) e.g. “ I love you.” I l o

III.One-Time Pad 2.Second, choose random bit string key (key pad) with same length as the plaintext 3.Third, compute XOR (eXclusive OR) of the two strings, bit by bit plaintext: … key pad: … Ciphertext: …

IV.Book Cipher 1.Similar to one-time pad 2.Uses book (poem, piece of music, newspaper) to which both sender and receiver have access 3.Starting at a predetermined place in the shared object, use the element of the object as random numbers for a on-time pad 4.Weaknesses due to predictability in written objects, possible availability of shared objects to third party

V.Hardware Implementation A. Transposition 1.P-Box (Permutation Box or P-Box) device B. Substitution 1.S-Box (Substitution Box or S-Box) device C. Product Cipher 1.Combines P-Boxes and S-Boxes

V.Hardware Implementation A. Transposition 1.P-Box (Permutation Box or P-Box) device B. Substitution 1.S-Box (Substitution Box or S-Box) device C. Product Cipher 1.Combines P-Boxes and S-Boxes