Question

Use the autokey cipher to encrypt the message NOW IS THE TIME TO DECIDE (ignoring spaces) using

a) the keystream with seed X followed by letters of the plaintext.

b) the keystream with seed X followed by letters of the ciphertext.

Short answer

Thus the encrypted message is then $\text{KBKEULAL XBUQ XHRHGKLH.}$.

Step-by-step solution

Step 1

Given:

$\text{NOW IS THE TIME TO DECIDE}$

(a) The keystream begins with the seed letter, which is X in this case.

Since we use the letters of the plaintext, the remaining keystream is the given plaintext string.

Keystream = $\text{X NO W IS THE TIME TO DE CID}$

$\text{Replace A by}00,\mathrm{B}\text{by}01,\mathrm{C}\text{by}02,\mathrm{D}\text{by}03,\mathrm{E}\text{by}04,\mathrm{F}\text{by}05,\mathrm{G}\text{by}06,\mathrm{Hby}07,\mathrm{I}$

$\text{by}08,\mathrm{J}\text{by}09,\mathrm{K}\text{by}10,\mathrm{L}\text{by}11,\mathrm{M}\text{by}12,\mathrm{N}\text{by}13,\mathrm{O}\text{by}14,\mathrm{P}\text{by}15,\mathrm{Q}\text{by}16,\mathrm{R}$

$\text{by}17,S\text{by}18,\text{T by}19,\mathrm{U}\text{by}20,\mathrm{V}\text{by}21,\mathrm{W}\text{by}22,\mathrm{X}\text{by}23,\mathrm{Y}\text{by}24\text{, and}Z\text{by}25$

Ciphertext =$1314220818190704190812041914030402080304$

Keystream =$2313142208181907041908120419140304020803$

Add the corresponding numbers in the ciphertext and the keystream.

$3627363020372611232720162333170706101107$

Step 2

Take moduloof each number:

$1001100420110011230120162307170706101107$

$\text{Replace}00\text{by}A,01\text{by}B,02\text{by}C,03\text{by}D,04\text{by E,}05\text{by F,}06\text{by G,}07\text{by H,}08$

$\text{|by I,}09\text{by J,}10\text{by}\mathrm{K},11\text{by L,}12\text{by}\mathrm{M},13\text{by}\mathrm{N},14\text{by}\mathrm{O},15\text{by}\mathrm{P},16\text{by}\mathrm{Q},17\text{by}$ $R,18\text{by}S,19\text{by}T,20\text{by}U,21\text{by}V,22\text{by}W,23\text{by}X,24\text{by}Y\text{and}25\text{by}Z\text{.}$

$\text{KBKEUL ALXBUQXHRHGKLH}$

Thus the encrypted message is then $\text{KBKEUL ALXBUQXHRHGKLH}$.