The one-time pad (OTP) is an encryption technique that cannot be cracked in cryptography. It requires the use of a single-use pre-shared key that is larger than or equal to the size of the message being sent. In this technique, a plaintext is paired with a random secret key (also referred to as a one-time pad). Then, each bit or character of the plaintext is encrypted by combining it with the corresponding bit or character from the pad using modular addition. The resulting ciphertext is impossible to decrypt or break if the following four conditions are met:
The key must be at least as long as the plaintext. The key must be truly random. The key must never be reused in whole or in part. The key must be kept completely secret by the communicating parties. These requirements make the OTP the only known encryption system that is mathematically proven to be unbreakable under the principles of information theory. Digital versions of one-time pad ciphers have been used by nations for critical diplomatic and military communication, but the problems of secure key distribution make them impractical for many applications. First described by Frank Miller in 1882, the one-time pad was re-invented in 1917. On July 22, 1919, U.S. Patent 1,310,719 was issued to Gilbert Vernam for the XOR operation used for the encryption of a one-time pad. One-time use came later, when Joseph Mauborgne recognized that if the key tape were totally random, then cryptanalysis would be impossible. To increase security, one-time pads were sometimes printed onto sheets of highly flammable nitrocellulose, so that they could easily be burned after use.
History Frank Miller in 1882 was the first to describe the one-time pad system for securing telegraphy. The next one-time pad system was electrical. In 1917, Gilbert Vernam (of AT&T Corporation) invented and later patented in 1919 (U.S. patent 1,310,719) a cipher based on teleprinter technology. Each character in a message was electrically combined with a character on a punched paper tape key. Joseph Mauborgne (then a captain in the U.S. Army and later chief of the Signal Corps) recognized that the character sequence on the key tape could be completely random and that, if so, cryptanalysis would be more difficult. Together they invented the first one-time tape system. The next development was the paper pad system. Diplomats had long used codes and ciphers for confidentiality and to minimize telegraph costs. For the codes, words and phrases were converted to groups of numbers (typically 4 or 5 digits) using a dictionary-like codebook. For added security, secret numbers could be combined with (usually modular addition) each code group before transmission, with the secret numbers being changed periodically (this was called superencryption). In the early 1920s, three German cryptographers (Werner Kunze, Rudolf Schauffler, and Erich Langlotz), who were involved in breaking such systems, realized that they could never be broken if a separate randomly chosen additive number was used for every code group. They had duplicate paper pads printed with lines of random number groups. Each page had a serial number and eight lines. Each line had six 5-digit numbers. A page would be used as a work sheet to encode a message and then destroyed. The serial number of the page would be sent with the encoded message. The recipient would reverse the procedure and then destroy his copy of the page. The German foreign office put this system into operation by 1923. A separate notion was the use of a one-time pad of letters to encode plaintext directly as in the example below. Leo Marks describes inventing such a system for the British Special Operations Executive during World War II, though he suspected at the time that it was already known in the highly compartmentalized world of cryptography, as for instance at Bletchley Park. The final discovery was made by information theorist Claude Shannon in the 1940s who recognized and proved the theoretical significance of the one-time pad system. Shannon delivered his results in a classified report in 1945 and published them openly in 1949. Prior to this, Soviet information theorist Vladimir Kotelnikov had independently proved the absolute security of the one-time pad; his results were delivered in 1941 in a report that apparently remains classified. There also exists a quantum analogue of the one time pad, which can be used to exchange quantum states along a one-way quantum channel with perfect secrecy, which is sometimes used in quantum computing. It can be shown that a shared secret of at least 2n classical bits is required to exchange an n-qubit quantum state along a one-way quantum channel (by analogue with the result that a key of n bits is required to exchange an n bit message with perfect secrecy). A scheme proposed in 2000 achieves this bound. One way to implement this quantum one-time pad is by dividing the 2n bit key into n pairs of bits. To encrypt the state, for each pair of bits i in the key, one would apply an X gate to qubit i of the state if and only if the first bit of the pair is 1, and apply a Z gate to qubit i of the state if and only if the second bit of the pair is 1. Decryption involves applying this transformation again, since X and Z are their own inverses. This can be shown to be perfectly secret in a quantum setting.
Example Suppose Alice wishes to send the message hello to Bob. Assume two pads of paper containing identical random sequences of letters were somehow previously produced and securely issued to both. Alice chooses the appropriate unused page from the pad. The way to do this is normally arranged for in advance, as for instance "use the 12th sheet on 1 May", or "use the next available sheet for the next message". The material on the selected sheet is the key for this message. Each letter from the pad will be combined in a predetermined way with one letter of the message. (It is common, but not required, to assign each letter a numerical value, e.g., a is 0, b is 1, and so on.) In this example, the technique is to combine the key and the message using modular addition, not unlike the Vigenère cipher. The numerical values of corresponding message and key letters are added together, modulo 26. So, if key material begins with XMCKL and the message is hello, then the coding would be done as follows:
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