Initialization vector

Encyclopedia

In cryptography

, an

that is typically required to be random or pseudorandom. Randomization

is crucial for encryption

schemes to achieve semantic security

, a property whereby repeated usage of the scheme under the same key does not allow an attacker to infer relationships between segments of the encrypted message. For block cipher

s, the use of an IV is described by so-called modes of operation

. Randomization is also required for other primitives, such as universal hash functions and message authentication code

s based thereon.

Some cryptographic primitives require the IV only to be non-repeating, and the required randomness is derived internally. In this case, the IV is commonly called a nonce

(

The size of the IV is dependent on the cryptographic primitive used; for block ciphers, it is generally the cipher's block size. Ideally, for encryption schemes, the unpredictable part of the IV has the same size as the key to compensate time-memory-data trade-off attacks. When the IV is chosen at random, the probability of collisions due to the birthday problem must be taken into account. Traditional stream ciphers such as RC4

do not support an explicit IV as input, and a custom solution for incorporating an IV into the cipher's key or internal state is needed. Some designs realized in practice are known to be insecure; the WEP

protocol is a notable example, and is prone to related-IV attacks.

is one of the most basic primitive

s in cryptography, and frequently used for data encryption

. However, by itself, it can only be used to encode a data block of a predefined size, called the block size

. For example, a single invocation of the AES

algorithm transforms a 128-bit plaintext

block into a ciphertext

block of 128 bits in size. The key, which is given as one input to the cipher, defines the mapping between plaintext and ciphertext. If data of arbitrary length is to be encrypted, a simple strategy is to split the data into blocks each matching the cipher's block size, and encrypt each block separately using the same key. This method is not secure, however: equal plaintext blocks get transformed into equal ciphertexts, and a third party observing the encrypted data may easily determine its content even when not knowing the encryption key.

To hide patterns in encrypted data while avoiding the re-issuing of a new key after each block cipher invocation a method is needed to randomize

the input data. In 1980, the NIST

published a national standard document designated FIPS

PUB 81, which specified four so-called block cipher modes of operation

s, each describing a different solution for encrypting a set of input blocks. The first mode implements the simple strategy described above, and was specified as the electronic codebook (ECB) mode. In contrast, each of the other modes describe a process where ciphertext from one block encryption step gets intermixed with the data from the next encryption step. To initiate this process, an additional input value is required to be mixed with the first block, and which is referred to as an

: by this property, it is practically impossible for an attacker to draw any knowledge from observed ciphertext. It can be shown that each of the three additional modes specified by the NIST are semantically secure under so-called chosen-plaintext attack

s.

encryption uniqueness is crucially important as plaintext may be trivially recovered otherwise.

Many schemes require the IV to be

. This is effected by selecting the IV at random or pseudo-randomly. In such schemes, the chance of a duplicate IV is negligible, but the effect of the birthday problem must be considered. As for the uniqueness requirement, a predictable IV may allow recovery of (partial) plaintext.

Depending on whether the IV for a cryptographic scheme must be random or only unique the scheme is either called

, though newer designs exist that combine both security solutions in so-called authenticated encryption

modes. While encryption and authenticated encryption modes usually take an IV matching the cipher's block size, authentication modes are commonly realized as deterministic algorithms, and the IV is set to zero or some other fixed value.

loss, unique to each cipher construction, related-IVs and other IV-related attacks are a known security issue for stream ciphers, which makes IV loading in stream ciphers a serious concern and a subject of ongoing research.

algorithm

called WEP (short for Wired Equivalent Privacy

) used a short, 24-bit IV, leading to reused IVs with the same key, which led to it being easily cracked. Packet injection

allowed for WEP to be cracked in times as short as several seconds. This ultimately led to the deprecation of WEP.

Cryptography

Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

, an

**initialization vector**(**IV**) is a fixed-size input to a cryptographic primitiveCryptographic primitive

Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build computer security systems. These routines include, but are not limited to, one-way hash functions and encryption functions.- Rationale :...

that is typically required to be random or pseudorandom. Randomization

Randomization

Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....

is crucial for encryption

Encryption

In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...

schemes to achieve semantic security

Semantic security

Semantic security is a widely used definition for security in an asymmetric key encryption algorithm. For a cryptosystem to be semantically secure, it must be infeasible for a computationally bounded adversary to derive significant information about a message when given only its ciphertext and...

