One-time pad

You can hide a secret message.

Use a special code key. This key is a secret. It must be a random set of letters. You use the key only one time. Then you must destroy it. Some people used paper that burns fast. This keeps the secret safe. Even a very smart person cannot break this code. It is a perfect way to hide things.

Can you keep a secret?

How do you hide a secret message? You can use a tool called a one-time pad. This is a special way to make a code. It uses a secret key made of random letters or numbers.

To use it, you pair each part of your message with a part of the key. You mix them together using math. The result is a scrambled message called ciphertext. To read it, the other person uses the same secret key. They perform the math in reverse to get the real message back.

This method is very special. A scientist named Claude Shannon proved it has perfect secrecy. This means it is mathematically impossible to break. Even a computer with infinite power cannot crack it!

But there are strict rules to keep it safe. First, the key must be truly random. Second, the key must be as long as the message. Third, you must never use the same key twice. Finally, the key must stay a total secret. In the past, spies even used paper that burned fast to destroy keys. This kept their secrets safe forever.

A one-time pad is a special way to hide secret messages. It is a type of encryption, which is a way to scramble information. This method is very famous because it is mathematically unbreakable. If you follow the rules, no one can ever read your message. Even the most powerful computers in the world cannot crack it. This makes it a very important tool for important secrets.

To make the code, you need a secret key. This key must be a string of truly random characters. You pair each part of your message with a part of the key. Then, you combine them using a math process called modular addition. For example, if you use letters, you turn them into numbers first. You add the message number and the key number together. If the sum goes past the end of the alphabet, you just start again from the beginning. The result is a scrambled message called ciphertext.

People have been working on these systems for a long time. Frank Miller first described a version for telegraphs in 1882. Later, Gilbert Vernam invented an electrical version for teleprinters. He received a patent for his work in 1919. Joseph Mauborgne helped improve the system by using random keys. He realized that a totally random key makes the code impossible to break. This led to the first one-time tape systems.

There are many important facts about how this works. The key must be at least as long as the message itself. It must also be kept completely secret by both people. You must never use any part of the key ever again. In the 1920s, German cryptographers used paper pads for this. Each page had a serial number and eight lines of numbers. They would destroy the paper immediately after they finished using it.

This concept links to how we protect information today. A scientist named Claude Shannon proved its perfect secrecy in 1949. He showed that the scrambled message gives no clues about the real one. Before him, Vladimir Kotelnikov had also proved this in 1941. Today, we can even use quantum physics to do something similar. While it is hard to use for everything, it remains the gold standard for safety.

A one-time pad (OTP) is a specialized encryption technique used to secure communications. Encryption is the process of scrambling a message so that only authorized people can read it. The one-time pad is unique because it is mathematically proven to be unbreakable. In the field of cryptography, this is known as information-theoretic security. This means that even an adversary with infinite computational power cannot crack the code. This makes the OTP the gold standard for protecting highly sensitive information.

The mechanism of a one-time pad relies on combining a plaintext message with a secret key. The plaintext is the original, readable message. The key, or the pad, must be a sequence of truly random characters. To encrypt, each character of the plaintext is paired with a corresponding character from the key. These are combined using modular addition. For example, if using the alphabet, you might assign each letter a number from 0 to 25. You add the message number to the key number. If the sum exceeds 25, you use the remainder after dividing by 26. This creates the ciphertext, which is the scrambled, unreadable version of the message.

For a one-time pad to remain perfectly secure, four strict conditions must be met. First, the key must be at least as long as the plaintext message. Second, the key must be truly random, meaning there are no predictable patterns. Third, the key must never be reused, either in whole or in part. Finally, the key must be kept completely secret by the communicating parties. If any of these rules are broken, the system becomes vulnerable to cryptanalysis. For instance, if a key is reused, an attacker might find a key that produces sensible text from two different messages.

The history of the one-time pad involves several important inventors and developments. Frank Miller first described a version of this system for securing telegraphy in 1882. In 1917, Gilbert Vernam of the AT&T Corporation invented an electrical version for teleprinter technology. He received a U.S. patent for this work in 1919. Vernam used an operation called XOR to combine characters electrically. Later, Joseph Mauborgne, a captain in the U.S. Army, realized that making the key tape completely random would make cryptanalysis impossible. This led to the creation of the first one-time tape systems.

Different versions of the pad have been used throughout history. In the early 1920s, German cryptographers used a paper pad system. They used pages containing lines of random numbers to encode messages. Each page had a serial number and eight lines, with each line containing six 5-digit numbers. The German foreign office put this system into operation by 1923. During World War II, Leo Marks described using a letter-based system for the British Special Operations Executive. To ensure security, some groups used pads printed on nitrocellulose, also known as flash paper. This material is highly flammable and burns almost instantly, leaving no ash behind for enemies to find.

The mathematical proof of the one-time pad's security was established by two different scientists. Vladimir Kotelnikov, a Soviet information theorist, proved its absolute security in a 1941 report. Later, Claude Shannon, an American information theorist, published his findings openly in 1949. Shannon used information theory to prove the concept of perfect secrecy. He showed that the ciphertext provides zero additional information about the plaintext. Because the key is truly random, a ciphertext could be translated into any possible message of the same length. Without the key, every possible message is equally likely to be the true one.

While the one-time pad is perfectly secure, it is difficult to use for everyday tasks. The main problem is secure key distribution. Both parties must share a key that is as large as the message they want to send. Moving these massive, secret keys safely is a major challenge. However, the concept lives on in modern science through quantum cryptography. A quantum analogue of the one-time pad can exchange quantum states with perfect secrecy. This uses a shared secret of at least 2n classical bits to exchange an n-qubit quantum state. This allows for secure communication using the principles of quantum computing.