Symmetric-key algorithms are

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

s for

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), ...

that use the same

cryptographic keys A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key c ...

for both the encryption of

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 ...

and the decryption of

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 plaintext ...

. The keys may be identical, or there may be a simple transformation to go between the two keys. The keys, in practice, represent a

shared secret In cryptography, a shared secret is a piece of data, known only to the parties involved, in a secure communication. This usually refers to the key of a symmetric cryptosystem. The shared secret can be a PIN code, a password, a passphrase, a b ...

between two or more parties that can be used to maintain a private information link. The requirement that both parties have access to the secret key is one of the main drawbacks of

symmetric Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...

-key encryption, in comparison to

public-key encryption Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic alg ...

(also known as asymmetric-key encryption). However, symmetric-key encryption algorithms are usually better for bulk encryption. With exception of 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, ...

they have a smaller key size, which means less storage space and faster transmission. Due to this, asymmetric-key encryption is often used to exchange the secret key for symmetric-key encryption.

Types

Symmetric-key encryption can use either

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 or

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. Stream ciphers encrypt the digits (typically

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), or letters (in substitution ciphers) of a message one at a time. An example is

ChaCha20 Salsa20 and the closely related ChaCha are stream ciphers developed by Daniel J. Bernstein. Salsa20, the original cipher, was designed in 2005, then later submitted to the eSTREAM European Union cryptographic validation process by Bernstein. Ch ...

Substitution cipher In cryptography, a substitution cipher is a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters (the most common), pairs of letters, t ...

s are well-known ciphers, but can be easily decrypted using a

frequency table In statistics, the frequency or absolute frequency of an event i is the number n_i of times the observation has occurred/been recorded in an experiment or study. These frequencies are often depicted graphically or tabular form. Types The cumula ...

. Block ciphers take a number of bits and encrypt them in a single unit, padding the plaintext to achieve a multiple of the block size. The

Advanced Encryption Standard The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001. AES is a variant ...

(AES) algorithm, approved by

NIST The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical s ...

in December 2001, uses 128-bit blocks.

Implementations

Examples of popular symmetric-key algorithms include

Twofish In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. It was one of the five finalists of the Advanced Encryption Standard contest, but it was not selected for standardization. Two ...

, Serpent, AES (Rijndael),

Camellia ''Camellia'' (pronounced or ) is a genus of flowering plants in the family Theaceae. They are found in tropical and subtropical areas in East Asia, eastern and South Asia, southern Asia, from the Himalayas east to Japan and Indonesia. There are ...

Salsa20 Salsa20 and the closely related ChaCha are stream ciphers developed by Daniel J. Bernstein. Salsa20, the original cipher, was designed in 2005, then later submitted to the eSTREAM European Union cryptographic validation process by Bernstein. Ch ...

Blowfish Tetraodontidae is a family of marine and freshwater fish in the order Tetraodontiformes. The family includes many familiar species variously called pufferfish, puffers, balloonfish, blowfish, blowers, blowies, bubblefish, globefish, swellfish, ...

, CAST5,

Kuznyechik Kuznyechik (, literally "grasshopper") is a symmetric block cipher. It has a block size of 128 bits and key length of 256 bits. It is defined in the National Standard of the Russian Federation GOST R 34.12-2015 and also in RFC 7801. The name of ...

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 ...

, DES, 3DES, Skipjack,

Safer Safer or SAFER may refer to: * FSO ''Safer'', a Yemeni floating oil storage and offloading vessel * Safer (surname) * Safar or safer, the second month of the Islamic calendar * As an acronym: ** SAFER, an initiative of the World Health Organizat ...

, and

IDEA In philosophy and in common usage, an idea (from the Greek word: ἰδέα (idea), meaning 'a form, or a pattern') is the results of thought. Also in philosophy, ideas can also be mental representational images of some object. Many philosophe ...

