Final answer:
To convert the plaintext 'PRIME' into ciphertext using multiplication by 5 in the mod 26 multiplicative cipher system, we multiply each letter's numerical value by 5 and take the result modulo 26. The resulting ciphertext is '9 23 14 2 20', which corresponds to the encrypted message 'JXOCU'.
Step-by-step explanation:
To convert the plaintext 'PRIME' into ciphertext using multiplication by 5 in the mod 26 multiplicative cipher system, we need to assign numerical values to each letter. In the English alphabet, 'A' is represented by 0, 'B' by 1, and so on. Therefore, 'P' is 15, 'R' is 17, 'I' is 8, 'M' is 12, and 'E' is 4.
To encrypt each letter, we multiply its numerical value by 5 and then take the result modulo 26. For example, encrypting 'P' gives (15 * 5) mod 26 = 9. Similarly, 'R' becomes (17 * 5) mod 26 = 23, 'I' becomes (8 * 5) mod 26 = 14, 'M' becomes (12 * 5) mod 26 = 2, and 'E' becomes (4 * 5) mod 26 = 20.
Therefore, the resulting ciphertext is '9 23 14 2 20', which corresponds to the encrypted message 'JXOCU'.