Block cipher mode of operation

In cryptography, modes of operation enable 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 partitioned into separate cipher blocks. Typically, the last block must also be extended to match the cipher's block length using a suitable padding scheme. A mode of operation describes the process of encrypting each of these blocks, and generally uses randomization based on an additional input value, often called an initialization vector, to allow doing so safely.

Modes of operation have primarily been defined for encryption and authentication. Historically, encryption modes have been studied extensively in regard to their error propagation properties under various scenarios of data modification. Later development regarded integrity protection as an entirely separate cryptographic goal from encryption. Some modern modes of operation combine encryption and authentication in an efficient way, and are known as authenticated encryption modes.

While modes of operation are commonly associated with symmetric encryption, they may also be applied to public-key encryption primitives such as RSA in principle (though in practice public-key encryption of longer messages is generally realized using hybrid encryption).

History and standardization

The earliest modes of operation, ECB, CBC, OFB, and CFB (see below for all), date back to 1981 and were specified in FIPS 81, DES Modes of Operation. In 2001, NIST revised its list of approved modes of operation by including AES as a block cipher and adding CTR mode in SP800-38A, Recommendation for Block Cipher Modes of Operation. Finally, in January, 2010, NIST added XTS-AES in SP800-38E, Recommendation for Block Cipher Modes of Operation: The XTS-AES Mode for Confidentiality on Storage Devices. Other confidentiality modes exist which have not been approved by NIST. For example, CTS is ciphertext stealing mode and available in many popular cryptographic libraries.

ECB, CBC, OFB, CFB, CTR, and XTS modes only provide confidentiality; to ensure an encrypted message is not accidentally modified or maliciously tampered requires a separate message authentication code such as CBC-MAC. The cryptographic community recognized the need for dedicated integrity assurances and NIST responded with HMAC, CMAC, and GMAC. HMAC was approved in 2002 as FIPS 198, The Keyed-Hash Message Authentication Code (HMAC), CMAC was released in 2005 under SP800-38B, Recommendation for Block Cipher Modes of Operation: The CMAC Mode for Authentication, and GMAC was formalized in 2007 under SP800-38D, Recommendation for Block Cipher Modes of Operation: Galois/Counter Mode (GCM) and GMAC.

After observing that compositing a confidentiality mode with a authenticity mode could be difficult and error prone, the cryptographic community began to supply modes which combined confidentiality and authenticity into a single cryptographic primitive. The modes are referred to as authenticated encryption, AE, and authenc. Examples of authenc modes are CCM (SP800-38C), GCM (SP800-38D), CWC, EAX, IAPM, and OCB.

Modes of operation are nowadays defined by a number of national and internationally recognized standards bodies. The most influential source is the US NIST. Other notable standards organizations include the international ISO and IEEE, the national ANSI, and the IETF.

Initialization vector (IV)

Main article: Initialization vector

An initialization vector (IV) is a block of bits that is used by several modes to randomize the encryption and hence to produce distinct ciphertexts even if the same plaintext is encrypted multiple times, without the need for a (usually lengthy) re-keying process.

An initialization vector has different security requirements than a key, so the IV usually does not need to be secret. However, in most cases, it is important that an initialization vector is never reused under the same key. For CBC and CFB, reusing an IV leaks some information about the first block of plaintext, and about any common prefix shared by the two messages. For OFB and CTR, reusing an IV completely destroys security. In CBC mode, the IV must, in addition, be unpredictable at encryption time; in particular, the (previously) common practice of re-using the last ciphertext block of a message as the IV for the next message is insecure (for example, this method was used by SSL 2.0). If an attacker knows the IV (or the previous block of ciphertext) before he specifies the next plaintext, he can check his guess about plaintext of some block that was encrypted with the same key before (this is known as the TLS CBC IV attack).