Use as a cryptographic primitive

Symmetric ciphers are commonly used to achieve other

cryptographic primitive Cryptographic primitives are well-established, low-level cryptography, cryptographic algorithms that are frequently used to build cryptographic protocols for computer security systems. These routines include, but are not limited to, one-way hash fun ...

s than just encryption. Encrypting a message does not guarantee that it will remain unchanged while encrypted. Hence, often a

message authentication code In cryptography, a message authentication code (MAC), sometimes known as an authentication tag, is a short piece of information used for authentication, authenticating and Data integrity, integrity-checking a message. In other words, it is used t ...

is added to a ciphertext to ensure that changes to the ciphertext will be noted by the receiver. Message authentication codes can be constructed from an

AEAD Authenticated Encryption (AE) is an encryption scheme which simultaneously assures the data confidentiality (also known as privacy: the encrypted message is impossible to understand without the knowledge of a secret key) and authenticity (in othe ...

cipher (e.g. AES-GCM). However, symmetric ciphers cannot be used for

non-repudiation In law, non-repudiation is a situation where a statement's author cannot successfully dispute its authorship or the validity of an associated contract. The term is often seen in a legal setting when the authenticity of a signature is being challeng ...

purposes except by involving additional parties. See th
ISO/IEC 13888-2 standard
Another application is to build

hash function A hash function is any Function (mathematics), function that can be used to map data (computing), data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a ...

s from block ciphers. See

one-way compression function In cryptography, a one-way compression function is a function that transforms two fixed-length inputs into a fixed-length output.Handbook of Applied Cryptography by Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone. Fifth Printing (August ...

for descriptions of several such methods.

Construction of symmetric ciphers

Many modern block ciphers are based on a construction proposed by

Horst Feistel Horst Feistel (January 30, 1915 – November 14, 1990) was a German-American cryptographer who worked on the design of ciphers at IBM, initiating research that culminated in the development of the Data Encryption Standard (DES) in the 1970s. The ...

. Feistel's construction makes it possible to build invertible functions from other functions that are themselves not invertible.

Security of symmetric ciphers

Symmetric ciphers have historically been susceptible to

known-plaintext attack The known-plaintext attack (KPA) is an attack model for cryptanalysis where the attacker has access to both the plaintext (called a crib) and its encrypted version (ciphertext). These can be used to reveal secret keys and code books. The term " ...

chosen-plaintext attack A chosen-plaintext attack (CPA) is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts.Ross Anderson, ''Security Engineering: A Guide to Building Dependable Distributed Systems'' ...

differential cryptanalysis Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in information input can a ...

and

linear cryptanalysis In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine Affine may describe any of various topics concerned with connections or affinities. It may refer to: * Affine, a Affinity_(law)#Terminology, relat ...

. Careful construction of the functions for each

round Round or rounds may refer to: Mathematics and science * Having no sharp corners, as an ellipse, circle, or sphere * Rounding, reducing the number of significant figures in a number * Round number, ending with one or more zeroes * Round (crypt ...

can greatly reduce the chances of a successful attack. It is also possible to increase the key length or the rounds in the encryption process to better protect against attack. This, however, tends to increase the processing power and decrease the speed at which the process runs due to the amount of operations the system needs to do. Most modern symmetric-key algorithms appear to be resistant to the threat of

post-quantum cryptography Post-quantum cryptography (PQC), sometimes referred to as quantum-proof, quantum-safe, or quantum-resistant, is the development of cryptographic algorithms (usually public-key algorithms) that are currently thought to be secure against a crypt ...

Quantum computers A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. C ...

would exponentially increase the speed at which these ciphers can be decoded; notably,

Grover's algorithm In quantum computing, Grover's algorithm, also known as the quantum search algorithm, is a quantum algorithm for unstructured search that finds with high probability the unique input to a black box function that produces a particular output value, ...

would take the square-root of the time traditionally required for a

brute-force attack In cryptography, a brute-force attack or exhaustive key search is a cryptanalytic attack that consists of an attacker submitting many possible keys or passwords with the hope of eventually guessing correctly. This strategy can theoretically be ...

, although these vulnerabilities can be compensated for by doubling key length. For example, a 128 bit AES cipher would not be secure against such an attack as it would reduce the time required to test all possible iterations from over 10 quintillion years to about six months. By contrast, it would still take a quantum computer the same amount of time to decode a 256 bit AES cipher as it would a conventional computer to decode a 128 bit AES cipher. For this reason, AES-256 is believed to be "quantum resistant".

