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CBC-MAC

CBC-MAC, or Cipher Block Chaining Message Authentication Code, is a mode of operation for block ciphers that generates a fixed-length message authentication code (MAC) to verify the integrity and authenticity of a message by processing it in chained blocks.^[1] It applies the block cipher iteratively to each message block, XORing the input with the previous ciphertext block (starting from an all-zero initialization vector), and outputs a truncated portion of the final ciphertext block as the tag.^[2] The algorithm authenticates an m-block message x = x_1 \dots x_m using a block cipher F with key k, computing y_0 = 0^[n](/page/N+), y_i = F_k(y_{i-1} \oplus x_i) for i = 1 to m, and deriving the s-bit tag from y_m (where n is the block size and s \leq n).^[2] This chaining ensures that any alteration to the message propagates through the computation, making the tag sensitive to changes. CBC-MAC was originally designed for fixed-length messages and has been widely adopted in financial systems, such as banking protocols using the Data Encryption Standard (DES).^[2] Standardized internationally in ISO/IEC 9797-1 since 1999, with the second edition in 2011 and an amendment in 2023, CBC-MAC serves as the basis for the first mechanism in the standard, known explicitly as the CBC mode for MAC generation.^[3]^[4] It was formerly specified in the now-withdrawn ANSI X9.9 (1986) for DES-based implementations in the United States, though modern uses often pair it with stronger ciphers like AES.^[2] Its simplicity and efficiency—requiring only m block cipher invocations—contributed to its popularity before more advanced variants emerged.^[1] Security analyses, notably from 2000, prove that if the underlying block cipher is a pseudorandom permutation (PRP), then CBC-MAC functions as a strongly pseudorandom function (PRF) and secure MAC against existential forgery under chosen-message attacks, with an advantage bound of approximately q^2 m^2 / 2^{n-1} for q queries (birthday-bound security).^[2] However, CBC-MAC is insecure for variable-length messages without proper padding, as attackers can exploit length-extension collisions to forge tags—e.g., two messages of lengths differing by a block can yield the same tag if crafted adversarially.^[5] To address this, NIST recommends variants like CMAC (in SP 800-38B), which modifies CBC-MAC with subkeys for arbitrary lengths while maintaining efficiency.^[5] CBC-MAC also forms the authentication component in combined modes like CCM (Counter with CBC-MAC) for authenticated encryption.

Overview

Definition and Purpose

A message authentication code (MAC) is a symmetric-key cryptographic primitive that takes a variable-length message and a secret key as inputs to produce a fixed-length output tag, which is typically much shorter than the message itself and used to verify both the integrity and authenticity of the transmitted data. Unlike unkeyed cryptographic hash functions, which provide only collision resistance for data integrity without authentication, a MAC requires the shared secret key for both tag generation and verification, ensuring that only parties possessing the key can generate valid tags or confirm the message's origin. The CBC-MAC, or Cipher Block Chaining Message Authentication Code, is a specific type of MAC constructed from a symmetric block cipher, operating as a deterministic function that processes the message under a secret key to yield a fixed-length authentication tag equal in size to the block cipher's output.^[6] Its primary purpose is to provide efficient message authentication in symmetric cryptography settings, leveraging existing block ciphers to assure data integrity against tampering and authenticity against forgery by unauthorized parties, without relying on separate hash functions.^[7] This makes CBC-MAC particularly suitable for resource-constrained environments. Developed in the 1980s as an efficient authentication mechanism utilizing prevalent block ciphers like DES, CBC-MAC was formalized in international standards to enable secure data protection in early cryptographic applications, including financial and telecommunications systems.^[8] By integrating seamlessly with block cipher primitives, it offered a practical alternative to more computationally intensive methods, promoting widespread adoption for verifying message legitimacy in symmetric-key protocols.^[9]

