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Galois/Counter Mode

Galois/Counter Mode

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Galois/Counter Mode is a mode 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...

 for symmetric key cryptographic 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 that has been widely adopted because of its efficiency and performance. GCM throughput rates for state of the art, high speed communication channels can be achieved with reasonable hardware resources .
It is an 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...

 algorithm designed to provide both data authenticity (integrity) and confidentiality. GCM mode is defined for block ciphers with a block size of 128 bits. GMAC is an authentication-only variant of the GCM which can be used as an incremental message authentication code. Both GCM and GMAC can accept initialization vectors of arbitrary length.

Different block cipher modes of operation can have significantly different performance and efficiency characteristics, even when used with the same block cipher. GCM can take full advantage of parallel processing, and an implementation can make efficient use of an instruction pipeline
Instruction pipeline
An instruction pipeline is a technique used in the design of computers and other digital electronic devices to increase their instruction throughput ....

 or a hadware pipeline. In contrast, the Cipher block chaining (CBC) mode of operation incurs significant pipeline stalls that hamper its efficiency and performance.

Encryption and authentication

As the name suggests, GCM mode combines the well-known counter mode of encryption with the new Galois mode of authentication. The key feature is that the Galois field multiplication used for authentication can be easily computed in parallel thus permitting higher throughput than the authentication algorithms that use chaining modes, like CBC. The GF(2128) field used is defined by the polynomial

The GHASH function is defined by

where H is a string of 128 zeros encrypted using the 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...

, A is data which is only authenticated (not encrypted), C is the 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...

, m is the number of 128 bit blocks in A, n is the number of 128 bit blocks in C (the final blocks of A and C need not be exactly 128 bits), and the variable Xi for i = 0, ..., m + n + 1 is defined as

where v is the bit length of the final block of A, u is the bit length of the final block of C, and denotes concatenation of bit strings.

GCM mode was designed by John Viega and David A. McGrew as an improvement to Carter–Wegman Counter CWC mode
CWC mode
In cryptography, CWC Mode is an AEAD block cipher mode of operation that provides both encryption and built-in message integrity, similar to CCM and OCB modes. Designed by Tadayoshi Kohno, John Viega and Doug Whiting, NIST is CWC mode for standardization...


On November 26, 2007 NIST announced the release of NIST Special Publication 800-38D Recommendation for Block Cipher Modes of Operation: Galois/Counter Mode (GCM) and GMAC making GCM and GMAC official standards.


GCM mode is used in the IEEE 802.1AE
IEEE 802.1AE
802.1AE is the IEEE MAC Security standard which defines connectionless data confidentiality and integrity for media access independent protocols...

 (MACsec) Ethernet security, ANSI (INCITS
The InterNational Committee for Information Technology Standards, or INCITS , is an ANSI-accredited forum of IT developers. It was formerly known as the X3 and NCITS....

) Fibre Channel
Fibre Channel
Fibre Channel, or FC, is a gigabit-speed network technology primarily used for storage networking. Fibre Channel is standardized in the T11 Technical Committee of the InterNational Committee for Information Technology Standards , an American National Standards Institute –accredited standards...

 Security Protocols (FC-SP), IEEE P1619
IEEE P1619
IEEE P1619 is an Institute of Electrical and Electronics Engineers standardization project for encryption of stored data, but more generically refers to the work of the IEEE P1619 Security in Storage Working Group , which includes a family of standards for protection of stored data and for the...

.1 tape storage, IETF
Internet Engineering Task Force
The Internet Engineering Task Force develops and promotes Internet standards, cooperating closely with the W3C and ISO/IEC standards bodies and dealing in particular with standards of the TCP/IP and Internet protocol suite...

Internet Protocol Security is a protocol suite for securing Internet Protocol communications by authenticating and encrypting each IP packet of a communication session...

 standards, SSH
- In science and technology :* Saffir–Simpson Hurricane Scale* Sea surface height, the topography of the ocean surface* Secure Shell, a network protocol for remote administration of Unix computers* Social sciences and humanities, a broad field of research...

  and TLS/SSL
Transport Layer Security
Transport Layer Security and its predecessor, Secure Sockets Layer , are cryptographic protocols that provide communication security over the Internet...

 . AES-GCM is included into the NSA Suite B Cryptography.


GCM is ideal for protecting packetized data, because it has minimum latency and minimum operation overhead.

GCM requires one block cipher operation and one 128-bit multiplication in the Galois field per each block (128 bit) of encrypted and authenticated data. The block cipher operations are easily pipelined or parallelized; the multiplication operations are easily pipelined, and can be parallelized with some modest effort (either by parallelizing the actual operation, or by adapting Horner's method as described in the original NIST submission, or both).

