Question

Alice used a transposition cipher to encrypt her messages to Bob. For added security, she encrypted the transposition cipher key using a substitution cipher, and kept the encrypted cipher in her computer. Trudy managed to get hold of the encrypted transposition cipher key. Can Trudy decipher Alice's messages to Bob? Why or why not?

Short answer

Yes, Trudy can decipher the messages if she decodes the substitution cipher to reveal the transposition key.

Step-by-step solution

Understanding the Basics of Transposition Cipher

A transposition cipher rearranges the letters of the plaintext according to a specific system. The actual letters remain the same, but their order is altered.

Introduction to the Substitution Cipher

A substitution cipher involves replacing each element of the plaintext with another element. Here, Alice uses it to encrypt the transposition cipher key, not the message itself.

Combining Ciphers for Security

Alice combines both ciphers: the actual communication is carried out using a transposition cipher, while the key to this cipher is encrypted with a substitution cipher. The security lies in successfully decrypting the substitution-encrypted key.

Trudy's Interception of the Encrypted Key

Trudy has intercepted the encrypted transposition cipher key, which is encrypted using a substitution cipher. Her task now is to break this substitution cipher to access the transposition key.

Decoding the Substitution Cipher

Substitution ciphers can be cracked, especially if the language and frequency of letters in the original language are known. If Trudy can decode the substitution cipher, she will retrieve the transposition key.

Deciphering Alice's Messages

If Trudy succeeds in obtaining the transposition key by breaking the substitution cipher, she can use it to decipher Alice's messages, which were encrypted using the transposition cipher.

Key concepts

Transposition Cipher

A transposition cipher is a method of encryption where the positions of the characters in the plaintext are changed according to a certain system. Unlike other ciphers, it does not alter the actual characters; instead, it simply shuffles their order. For example, if a simple message like "HELLO" is encrypted, it could become "OLEHL". The key to encrypting and decrypting a message with a transposition cipher lies in the understanding of the system used for rearranging the letters. This makes it critical that the sequence or pattern is kept secret to ensure that unauthorized users cannot rearrange the letters correctly.

Substitution Cipher

Unlike the transposition cipher, a substitution cipher works by replacing each letter or symbol in the plaintext with another letter or symbol. This changes not merely the positions of the characters, but their identities as well. For example, in a simple substitution cipher like Caesar Cipher, each letter in the plaintext is shifted a certain number of places down the alphabet. If the shift is three positions, then each 'A' becomes 'D', each 'B' becomes 'E', and so on. This method is generally simple to employ, but when applied to encrypt keys, like in Alice’s situation, it adds an additional layer of complexity for anyone attempting to decrypt the message without the proper key or system.

Encryption Key

An encryption key is a piece of information that determines the functional output of a cryptographic algorithm. In the scenario of Alice and Bob, the encryption key is used first in a transposition cipher to secure the original message and then further encrypted itself using a substitution cipher. This process keeps both the message and the method of decoding it protected. Keys are essential for both encrypting and decrypting messages and must be kept confidential to ensure message security.

Message Security

Message security is the ultimate goal of cryptography. By using multiple layers of encryption like Alice did — first with the transposition cipher for the message and then with a substitution cipher for the key — stronger security is achieved. Each layer of security restricts unauthorized access and makes it more challenging for someone like Trudy to intercept and read the message or retrieve the keys. However, if one of these security measures can be breached, for instance, if Trudy manages to decode the substitution cipher, she may be able to get the key and read the transposed message. This highlights the importance of strong encryption methods and careful management of keys to maintain secure communication.