Key management

Key establishment

Symmetric-key algorithms require both the sender and the recipient of a message to have the same secret key. All early cryptographic systems required either the sender or the recipient to somehow receive a copy of that secret key over a physically secure channel. Nearly all modern cryptographic systems still use symmetric-key algorithms internally to encrypt the bulk of the messages, but they eliminate the need for a physically secure channel by using

Diffie–Hellman key exchange Diffie–Hellman (DH) key exchangeSynonyms of Diffie–Hellman key exchange include: * Diffie–Hellman–Merkle key exchange * Diffie–Hellman key agreement * Diffie–Hellman key establishment * Diffie–Hellman key negotiation * Exponential ke ...

or some other public-key protocol to securely come to agreement on a fresh new secret key for each session/conversation (forward secrecy).

Key generation

When used with asymmetric ciphers for key transfer, pseudorandom key generators are nearly always used to generate the symmetric cipher session keys. However, lack of randomness in those generators or in their

initialization vector In cryptography, an initialization vector (IV) or starting variable is an input to a cryptographic primitive being used to provide the initial state. The IV is typically required to be random or pseudorandom, but sometimes an IV only needs to be un ...

s is disastrous and has led to cryptanalytic breaks in the past. Therefore, it is essential that an implementation use a source of high

entropy Entropy is a scientific concept, most commonly associated with states of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the micros ...

for its initialization.

Reciprocal cipher

A reciprocal cipher is a cipher where, just as one enters the

into the

system to get the

, one could enter the ciphertext into the same place in the system to get the plaintext. A reciprocal cipher is also sometimes referred as self-reciprocal cipher. Practically all mechanical cipher machines implement a reciprocal cipher, a mathematical involution on each typed-in letter. Instead of designing two kinds of machines, one for encrypting and one for decrypting, all the machines can be identical and can be set up (keyed) the same way. Examples of reciprocal ciphers include: *

Atbash Atbash (; also transliterated Atbaš) is a monoalphabetic substitution cipher originally used to encrypt the Hebrew alphabet. It can be modified for use with any known writing system with a standard collating order. Encryption The Atbash ciph ...

* Beaufort cipher *

Enigma machine The Enigma machine is a cipher device developed and used in the early- to mid-20th century to protect commercial, diplomatic, and military communication. It was employed extensively by Nazi Germany during World War II, in all branches of the W ...

* Marie Antoinette and Axel von Fersen communicated with a self-reciprocal cipher. * the Porta polyalphabetic cipher is self-reciprocal. * Purple cipher Greg Goebel
"US Codebreakers In The Shadow Of War"
2018. *

ROT13 ROT13 is a simple letter substitution cipher that replaces a letter with the 13th letter after it in the Latin alphabet. ROT13 is a special case of the Caesar cipher which was developed in ancient Rome, used by Julius Caesar in the 1st centur ...

* XOR cipher *

Vatsyayana cipher Mlecchita Vikalpa is one of the 64 arts listed in Vatsyayana's Kamasutra, translated into English as "the art of understanding writing in cypher, and the writing of words in a peculiar way". The list appears in Chapter 3 of Part I of Kamasutra a ...

The majority of all modern ciphers can be classified as either a

, most of which use a reciprocal XOR cipher combiner, or a

, most of which use a

Feistel cipher In cryptography, a Feistel cipher (also known as Luby–Rackoff block cipher) is a symmetric structure used in the construction of block ciphers, named after the German-born physicist and cryptographer Horst Feistel, who did pioneering resear ...

Lai–Massey scheme The Lai–Massey scheme is a cryptographic structure used in the design of block ciphers, an alternative to the Feistel network for converting a non-invertible keyed round function to an invertible keyed cipher. It is used in IDEA and IDEA NXT. ...

with a reciprocal transformation in each round.

Notes

References

{{DEFAULTSORT:Symmetric-Key Algorithm Cryptographic algorithms