Padding

Main article: Padding (cryptography)

A block cipher works on units of a fixed size (known as a block size), but messages come in a variety of lengths. So some modes (namely ECB and CBC) require that the final block be padded before encryption. Several padding schemes exist. The simplest is to add null bytes to the plaintext to bring its length up to a multiple of the block size, but care must be taken that the original length of the plaintext can be recovered; this is so, for example, if the plaintext is a C style string which contains no null bytes except at the end. Slightly more complex is the original DES method, which is to add a single one bit, followed by enough zero bits to fill out the block; if the message ends on a block boundary, a whole padding block will be added. Most sophisticated are CBC-specific schemes such as ciphertext stealing or residual block termination, which do not cause any extra ciphertext, at the expense of some additional complexity. Schneier and Ferguson suggest two possibilities, both simple: append a byte with value 128 (hex 80), followed by as many zero bytes as needed to fill the last block, or pad the last block with n bytes all with value n.

CFB, OFB and CTR modes do not require any special measures to handle messages whose lengths are not multiples of the block size, since the modes work by XORing the plaintext with the output of the block cipher. The last partial block of plaintext is XORed with the first few bytes of the last keystream block, producing a final ciphertext block that is the same size as the final partial plaintext block. This characteristic of stream ciphers makes them suitable for applications that require the encrypted ciphertext data to be the same size as the original plaintext data, and for applications that transmit data in streaming form where it is inconvenient to add padding bytes.

Electronic codebook (ECB)

The simplest of the encryption modes is the electronic codebook (ECB) mode. The message is divided into blocks and each block is encrypted separately.

The disadvantage of this method is that identical plaintext blocks are encrypted into identical ciphertext blocks; thus, it does not hide data patterns well. In some senses, it doesn't provide serious message confidentiality, and it is not recommended for use in cryptographic protocols at all. A striking example of the degree to which ECB can leave plaintext data patterns in the ciphertext is shown below; a pixel-map version of the image on the left was encrypted with ECB mode to create the center image, versus a non-ECB mode for the right image.

Original	Encrypted using ECB mode	Other modes than ECB results in pseudo-randomness

The image on the right is how the image might appear encrypted with CBC, CTR or any of the other more secure modes—indistinguishable from random noise. Note that the random appearance of the image on the right does not indicate whether the image has been securely encrypted; many kinds of insecure encryption have been developed which would produce output just as 'random-looking'.

ECB mode can also make protocols without integrity protection even more susceptible to replay attacks, since each block gets decrypted in exactly the same way. For example, the Phantasy Star Online: Blue Burst online video game uses Blowfish in ECB mode. Before the key exchange system was cracked leading to even easier methods, cheaters repeated encrypted "monster killed" message packets, each an encrypted Blowfish block, to illegitimately gain experience points quickly.

Cipher-block chaining (CBC)

CBC mode of operation was invented by IBM in 1976. In the cipher-block chaining (CBC) mode, each block of plaintext is XORed with the previous ciphertext block before being encrypted. This way, each ciphertext block is dependent on all plaintext blocks processed up to that point. Also, to make each message unique, an initialization vector must be used in the first block.

If the first block has index 1, the mathematical formula for CBC encryption is

$C_{i}=E_{K}(P_{i}\oplus C_{i-1}),C_{0}=IV$

while the mathematical formula for CBC decryption is

$P_{i}=D_{K}(C_{i})\oplus C_{i-1},C_{0}=IV$

CBC has been the most commonly used mode of operation. Its main drawbacks are that encryption is sequential (i.e., it cannot be parallelized), and that the message must be padded to a multiple of the cipher block size. One way to handle this last issue is through the method known as ciphertext stealing.

Note that a one-bit change in a plaintext affects all following ciphertext blocks. A plaintext can be recovered from just two adjacent blocks of ciphertext. As a consequence, decryption can be parallelized, and a one-bit change to the ciphertext causes complete corruption of the corresponding block of plaintext, and inverts the corresponding bit in the following block of plaintext.

Propagating cipher-block chaining (PCBC)

The propagating cipher-block chaining or plaintext cipher-block chaining mode was designed to cause small changes in the ciphertext to propagate indefinitely when decrypting, as well as when encrypting.

Encryption and decryption algorithms are as follows:

$C_{i}=E_{K}(P_{i}\oplus P_{i-1}\oplus C_{i-1}),P_{0}\oplus C_{0}=IV$

$P_{i}=D_{K}(C_{i})\oplus P_{i-1}\oplus C_{i-1},P_{0}\oplus C_{0}=IV$

PCBC is used in Kerberos v4 and WASTE, most notably, but otherwise is not common. On a message encrypted in PCBC mode, if two adjacent ciphertext blocks are exchanged, this does not affect the decryption of subsequent blocks. For this reason, PCBC is not used in Kerberos v5.