, a property whereby repeated usage of the scheme under the same key does not allow an attacker to infer relationships between segments of the encrypted message. For block cipher

Block cipher

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext...

s, the use of an IV is described by so-called modes of operation

Block cipher modes of operation

In cryptography, modes of operation is the procedure of enabling the repeated and secure use of a block cipher under a single key.A block cipher by itself allows encryption only of a single data block of the cipher's block length. When targeting a variable-length message, the data must first be...

. Randomization is also required for other primitives, such as universal hash functions and message authentication code

Message authentication code

In cryptography, a message authentication code is a short piece of information used to authenticate a message.A MAC algorithm, sometimes called a keyed hash function, accepts as input a secret key and an arbitrary-length message to be authenticated, and outputs a MAC...

s based thereon.

Some cryptographic primitives require the IV only to be non-repeating, and the required randomness is derived internally. In this case, the IV is commonly called a nonce

Cryptographic nonce

In security engineering, nonce is an arbitrary number used only once to sign a cryptographic communication. It is similar in spirit to a nonce word, hence the name. It is often a random or pseudo-random number issued in an authentication protocol to ensure that old communications cannot be reused...

(

*number used once*), and the primitives are described as*stateful*as opposed to*randomized*. This is because the IV need not be explicitly forwarded to a recipient but may be derived from a common state updated at both sender and receiver side. (In practice, a short nonce is still transmitted along with the message to consider message loss.) An example of stateful encryption schemes is the counter mode of operation, which uses a sequence number as a nonce.The size of the IV is dependent on the cryptographic primitive used; for block ciphers, it is generally the cipher's block size. Ideally, for encryption schemes, the unpredictable part of the IV has the same size as the key to compensate time-memory-data trade-off attacks. When the IV is chosen at random, the probability of collisions due to the birthday problem must be taken into account. Traditional stream ciphers such as RC4

RC4

In cryptography, RC4 is the most widely used software stream cipher and is used in popular protocols such as Secure Sockets Layer and WEP...

do not support an explicit IV as input, and a custom solution for incorporating an IV into the cipher's key or internal state is needed. Some designs realized in practice are known to be insecure; the WEP

Wired Equivalent Privacy

Wired Equivalent Privacy is a weak security algorithm for IEEE 802.11 wireless networks. Introduced as part of the original 802.11 standard ratified in September 1999, its intention was to provide data confidentiality comparable to that of a traditional wired network...

protocol is a notable example, and is prone to related-IV attacks.

## Motivation

A block cipherBlock cipher

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext...

is one of the most basic primitive

Cryptographic primitive

Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build computer security systems. These routines include, but are not limited to, one-way hash functions and encryption functions.- Rationale :...

s in cryptography, and frequently used for data encryption

Encryption

In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...

. However, by itself, it can only be used to encode a data block of a predefined size, called the block size

Block size (cryptography)

In modern cryptography, symmetric key ciphers are generally divided into stream ciphers and block ciphers. Block ciphers operate on a fixed length string of bits. The length of this bit string is the block size...

. For example, a single invocation of the AES

Advanced Encryption Standard

Advanced Encryption Standard is a specification for the encryption of electronic data. It has been adopted by the U.S. government and is now used worldwide. It supersedes DES...

algorithm transforms a 128-bit plaintext

Plaintext

In cryptography, plaintext is information a sender wishes to transmit to a receiver. Cleartext is often used as a synonym. Before the computer era, plaintext most commonly meant message text in the language of the communicating parties....

block into a ciphertext

Ciphertext

In cryptography, ciphertext 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 that is unreadable by a human or computer without the proper cipher...

block of 128 bits in size. The key, which is given as one input to the cipher, defines the mapping between plaintext and ciphertext. If data of arbitrary length is to be encrypted, a simple strategy is to split the data into blocks each matching the cipher's block size, and encrypt each block separately using the same key. This method is not secure, however: equal plaintext blocks get transformed into equal ciphertexts, and a third party observing the encrypted data may easily determine its content even when not knowing the encryption key.