Relation to Block Ciphers and CBC Mode

CBC-MAC is constructed using a symmetric-key block cipher, which operates on fixed-size input blocks, typically 64 or 128 bits, to provide pseudorandom permutations under a secret key.^[2] For instance, the Advanced Encryption Standard (AES) serves as a common underlying block cipher for CBC-MAC implementations, employing 128-bit blocks regardless of the key length chosen (128, 192, or 256 bits). The block cipher must be secure against chosen-plaintext attacks to ensure the overall integrity of the authentication mechanism, as weaknesses in the primitive could compromise the MAC's security.^[2] The core of CBC-MAC draws from the Cipher Block Chaining (CBC) mode of operation, a standard technique for processing sequential data blocks with a block cipher. In CBC mode, encryption begins with an initialization vector (IV) that is XORed with the first plaintext block before encryption; subsequent blocks are each XORed with the immediately preceding ciphertext block prior to encryption, creating a dependency chain that diffuses changes across the output.^[10] This chaining prevents identical plaintext blocks from producing identical ciphertext blocks, enhancing security over simpler modes like Electronic Codebook (ECB). Decryption reverses the process by applying the inverse cipher and XORing with the prior ciphertext or IV.^[10] In adapting CBC mode for CBC-MAC, the same secret key is used for all block encryptions throughout the message processing, without requiring multiple keys or key derivation. Unlike CBC encryption, CBC-MAC initializes the chaining with a fixed all-zero block instead of a variable IV, and it assumes messages of exact multiples of the block size with no padding applied. The construction discards all intermediate ciphertext values, retaining only the final chained block as the authentication tag, which serves to verify message integrity rather than enable plaintext recovery. This shift in purpose—from confidentiality in CBC encryption to authentication in CBC-MAC—eliminates the need for an IV's unpredictability while leveraging the chaining for diffusion properties essential to resisting forgery.^[2]

Algorithm Construction

Initialization Vector and Key Setup

The CBC-MAC algorithm requires a secret key K that matches the key length supported by the underlying block cipher, such as 128 bits for AES-128.^[11] This key must be randomly generated with uniform distribution and maintained in strict secrecy to ensure the security of the authentication process.^[11] Unlike the CBC encryption mode, which employs a random initialization vector (IV) to achieve semantic security, CBC-MAC uses a fixed IV consisting of an all-zero string of length equal to the block size n (denoted $0^n) to produce a deterministic output for a given message and key.^[11] This choice ensures that the same message always yields the same tag, which is essential for message authentication verification.^[11] In the setup phase, the secret key K is loaded into the block cipher, and the initial chaining value H_0 is set to the zero vector $0^n.^[11] For example, when using a 64-bit block cipher like DES, the IV is $0^{64}.

Message Processing Steps

The input message M, assumed to be of fixed length that is a positive multiple of the block cipher's block size n, is partitioned into m sequential blocks M_1, M_2, \dots, M_m, each consisting of n bits.^[12] The processing initializes a chaining value C_0 as the all-zero block of n bits, serving as the zero initialization vector.^[12] For each block index i from 1 to m, the algorithm iteratively computes the next chaining value according to the formula

C_i = E_K(M_i \oplus C_{i-1}),

where E_K denotes the block cipher's encryption function under the secret key K, and \oplus represents the bitwise exclusive-or operation.^[12] This operation applies the block cipher to the XOR of the current message block and the previous chaining value.^[12] Through this block-by-block chaining, each intermediate C_i incorporates information from all prior blocks M_1 through M_i, establishing a cumulative dependency that propagates across the entire message and diffuses any alterations in early blocks to subsequent computations.^[12]

