Question

You are a spy, and, conveniently, have a library with an infinite number of books at your disposal. Your operator also has such a library at his disposal. You have initially agreed to use Lord of the Rings as a one-time pad. Explain how you could use these assets to generate an infinitely long one-time pad.

Short answer

The spy can use book text as a key sequence; convert text to numbers for encryption/decryption, and extend it indefinitely by reading further, ensuring secrecy.

Step-by-step solution

Understanding One-Time Pads

A one-time pad is a cryptographic technique where plain text is converted to ciphertext using a unique, random key that is as long as the plain text. The key is used only once, ensuring the security of the message as long as the key remains secret and is truly random.

Establishing Starting Point

Both the spy and the operator decide on a starting book and page number from the Lord of the Rings series to ensure synchronization. This choice is secure since both parties have access to identical libraries.

Generating the Key

Using the text from the chosen page, convert each character into numerical values (such as ASCII codes), creating a series of numbers. This sequence acts as the initial part of your key.

Extending the Key

To generate an infinitely long one-time pad, continue taking sequential characters from subsequent pages or sections of the book series, converting them to numbers. Since books can be chosen randomly and incrementally, the pad extends indefinitely.

Encrypting the Message

Convert the plain text message into numerical values as well. Add each corresponding numerical value from the message and the one-time pad together and then use modulo arithmetic (e.g., modulo 256 for ASCII) to handle wrap-around values, forming the ciphertext.

Decryption Process

The operator takes the ciphertext and uses the shared key sequence from their library. They convert the key and ciphertext back into numerical values, subtracting the key from the ciphertext, and apply modulo arithmetic to retrieve the original numerical values of the plain text.

Key concepts

One-Time Pad

The one-time pad (OTP) is one of the simplest and most secure methods of encryption. It uses a secure, random key of the same length as the message to convert plaintext into ciphertext. The beauty of the OTP lies in its ability to provide perfect secrecy when used correctly. The rule for perfect secrecy is that the key must be completely random, used only once, and kept secret. If these conditions are met, it is theoretically impossible for anyone to decrypt the message without the key.

Imagine writing a message and then using a random letter for each character of your message to create a key. Your original message becomes unreadable. This ensures that even if someone intercepts your message, without the key, they are merely looking at gibberish. This method of encryption is practically foolproof, provided you maintain the randomness and the secrecy of your key.

Encryption

Encryption is the process of converting readable text, known as plaintext, into an unreadable format, or ciphertext. This obscures the message's content, securing it from unauthorized viewers.

In the case of the one-time pad, encryption involves combining each character of the plaintext with the corresponding character of the key. This is done using numerical values, such as ASCII codes. For example, if 'A' is represented by 65 and the corresponding key is the letter 'B', represented by 66, you add these values:

• 65 (plaintext) + 66 (key) = 131

This new number is transformed back into a character using modulo arithmetic, helping handle numbers beyond typical ASCII limits, often using modulo 256. The resulting characters form the ciphertext, which looks random to anyone without the key.

Decryption

Decryption is essentially the reverse of the encryption process. It involves converting the ciphertext back to plaintext using the same key used for encryption. This process ensures the receiver understands the original message.

To decrypt a message encrypted with a one-time pad, the receiver must have the same key. They subtract the corresponding key character value from each character in the ciphertext:

• If the ciphertext gives you a value of 131 and the key is 66, you perform:
  131 (ciphertext) - 66 (key) = 65

Again, modulo arithmetic might be necessary. The resulting value, 65, correlates back to the letter 'A', revealing the original plaintext. This process shows that while encryption hides the message, decryption unveils it using the shared key used during encryption.

Key Generation

Key generation is a crucial component of the one-time pad encryption process. The key must be as long as the message to ensure complete security. In our scenario with an infinite library, the key is generated from the text of books, ensuring its randomness.

The process begins with selecting a sequence from a shared text, like a page or chapter from "The Lord of the Rings." Every character from this text can be converted to a numeric value, forming the initial key sequence. Each subsequent page or section expands the key, allowing it to match any message length.

For effective security, both parties must use the key just once and destroy it thereafter. By doing so, they prevent any potential decoding attempts, safeguarding their communication with an infinite source of randomness.