Intel has added the PCLMULQDQ instruction, highlighting its use for GCM http://software.intel.com/en-us/articles/intel-carry-less-multiplication-instruction-and-its-usage-for-computing-the-gcm-mode. This instruction enables fast multiplication over GF(2^n), and can be used with any field representation.

Impressive performance results have been published for GCM on a number of platforms. Käsper and Schwabe described a "Faster and Timing-Attack Resistant AES-GCM"
that achieves 10.68 cycles per byte AES-GCM authenticated encryption on 64-bit Intel processors. Dai et al report 3.5 cycles per byte for the same algorithm when using Intel's AES-NI and PCLMULQDQ instructions .

When both authentication and encryption need to be performed on a message, a software implementation can achieve speed gains by overlapping the execution of those operations. Performance is increased by exploiting instruction level parallelism by interleaving operations. This process is called function stitching , and while in principle it can be applied to any combination of cryptographic algorithms, GCM is especially suitable. Manley and Gregg show the ease of optimizing when using function-stitching with GCM, and present a program generator that takes an annotated C version a cryptographic algorithm and generates code that runs well on the target processor.


According to the authors' statement, GCM is unencumbered by patents.


GCM has been proven secure in the concrete security model . It is secure when it is used with a block cipher mode of operation that is indistinguishable from a random permutation; however security depends on choosing a unique initialization vector
Initialization vector
In cryptography, an initialization vector is a fixed-size input to a cryptographic primitive that is typically required to be random or pseudorandom...

 for every encryption performed with the same key (see stream cipher attack
Stream cipher attack
Stream ciphers, where plaintext bits are combined with a cipher bit stream by an exclusive-or operation , can be very secure if used properly. However they are vulnerable to attack if certain precautions are not followed:*keys must never be used twice...

). NIST Special Publication 800-38D includes guidelines for initialization vector selection.

The authentication strength depends on the length of the authentication tag, as with all symmetric message authentication codes. However, the use of shorter authentication tags with GCM is discouraged. The bit-length of the tag, denoted t, is a security parameter. In general, t may be any one of the following five values: 128, 120, 112, 104, or 96. For certain applications, t may be 64 or 32, but the use of these two tag lengths constrains the length of the input data and the lifetime of the key. Appendix C in NIST SP 800-38D provides guidance for these constraints (for example, if t = 32 and the maximal packet size is 210 bytes, then the authentication decryption function should be invoked no more than 211 times; if t = 64 and the maximal packet size is 215 bytes, then the authentication decryption function should be invoked no more than 232 times).

As with any message authentication code, if the adversary chooses a t-bit tag at random, it is expected to be correct for given data with probability 2t. With GCM, however, an adversary can choose tags that increase this probability, proportional to the total length of the ciphertext and additional authenticated data (AAD). Consequently, GCM is not well-suited for use with very short tag lengths or very long messages.

Ferguson and Saarinen independently described how an attacker can perform optimal attacks against GCM authentication, which meet the lower bound on its security.
Ferguson showed that, if n denotes the total number of blocks in the encoding (the input to the GHASH function), then there is a method of constructing a targeted ciphertext forgery that is expected to succeed with a probability of approximately n2t. If the tag length t is shorter than 128, then each successful forgery in this attack increases the probability that subsequent targeted forgeries will succeed, and leaks information about the hash subkey, H. Eventually, H may be compromised entirely and the authentication assurance is completely lost.

Independent of this attack, an adversary may attempt to systematically guess many different tags for a given input to authenticated decryption, and thereby increase the probability that one (or more) of them, eventually, will be accepted as valid. For this reason, the system or protocol that implements GCM should monitor and, if necessary, limit the number of unsuccessful verification attempts for each key.

Saarinen described GCM weak key
Weak key
In cryptography, a weak key is a key, which, used with a specific cipher, makes the cipher behave in some undesirable way. Weak keys usually represent a very small fraction of the overall keyspace, which usually means that, if one generates a random key to encrypt a message, weak keys are very...

s This work gives some valuable insights into how polynomial hash based authentication works. More precisely, this work describes a particular way of forging a GCM message, given a valid GCM message, which works with probability of about n/2^128 for messages that are n*128 bits long. However, this work does not show a more effective attack than was previously known; the success probability in Observation 1 of this paper matches that of Lemma 2 from the INDOCRYPT 2004 analysis (setting w=128 and l=n*128). Saarinen also described a GCM variant Sophie Germain Counter Mode
Sophie Germain Counter Mode
A new mode called Sophie Germain Counter Mode has been proposed as a variant of the Galois/Counter Mode Galois/Counter Mode of operation for block ciphers...

(SGCM), continuing the GCM tradition of including a mathematician in the name of the mode.

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