Early pseudo-random numbers used a linear congruential generator. Choose an inte

Question

  Early pseudo-random numbers used a linear congruential generator. Choose an integer n, choose integers a and b, and iterate the formula: ax+b mod n, to get a stream of values  for x, starting at an initial x called a seed.   Show that using CBC mode, how to attack this cipher. You may use a Chosen Plaintext Attack, if using a chosen plaintext helps.  Note: Use addition mod n, rather than XOR as the way to combine the previous ciphertext with the new message. The F_k function is the arithmetic computation ax+b mod n. So the plaintext and ciphertext space are 0, ... , n-1. 

Explanation / Answer

From the above Context, we taken the following is the one of the way to know about

The affine cipher on a 26-letter alphabet is defined by

eK(x) = ax+b mod 26, where 0 a, b 25. The key is (a, b).

Ciphertext c = eK(x) is decrypted using dK(c) =(c b)a1 mod 26, with the necessary and sufficient condition for invariability that gcd(a, 26) = 1.

Shift ciphers are a subclass defined by a = 1.

For integers n>1, let Z_n = {0,...,n-1} ("the integers modulo n"). We can define addition and multiplication operations on Z_n by

    a + b := (a + b) mod n

Suppose you have to do write like this one also

Shift cipher is a special case of substitution cipher.

Another special case: Affine cipher: P = C = Z_{26} as before.

          e_k(x) = (ax + b) mod 26.

Where k = (a,b) and a,b in Z_{26}

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.