Lecture 4DECIPHERING CLASSICAL CIPHER

SYSTEMS

By:NOOR DHIA AL- SHAKARCHY

2012-2013

SIMPLE SUBSTITUTION CIPHERS:Ek(M) = F(m1) F(m2) … ..F(mN) =CDK(M) = F(c1) F(c2) ….. ..F(cN) = M Where: N : is the length of the message. M : is plaintext message given by M = ( m1, m2, … ..,mN). C : is ciphertext message given by C = (c1,c2,… .., cN).There are many types of simple substitution ciphers according to its

equations used to encryption, they:• Shifted alphabet (Caesar cipher): C = Ek(M) = F(a) = (a + k) mod n M = DK(M) = (Ek(M) – K ) mod n = ( c – k ) mod n Where k : is the number of positions to be shifted. a : is a single character of the alphabet. n : is the size of the alphabet.

SIMPLE SUBSTITUTION CIPHERS:Example:If k =3 then we can decrypted the following ciphertext as:

C = U H Q D L V V D Q F H Dk(M) = R E N A I S S A N C E = MNOTE:-Sometimes when we apply the equation of decipher the ciphertext to

plaintext , the result becom negative value.And in this case we adding the value of n to this equation to avoid the

negative value as see in example.K = U = 20 ; C = F = 5; ∑ A … ZM = (5 – 20 ) Mod 26 = -15 Mod 26 (Adding 26 ) = 26 – 15 Mod 26 = 11 Mod 26 = 11 = L

SIMPLE SUBSTITUTION CIPHERS:• Multiplication based (decimation): C = Ek(M) = F(a) = ak mod n Where k, n are relatively prime in order to produce a complete set of

residues. M = DK(M) = a = [ c * inv (k, n)] mod nNOTE:-The algorithm inv(k, n) returnes the value of a according to the

equation C = ak mod n and this algorithm gives as later.Addition and multiplication (affine):The encryption equation Ek(M):F(a) = (ak1+k0) mod nWhere k1 and n are relatively primeThe decryption equation Dk(C): C – (K0 mod n) = aK1 mod n a = [ (C-(K0 mod n)) * inv (K1, n)]

STREAM CIPHER SYSTEMSIs a system in which the key is fed to an algorithm, which uses

the key to generate finite sequence. The algorithm is usually referred to as the sequence generator or key stream generator. stream cipher systems produced long sequence of displacement which were applied character by character to the plaintext message.

The encryption and decryption process are:C = EKi(mi) = K Ө M …….. to encryption

M = DKi(ci) = C Ө K

= ( M Ө K ) Ө K = M ….. to decryptionK Ө K = 0 and K Ө 0 = K

mi message

Key generator

I0

Initial value

mi message

Ci ciphertextessageXOR

(mixer)

Kikey

I0

Initial value

Encryption Decryption

Key generator

Ki

key

XOR

(mixer)

A B XOR

0 0 0

0 1 1

1 0 1

1 1 0 XOR- Table

Stream cipher process

STREAM CIPHER SYSTEMSThe type of stream cipher systems:-• According to repeated key :

– Periodic: if the key repeats after d characters (bits).– Not periodic : if the key not repeats that’s mean the key is

long enough to avoid repeation. • According to generate the key:• Synchronous: the stream message generated alone and

the stream key generated alone also with out dependent on another. The stream Ciphertext generated by mixed them by XOR mixer.

• Self- synchronous: the stream message generated alone and the stream key generated in depending on previous Ciphertext.