In
cryptography
Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...
, a keystream is a
stream
A stream is a continuous body of water, body of surface water Current (stream), flowing within the stream bed, bed and bank (geography), banks of a channel (geography), channel. Depending on its location or certain characteristics, a strea ...
of
random
In common usage, randomness is the apparent or actual lack of definite pattern or predictability in information. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. ...
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. Pseudorandom number generators are often used in computer programming, as tradi ...
characters that are combined with a
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 an encrypted message (the ciphertext).
The "characters" in the keystream can be
bit
The bit is the most basic unit of information in computing and digital communication. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as ...
s,
byte
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable un ...
s, numbers or actual characters like A-Z depending on the usage case.
Usually each character in the keystream is either added, subtracted or
XORed with a character in the plaintext to produce the ciphertext, using
modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to mo ...
.
Keystreams are used in the
one-time pad
The one-time pad (OTP) is an encryption technique that cannot be Cryptanalysis, 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, ...
cipher and in most
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 keystrea ...
s.
Block cipher
In cryptography, a block cipher is a deterministic algorithm that operates on fixed-length groups of bits, called ''blocks''. Block ciphers are the elementary building blocks of many cryptographic protocols. They are ubiquitous in the storage a ...
s can also be used to produce keystreams. For instance, CTR mode is a
block mode that makes a block cipher produce a keystream and thus turns the block cipher into a stream cipher.
Example
In this simple example we use the English alphabet of 26 characters from a-z. Thus we can not encrypt numbers, commas, spaces and other symbols. The random numbers in the keystream then have to be at least between 0 and 25.
To encrypt we add the keystream numbers to the plaintext. And to decrypt we subtract the same keystream numbers from the ciphertext to get the plaintext.
If a ciphertext number becomes larger than 25 we wrap it to a value between 0-25. Thus 26 becomes 0 and 27 becomes 1 and so on. (Such wrapping is called
modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic operations for integers, other than the usual ones from elementary arithmetic, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to mo ...
.)
Here the plaintext message "attack at dawn" is combined by addition with the keystream "kjcngmlhylyu" and produces the ciphertext "kcvniwlabluh".
References
*
Handbook of Applied Cryptography' by Menezes, van Oorschot and Vanstone (2001), chapter 1, 6 and 7.
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Stream ciphers