Cipher feedback (CFB)

The cipher feedback (CFB) mode, a close relative of CBC, makes a block cipher into a self-synchronizing stream cipher. Operation is very similar; in particular, CFB decryption is almost identical to CBC encryption performed in reverse:

$C_{i}=E_{K}(C_{i-1})\oplus P_{i}$

$P_{i}=E_{K}(C_{i-1})\oplus C_{i}$

$C_{0}=\ {\mbox{IV}}$

This simplest way of using CFB described above is not any more self-synchronizing than other cipher modes like CBC. If a whole blocksize of ciphertext is lost both CBC and CFB will synchronize, but losing only a single byte or bit will permanently throw off decryption. To be able to synchronize after the loss of only a single byte or bit, a single byte or bit must be encrypted at a time. CFB can be used this way when combined with a shift register as the input for the block cipher.

To use CFB to make a self-synchronizing stream cipher that will synchronize for any multiple of x bits lost, start by initializing a shift register the size of the block size with the initialization vector. This is encrypted with the block cipher, and the highest x bits of the result are XOR'ed with x bits of the plaintext to produce x bits of ciphertext. These x bits of output are shifted into the shift register, and the process repeats with the next x bits of plaintext. Decryption is similar, start with the initialization vector, encrypt, and XOR the high bits of the result with x bits of the ciphertext to produce x bits of plaintext. Then shift the x bits of the ciphertext into the shift register.

In notation, where S_i is the ith state of the shift register, a << x is a shifted up x bits, head(a, x) is the x highest bits of a and n is number of bits of IV:

$C_{i}={\mbox{head}}(E_{K}(S_{i-1}),x)\oplus P_{i}$

$P_{i}={\mbox{head}}(E_{K}(S_{i-1}),x)\oplus C_{i}$

$S_{i}=\ ((S_{i-1}<<x)+C_{i}){\mbox{ mod }}2^{n}$

$S_{0}=\ {\mbox{IV}}$

If x bits are lost from the ciphertext, the cipher will output incorrect plaintext until the shift register once again equals a state it held while encrypting, at which point the cipher has resynchronized. This will result in at most one blocksize of output being garbled.

Like CBC mode, changes in the plaintext propagate forever in the ciphertext, and encryption cannot be parallelized. Also like CBC, decryption can be parallelized. When decrypting, a one-bit change in the ciphertext affects two plaintext blocks: a one-bit change in the corresponding plaintext block, and complete corruption of the following plaintext block. Later plaintext blocks are decrypted normally.

CFB shares two advantages over CBC mode with the stream cipher modes OFB and CTR: the block cipher is only ever used in the encrypting direction, and the message does not need to be padded to a multiple of the cipher block size (though ciphertext stealing can also be used to make padding unnecessary).

Output feedback (OFB)

The output feedback (OFB) mode makes a block cipher into a synchronous stream cipher. It generates keystream blocks, which are then XORed with the plaintext blocks to get the ciphertext. Just as with other stream ciphers, flipping a bit in the ciphertext produces a flipped bit in the plaintext at the same location. This property allows many error correcting codes to function normally even when applied before encryption.

Because of the symmetry of the XOR operation, encryption and decryption are exactly the same:

$C_{i}=P_{i}\oplus O_{i}$

$P_{i}=C_{i}\oplus O_{i}$

$O_{i}=\ E_{K}(O_{i-1})$

$O_{0}=\ {\mbox{IV}}$

Each output feedback block cipher operation depends on all previous ones, and so cannot be performed in parallel. However, because the plaintext or ciphertext is only used for the final XOR, the block cipher operations may be performed in advance, allowing the final step to be performed in parallel once the plaintext or ciphertext is available.

It is possible to obtain an OFB mode keystream by using CBC mode with a constant string of zeroes as input. This can be useful, because it allows the usage of fast hardware implementations of CBC mode for OFB mode encryption.

