Question

Suppose there is a hypothetical language with only the three letters p; q; r which occur with probabilities 0.8,0.15, and 0.05 , respectively. If I encrypt a sequence of plaintext from this language using one of the early ciphers, and the index of coincidence of the ciphertext is calculated to be 0.665 . Among the following ciphers, which type is most likely?

a. Hill cihper with key length 2
b. One time pad
c. Vigenere cipher
d. Monoalphabetic Substitution

Answer 1

The most likely cipher used in encrypting a sequence from a language with three letters of given probabilities and an index of coincidence of 0.665 is a one-time pad, which is consistent with the almost uniform distribution indicated by the index.

Step-by-step explanation:

When considering a hypothetical language with only the three letters p, q, r occurring with probabilities 0.8, 0.15, and 0.05 respectively, and given that the index of coincidence of the ciphertext is 0.665, the type of cipher most likely used is a one-time pad. This conclusion is based on the fact that a one-time pad, when used correctly, produces ciphertext where letters appear with equal probability, resulting in an index of coincidence close to that of random text, which is approximately 0.666. This is much higher than what would be expected from the other ciphers mentioned where the inherent structure of the language (letter frequencies) would likely persist, leading to an index of coincidence more aligned with the probabilities given (0.8 for 'p', etc.). A Hill cipher, Vigenère cipher, or monoalphabetic substitution would not produce such a uniformly distributed ciphertext as they depend on the structure of the key and the plaintext.