To hide patterns in encrypted data while avoiding the re-issuing of a new key after each block cipher invocation a method is needed to randomize

Randomization

Randomization is the process of making something random; this means:* Generating a random permutation of a sequence .* Selecting a random sample of a population ....

the input data. In 1980, the NIST

National Institute of Standards and Technology

The National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory, otherwise known as a National Metrological Institute , which is a non-regulatory agency of the United States Department of Commerce...

published a national standard document designated FIPS

Federal Information Processing Standard

A Federal Information Processing Standard is a publicly announced standardization developed by the United States federal government for use in computer systems by all non-military government agencies and by government contractors, when properly invoked and tailored on a contract...

PUB 81, which specified four so-called block cipher modes of operation

Block cipher modes of operation

In cryptography, modes of operation is the procedure of enabling the repeated and secure use of a block cipher under a single key.A block cipher by itself allows encryption only of a single data block of the cipher's block length. When targeting a variable-length message, the data must first be...

s, each describing a different solution for encrypting a set of input blocks. The first mode implements the simple strategy described above, and was specified as the electronic codebook (ECB) mode. In contrast, each of the other modes describe a process where ciphertext from one block encryption step gets intermixed with the data from the next encryption step. To initiate this process, an additional input value is required to be mixed with the first block, and which is referred to as an

*initialization vector*. For example, the cipher-block chaining (CBC) mode requires a random value of the cipher's block size as additional input, and adds it to the first plaintext block before subsequent encryption. In turn, the ciphertext produced in the first encryption step is added to the second plaintext block, and so on. The ultimate goal for encryption schemes is to provide semantic securitySemantic security

Semantic security is a widely used definition for security in an asymmetric key encryption algorithm. For a cryptosystem to be semantically secure, it must be infeasible for a computationally bounded adversary to derive significant information about a message when given only its ciphertext and...

: by this property, it is practically impossible for an attacker to draw any knowledge from observed ciphertext. It can be shown that each of the three additional modes specified by the NIST are semantically secure under so-called chosen-plaintext attack

Chosen-plaintext attack

A chosen-plaintext attack is an attack model for cryptanalysis which presumes that the attacker has the capability to choose arbitrary plaintexts to be encrypted and obtain the corresponding ciphertexts. The goal of the attack is to gain some further information which reduces the security of the...

s.

## Properties

Properties of an IV depend on the cryptographic scheme used. A basic requirement is*uniqueness*, which means that no IV may be reused under the same key. For block ciphers, repeated IV values devolve the encryption scheme into electronic codebook mode: equal IV and equal plaintext result in equal ciphertext. In stream cipherStream cipher

In cryptography, a stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream . In a stream cipher the plaintext digits are encrypted one at a time, and the transformation of successive digits varies during the encryption...

encryption uniqueness is crucially important as plaintext may be trivially recovered otherwise.

Stream ciphers encrypt plaintext*Example:**P*to ciphertext*C*by deriving a key stream*K*from a given key and IV and computing*C*as*C*=*P*xor*K*. Assume that an attacker has observed two messages*C*_{1}and*C*_{2}both encrypted with the same key and IV. Then knowledge of either*P*_{1}or*P*_{2}reveals the other plaintext since*C*_{1}xor*C*_{2}= (*P*_{1}xor K) xor (*P*_{2}xor K) =*P*_{1}xor*P*_{2}.

Many schemes require the IV to be

*unpredictable*by an adversaryAdversary (cryptography)

In cryptography, an adversary is a malicious entity whose aim is to prevent the users of the cryptosystem from achieving their goal...

. This is effected by selecting the IV at random or pseudo-randomly. In such schemes, the chance of a duplicate IV is negligible, but the effect of the birthday problem must be considered. As for the uniqueness requirement, a predictable IV may allow recovery of (partial) plaintext.

Consider a scenario where a legitimate party called Alice encrypts messages using the cipher-block chaining mode. Consider further that there is an adversary called Eve that can observe these encryptions and is able to forward plaintext messages to Alice for encryption (in other words, Eve is capable of a chosen-plaintext attack*Example:*Chosen-plaintext attackA chosen-plaintext attack is an attack model for cryptanalysis which presumes that the attacker has the capability to choose arbitrary plaintexts to be encrypted and obtain the corresponding ciphertexts. The goal of the attack is to gain some further information which reduces the security of the...

