91Ó°ÊÓ

The ciphertext message produced by the knapsack cryptosystem employing the superincreasing sequence \(1,3,5,11,35\), modulus \(m=73\), and multiplier \(a=5\) is 55,15 , \(124,109,25,34\). Obtain the plaintext message. [Hint: Note that \(5 \cdot 44 \equiv 1(\bmod 73) .\) ]

A long string of ciphertext resulting from a Hill cipher $$ \begin{aligned} C_{1} & \equiv a P_{1}+b P_{2}(\bmod 26) \\ C_{2} & \equiv c P_{1}+d P_{2}(\bmod 26) \end{aligned} $$ revealed that the most frequently occurring two-letter blocks were \(H O\) and \(P P\), in that order. (a) Find the values of \(a, b, c\), and \(d\). [Hint: The most common two-letter blocks in the English language are \(T H\), followed by \(H E .]\) (b) What is the plaintext for the intercepted message PPIH HOG RAPVT?

Suppose that the message GO SOX is to be enciphered using Verman's telegraph cipher. (a) Express the message in Baudot code. (b) If the enciphering key is $$ 0111010111101010100110010 $$ obtain the alphabetic form of the ciphertext.

A plaintext message expressed in Baudot code has been converted by the Verman cipher into the string $$ 110001110000111010100101111111 $$ If it is known that the key used for encipherment was $$ 011101011001011110001001101010 $$ recover the message in its alphabetic form.

Decrypt the ciphertext $$ \begin{array}{lllll} 1030 & 1511 & 0744 & 1237 & 1719 \end{array} $$ that was encrypted using the RSA algorithm with key \((n, k)=(2623,869) .\) [Hint: The recovery exponent is \(j=29 .\) ]