Using OFB mode with a partial block as feedback like CFB mode reduces the average cycle length by a factor of $2^{32}$ or more. A mathematical model proposed by Davies and Parkin and substantiated by experimental results showed that only with full feedback an average cycle length near to the obtainable maximum can be achieved. For this reason, support for truncated feedback was removed from the specification of OFB.

Counter (CTR)

Note: CTR mode (CM) is also known as Integer Counter Mode (ICM) and Segmented Integer Counter (SIC) mode

Like OFB, counter mode turns a block cipher into a stream cipher. It generates the next keystream block by encrypting successive values of a "counter". The counter can be any function which produces a sequence which is guaranteed not to repeat for a long time, although an actual counter is the simplest and most popular. The usage of a simple deterministic input function used to be controversial; critics argued that "deliberately exposing a cryptosystem to a known systematic input represents an unnecessary risk." By now, CTR mode is widely accepted, and problems resulting from the input function are recognized as a weakness of the underlying block cipher instead of the CTR mode. Nevertheless, there are specialized attacks like a Hardware Fault Attack that is based on the usage of a simple counter function as input.

CTR mode has similar characteristics to OFB, but also allows a random access property during decryption. CTR mode is well suited to operation on a multi-processor machine where blocks can be encrypted in parallel.

Note that the nonce in this graph is the same thing as the initialization vector (IV) in the other graphs. The IV/nonce and the counter can be concatenated, added, or XORed together to produce the actual unique counter block for encryption.

Error propagation

Before the wide spread use of message authentication codes and authenticated encryption, it was common to discuss the "error propagation" properties as a selection criterion for a mode of operation. It might be observed, for example, that a one-block error in the transmitted ciphertext would result in a one-block error in the reconstructed plaintext for ECB mode encryption, while in CBC mode such an error would affect two blocks.

Some felt that such resilience was desirable in the face of random errors (eg, line noise), while others argued that error correcting increased the scope for attackers to maliciously tamper with a message.

However, when proper integrity protection is used, such an error will result (with high probability) in the entire message being rejected. If resistance to random error is desirable, error-correcting codes should be applied to the ciphertext before transmission.

Authenticated Encryption

Main article: Authenticated encryption

A number of modes of operation have been designed to combine confidentiality and authentication in a single cryptographic primitive. Examples of such modes are XCBC, IACBC, IAPM, OCB, EAX, CWC, CCM, and GCM. Authenticated encryption modes are classified as single pass modes or double pass modes. Unfortunately for the cryptographic user community, many of the single pass authenticated encryption algorithms (such as OCB mode) are patent encumbered.

In addition, some modes also allow for the authentication of unencrypted associated data, and these are called AEAD (Authenticated-Encryption with Associated-Data) schemes. For example, EAX mode is a double pass AEAD scheme while OCB mode is single pass.

Other modes and other cryptographic primitives

Many more modes of operation for block ciphers have been suggested. Some have been accepted, fully described (even standardized), and are in use. Others have been found insecure, and should never be used. Still others don't categorize as confidentiality, authenticity, or authenticated encryption - for example Key Feedback Mode (KFM) and AES-hash.

NIST maintains a list of proposed modes for block ciphers at Modes Development.

Disk encryption often uses special purpose modes specifically designed for the application. Tweakable narrow-block encryption modes (LRW, XEX, and XTS) and wide-block encryption modes (CMC and EME) are designed to securely encrypt sectors of a disk. (See disk encryption theory)

Block ciphers can also be used in other cryptographic protocols. They are generally used in modes of operation similar to the block modes described here. As with all protocols, to be cryptographically secure, care must be taken to build them correctly.

There are several schemes which use a block cipher to build a cryptographic hash function. See one-way compression function for descriptions of several such methods.

Cryptographically secure pseudorandom number generators (CSPRNGs) can also be built using block ciphers.

Message authentication codes (MACs) are often built from block ciphers. CBC-MAC, OMAC and PMAC are examples.

Authenticated encryption also uses block ciphers as components. It means to both encrypt and MAC at the same time. That is to both provide confidentiality and authentication. IAPM, CCM, CWC, EAX, GCM and OCB are such authenticated encryption modes.

See also

• Disk encryption
• Message authentication code
• Authenticated encryption
• One-way compression function