). Now assume that Alice has sent a message consisting of an initialization vector*IV*_{1}and starting with a ciphertext block*C*. Let further_{Alice}*P*denote the first plaintext block of Alice's message, let_{Alice}*E*denote encryption, and let*P*be Eve's guess for the first plaintext block. Now, if Eve can determine the initialization vector_{Eve}*IV*_{2}of the next message she will be able to test her guess by forwarding a plaintext message to Alice starting with (*IV*_{2}xor*IV*_{1}xor*P*)); if her guess was correct this plaintext block will get encrypted to_{Eve}*C*by Alice. This is because of the following simple observation:_{Alice}*C*=_{Alice}*E*(*IV*_{1}xor*P*) =_{Alice}*E*(*IV*_{2}xor (*IV*_{2}xor*IV*_{1}xor*P*))._{Alice}

Depending on whether the IV for a cryptographic scheme must be random or only unique the scheme is either called

*randomized*or*stateful*. While randomized schemes always require the IV chosen by a sender to be forwarded to receivers, stateful schemes allow sender and receiver to share a common IV state, which is updated in a predefined way at both sides.## Block ciphers

Block cipher processing of data is usually described as a mode of operation. Modes are primarily defined for encryption as well as authenticationAuthentication

Authentication is the act of confirming the truth of an attribute of a datum or entity...

, though newer designs exist that combine both security solutions in so-called authenticated encryption

Authenticated encryption

Authenticated Encryption is a block cipher mode of operation which simultaneously provides confidentiality, integrity and authenticity assurances on the data. It became readily apparent that securely compositing a confidentiality mode with an authentication mode could be error prone and difficult...

modes. While encryption and authenticated encryption modes usually take an IV matching the cipher's block size, authentication modes are commonly realized as deterministic algorithms, and the IV is set to zero or some other fixed value.

## Stream ciphers

In stream ciphers, IVs are loaded into the keyed internal secret state of the cipher, after which a number of cipher rounds is executed prior to releasing the first bit of output. For performance reasons, designers of stream ciphers try to keep that number of rounds as small as possible, but because determining the minimal secure number of rounds for stream ciphers is not a trivial task, and considering other issues such as entropyInformation entropy

In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits...

loss, unique to each cipher construction, related-IVs and other IV-related attacks are a known security issue for stream ciphers, which makes IV loading in stream ciphers a serious concern and a subject of ongoing research.

## WEP IV

The 802.11 encryptionEncryption

In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...

algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

called WEP (short for Wired Equivalent Privacy

Wired Equivalent Privacy

Wired Equivalent Privacy is a weak security algorithm for IEEE 802.11 wireless networks. Introduced as part of the original 802.11 standard ratified in September 1999, its intention was to provide data confidentiality comparable to that of a traditional wired network...

) used a short, 24-bit IV, leading to reused IVs with the same key, which led to it being easily cracked. Packet injection

Packet injection

Packet injection is a computer networking term which refers to sending a packet on a network into an already established connection, usually by a party not otherwise participating in the said connection. This is accomplished by crafting a packet using raw sockets...

allowed for WEP to be cracked in times as short as several seconds. This ultimately led to the deprecation of WEP.

## See also

- Cryptographic nonceCryptographic nonceIn security engineering, nonce is an arbitrary number used only once to sign a cryptographic communication. It is similar in spirit to a nonce word, hence the name. It is often a random or pseudo-random number issued in an authentication protocol to ensure that old communications cannot be reused...
- Padding (cryptography)Padding (cryptography)-Classical cryptography:Official messages often start and end in predictable ways: My dear ambassador, Weather report, Sincerely yours, etc. The primary use of padding with classical ciphers is to prevent the cryptanalyst from using that predictability to find cribs that aid in breaking the...
- Salt (cryptography)Salt (cryptography)In cryptography, a salt consists of random bits, creating one of the inputs to a one-way function. The other input is usually a password or passphrase. The output of the one-way function can be stored rather than the password, and still be used for authenticating users. The one-way function...
- Block cipher modes of operationBlock cipher modes of operationIn cryptography, modes of operation is the procedure of enabling the repeated and secure use of a block cipher under a single key.A block cipher by itself allows encryption only of a single data block of the cipher's block length. When targeting a variable-length message, the data must first be...
- CipherSaberCipherSaberCipherSaber is a simple symmetric encryption protocol based on the RC4 stream cipher. Its goals are both technical and political: it gives reasonably strong protection of message confidentiality, yet it's designed to be simple enough that even novice programmers can memorize the algorithm and...

(RC4 with IV)