Gilbert Sandford Vernam (April 3, 1890 – February 7, 1960) was a

Worcester Polytechnic Institute Worcester Polytechnic Institute (WPI) is a Private university, private research university in Worcester, Massachusetts. Founded in 1865 in Worcester, WPI was one of the United States' first engineering and technology universities and now has 14 ac ...

1914 graduate and

AT&T AT&T Inc. is an American multinational telecommunications holding company headquartered at Whitacre Tower in Downtown Dallas, Texas. It is the world's largest telecommunications company by revenue and the third largest provider of mobile ...

Bell Labs Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by mul ...

engineer who, in 1917, invented an additive polyalphabetic

stream cipher stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream (keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream ...

and later co-invented an automated

one-time pad In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ra ...

cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode ...

. Vernam proposed a teleprinter cipher in which a previously prepared key, kept on

paper tape Five- and eight-hole punched paper tape Paper tape reader on the Harwell computer with a small piece of five-hole tape connected in a circle – creating a physical program loop Punched tape or perforated paper tape is a form of data storage ...

, is combined character by character with the

plaintext In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted. Overview With the advent of comp ...

message to produce the

ciphertext In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintex ...

. To decipher the ciphertext, the same key would be again combined character by character, producing the

. Vernam later worked for the

Postal Telegraph Company Postal Telegraph Company (Postal Telegraph & Cable Corporation) was a major operator of telegraph networks in the United States prior to its consolidation with Western Union in 1943.Nonnenmacher, TomasHistory of the U.S. Telegraph Industry/ref> ...

, and became an employee of

Western Union The Western Union Company is an American multinational financial services company, headquartered in Denver, Colorado. Founded in 1851 as the New York and Mississippi Valley Printing Telegraph Company in Rochester, New York, the company cha ...

when that company acquired Postal in 1943. His later work was largely with automatic switching systems for

telegraph Telegraphy is the long-distance transmission of messages where the sender uses symbolic codes, known to the recipient, rather than a physical exchange of an object bearing the message. Thus flag semaphore is a method of telegraphy, whereas ...

networks.

Vernam's patent

The combining function Vernam specified in , issued July 22, 1919, is the

XOR Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false). It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...

operation, applied to the individual impulses or bits used to encode the characters in the

Baudot code The Baudot code is an early character encoding for telegraphy invented by Émile Baudot in the 1870s. It was the predecessor to the International Telegraph Alphabet No. 2 (ITA2), the most common teleprinter code in use until the advent of ASCII ...

. Vernam did not use the term "XOR" in the patent, but he implemented that operation in

relay A relay Electromechanical relay schematic showing a control coil, four pairs of normally open and one pair of normally closed contacts An automotive-style miniature relay with the dust cover taken off A relay is an electrically operated switch ...

logic. In the example Vernam gave, the

is ''A'', encoded as "" in Baudot, and the key character is ''B'', encoded as "". The resulting ciphertext will be "", which encodes a ''G''. Combining the ''G'' with the key character ''B'' at the receiving end produces "", which is the original plaintext ''A''. The

NSA The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collec ...

has called this patent "perhaps one of the most important in the history of cryptography.".

One-time pad

Shortly thereafter, Joseph Mauborgne, at that time a captain in the US Army Signal Corps, proposed, in addition, that the paper tape key contain

random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual ran ...

information. The two ideas, when themselves combined, implement an automatic form of the

, though neither inventor used the name then.

Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts I ...

, also at Bell Labs, proved that the one-time pad, properly implemented, is unbreakable in his

World War II World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the World War II by country, vast majority of the world's countries—including all of the great power ...

research that was later published in October 1949. He also proved that any unbreakable system must have essentially the same characteristics as the one-time pad: the key must be truly random, as large as the plaintext, never reused in whole or part, and kept secret.

The Vernam cipher

In modern terminology, a Vernam cipher is a symmetrical

in which the plaintext is combined with a random or

pseudorandom A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Background The generation of random numbers has many uses, such as for rand ...

stream of data (the "keystream") of the same length, to generate the ciphertext, using the Boolean "exclusive or" (XOR) function. This is symbolised by ⊕ and is represented by the following "

truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arg ...

", where + represents "true" and − represents "false". Other names for this function are: Not equal (NEQ),

modulo In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the '' modulus'' of the operation). Given two positive numbers and , modulo (often abbreviated as ) is ...

2 addition (without 'carry') and modulo 2 subtraction (without 'borrow'). The cipher is reciprocal in that the identical keystream is used both to encipher plaintext to ciphertext and to decipher ciphertext to yield the original plaintext: ::::Plaintext ⊕ Key = Ciphertext and: ::::Ciphertext ⊕ Key = Plaintext If the keystream is truly random and used only once, this is effectively a

. Substituting pseudorandom data generated by a

cryptographically secure pseudo-random number generator A cryptographically secure pseudorandom number generator (CSPRNG) or cryptographic pseudorandom number generator (CPRNG) is a pseudorandom number generator (PRNG) with properties that make it suitable for use in cryptography. It is also loosely kno ...

is a common and effective construction for a stream cipher.

RC4 In cryptography, RC4 (Rivest Cipher 4, also known as ARC4 or ARCFOUR, meaning Alleged RC4, see below) is a stream cipher. While it is remarkable for its simplicity and speed in software, multiple vulnerabilities have been discovered in RC4, ren ...

is an example of a Vernam cipher that is widely used on the Internet. If, however, the same keystream is used for two messages, known to cryptanalysts as a depth, the effect of the keystream can be eliminated, leaving the two plaintexts XORed together. The result is equivalent to a

Running key cipher In classical cryptography, the running key cipher is a type of polyalphabetic substitution cipher in which a text, typically from a book, is used to provide a very long keystream. Usually, the book to be used would be agreed ahead of time, while t ...

and the two plaintexts may be separated by linguistic cryptanalytical techniques. ::::Ciphertext1 ⊕ Ciphertext2 = Plaintext1 ⊕ Plaintext2 An operator's mistake of this sort famously allowed the

Cryptanalysis of the Lorenz cipher Cryptanalysis of the Lorenz cipher was the process that enabled the British to read high-level German army messages during World War II. The British Government Code and Cypher School (GC&CS) at Bletchley Park decrypted many communications betwe ...

by the British at

Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes (Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...

during

. They diagnosed how the keystream was generated, worked out how to break the cipher, and read vast quantities of high-level messages to and from German high command without ever seeing an actual Lorenz machine.

Notes

References

* * * . Transcript of a lecture given by Prof. Tutte at the

University of Waterloo The University of Waterloo (UWaterloo, UW, or Waterloo) is a public research university with a main campus in Waterloo, Ontario, Canada. The main campus is on of land adjacent to "Uptown" Waterloo and Waterloo Park. The university also operates ...

* * * * Also in {{DEFAULTSORT:Vernam, Gilbert 1890 births 1960 deaths Pre-computer cryptographers

Vernam cipher Vernam is a surname. Notable people with the surname include: * Charles Vernam (born 1996), English professional footballer *Gilbert Vernam (1890–1960), invented an additive polyalphabetic stream cipher and later co-invented an automated one-tim ...

Scientists at Bell Labs Worcester Polytechnic Institute alumni

Vernam's patent

One-time pad

The Vernam cipher

Notes

See also

References