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OTT
Digital bit-wise XOR operation
The Vernam Cipher is a symmetric cryptographic principle for adding
a key stream to a plaintext, invented in 1917 by Gilbert Vernam (1890-1960).
It is based on the principle that each plaintext
character is 'mixed' with one character from a key stream.
If a truly random key stream is used, the result will be a truly
random ciphertext which bears no relation to the original plaintext.
In that case the cipher is similar to the unbreakable
One-Time Pad (OTP).
As it was generally used with teleprinters
and 5-level punched tape,
the system is also known as One-Time Tape
or OTT.
If the resulting ciphertext in the OTT system described above is truly random,
it can safely be sent over the air, without the risk of being deciphered
by an eavesdropper.
All the recipient has to do is mix the ciphertext with the same OTT
to reveal the original plaintext.
One only has to guarantee that the OTT is truly random, that there are only
two copies of it, that both copies are destroyed immediately
after use and that they are only used once. (More about security below.)
The above became possible after the introduction of digital telegraphy,
also known as Teletype 1
or Telex.
With a teletypewriter, each character is substituted by a digital 5-bit code –
represented by the 5 holes in a punched paper tape –
commonly used with telex machines.
This is commonly known as ITA2
or the Baudot-Murray code.
Digital codes can also be represented by a series of '1's and '0's,
where 1 represents the presence of
a hole and 0 represents the absense of a hole.
The ciphertext is created by applying the logical
XOR operation (exclusive-or) to the individual bits of plaintext
and the key stream.
The advantage of using the XOR operation for this,
is that it can be reverted, simply by carrying out the same operation again.
In other words:
plaintext + key = ciphertext
⇒
ciphertext + key = plaintext
In mathematics, the XOR operation is known as modulo-2 addition.
In our case, the individual bits of the plaintext are XOR-ed
with the individual bits of the key.
The resulting bit will only be '1' if the two
input bits are different. If they are equal (both 1 or both 0),
the result will be '0'.
Take the letter 'A', which is represented by 00011, and add it to
the letter 'B', represented by 11001.
A bit-wise XOR operation yields 11010 which,
in the ITA2 table, is the letter 'G'.
In fact, each bit from the key tells us whether or not the corresponding
bit from the plaintext should be inverted.
By inverting these key-bits again, as shown above,
the original character is revealed.
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Although 'Teletype' is actually a brand name of the Teletype Corporation,
it has become a generic expression for
digital 5-bit telegraphy. The system
is also known as Teleprinter, Teletypewriter and Telex.
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XOR = Exclusive OR.
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The principle of the Vernam Cipher is perhaps easier understood by
looking at a message stored on a punched paper tape. In the example
below, we want to transmit the word HELLO which is stored on the
plain text tape.
We also have a pre-recorded key tape, with a series of random
characters; in this case the sequence AXHJB.
The contents of the plaintext tape are now XOR-ed with the
contents of the key tape.
The result (KMIVE) is shown here as the ciphertext tape:
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Mixing of the plaintext and the key
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Now let us see what happens if we repeat this operation on the
resulting ciphertext tape with the letters 'KMIVE'.
In the illustration below,
the ciphertext tape is on the left. It is XOR-ed with a copy of the
original key tape (AXHJB), which results in the original plaintext: 'HELLO'.
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Mixing of the ciphertext and the key
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This process of applying the XOR-operation to text and key
is often called mixing, and the cipher machines that use the
Vernam principle, are therefore known as mixers.
In the days when teletype systems were in widespread use, technicians
were often so experienced that they could read a text directly from
a paper tape, simply by looking at the holes and reading the bit patterns.
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Mixing of the ciphertext and the key with the human eye
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The same was often true for the maintenance engineers of OTT cipher
machines. By taking a ciphertext tape, overlaying it with a key tape
and then holding it against a bright light source,
they were often able to 'read' the plaintext directly.
This is illustrated in the above drawing, in which each half-transparent
hole should be interpreted as as a binary '1'.
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Mixing of the plaintext and the key with the human eye
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Although the OTP was, and still is,
the only cipher that is totally secure by design,
many systems based on the Vernam Cipher were
replaced by cipher systems that use a pseudo-random number
generator (PRNG) with a long period. If both ends of the
communication link initialize their pseudo-random key
generators identically, the Vernam principle can still be
applied.
With this method, the initialization of the pseudo-random generator
has become the key
or seed,
or initialization vector, which is typically much shorter than the
message itself. Such a short key produces far less distribution
problems, but also results in a reduced security of the cipher.
In practice it's a trade-off between the desired secrecy level
and the strength of the key.
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OTT cipher machines
mixers
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Cipher machines, intended for operation with teleprinter signals,
that use the Vernam Cipher, are generally called mixers
or mixing machines.
In most cases, they are equipped with two paper-tape readers,
one for the plaintext tape and one for the key tape.
➤ More information
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Modern use of the Vernam Cipher
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The Vernam Cipher can also be implemented with modern computer technology.
Instead of the 5-bit word of a teletype system, computer words consist
of 8 or even more bits. The principle, however, remains the same as
the XOR-operation is applied to the individual bits of the data word.
The use of the XOR-operation is still at the heart of many
cryptographic algorithms today.
One warning however: always use a dedicated device for
One-Time Pad
communication,
and never use a common personal computer (PC), a tablet or a smart phone,
with a piece of software. Such systems are inherently usafe.
There is no such thing as a secure personal computer.
➤ More about the One-Time Pad (OTP)
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© Crypto Museum. Created: Saturday 11 August 2012. Last changed: Wednesday, 26 August 2026 - 17:30 CET.
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