One-time pad

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.