Final Tag Computation

In the CBC-MAC construction, after processing all message blocks through the chaining mechanism, the final chaining value C_m directly serves as the authentication tag T. Specifically, for an m-block message divided into blocks m_1, m_2, \dots, m_m, the computation begins with an initialization vector of zero, and each subsequent chaining value is derived as C_i = E_K(C_{i-1} \oplus m_i) for i = 1 to m, where E_K is the underlying block cipher under key K and C_0 = 0^n. Upon completion, T = C_m, providing a fixed-output value that encapsulates the entire message authentication.^[13] The length of the tag T matches the block size of the underlying cipher, ensuring it inherits the full output length for security purposes in the basic scheme. For instance, when using AES as the block cipher, the tag is 128 bits long. In practical implementations, the tag may be truncated to a shorter length s \leq n bits to balance security and efficiency, though the full block output is used in the core computation before any truncation.^[13] To verify the tag, the recipient independently recomputes the CBC-MAC value T' from the received message and shared key K, then checks whether T' = T; equality confirms message integrity and authenticity. Unlike certain other message authentication codes that apply a final hash function or additional encryption step to the chaining output, CBC-MAC employs no further processing beyond outputting C_m as the tag, maintaining its simplicity as a direct derivative of the block cipher chaining.^[13]

Security for Fixed-Length Messages

Provable Security Bounds

The CBC-MAC for fixed-length messages is proven to be a pseudorandom function (PRF) assuming the underlying block cipher behaves as a pseudorandom permutation (PRP).^[14] This security model captures the indistinguishability of CBC-MAC outputs from a truly random function, even against adaptive adversaries querying the MAC on distinct messages of the same length.^[14] The distinguishing advantage of an adversary making q queries is at most approximately \frac{q^2 m^2}{2^{n-1}}, where n denotes the block size in bits and m is the fixed number of blocks in the messages.^[2] This bound arises from the birthday paradox applied to intermediate chaining values, combined with the security of the underlying PRP, ensuring that collisions in the internal state—which could reveal structure—are unlikely until roughly $2^{n/2} / m queries.^[2] Earlier analyses provided guarantees of this form, but the refined bound from Black, Halevi, Krawczyk, Krovetz, and Rogaway (2002) tightens the constants to approximately q^2 m^2 / 2^n for practical fixed-length scenarios, emphasizing scalability for moderate query volumes.^[14] As a consequence of its PRF security, CBC-MAC resists existential forgery under chosen-message attacks when restricted to messages of identical, known length.^[13] The forgery advantage remains bounded by the PRF distinguishing advantage, typically negligible provided messages are distinct and the length is fixed in advance, as this prevents adversaries from exploiting length-based extensions to construct valid forgeries.^[13] This property holds under the same PRP assumption on the block cipher, with the core theorem tracing to foundational work by Rogaway (2001) and refined in subsequent analyses.^[13]

Distinguishing Attacks

Distinguishing attacks on CBC-MAC for fixed-length messages exploit the structure of the algorithm to differentiate it from a truly random function, revealing the limits of its pseudorandomness. A key example is a birthday-bound attack that leverages the permutation property of the underlying block cipher. The adversary constructs q \approx 2^{n/2} fixed-length messages, where n is the block size, that differ only in their first block while keeping the remaining blocks identical. In CBC-MAC, the chaining value after processing the first block is F_k(m_1 \oplus 0), and since F_k is a pseudorandom permutation, these chaining values are distinct for distinct first blocks. The identical subsequent blocks then produce distinct inputs to the final F_k, resulting in distinct tags with probability 1—no collisions occur.^[13] In contrast, under a random function oracle, the probability of at least one tag collision among q outputs is approximately $1 - e^{-q(q-1)/2^{n+1}} \approx 0.63 for q \approx 1.18 \times 2^{n/2}. The adversary declares the oracle CBC-MAC if no collision is observed and random otherwise, succeeding with constant advantage.^[13] This attack requires O(2^{n/2}) queries and time, demonstrating that CBC-MAC's security as a fixed-input-length pseudorandom function (FIL-PRF) is bounded by the birthday paradox, with distinguishing advantage \Theta(q^2 m^2 / 2^n).^[13] The bound is tight, as matching upper bounds are proven under the assumption that the block cipher is a secure PRF or PRP.^[13] While CBC-MAC achieves provable PRF security for fixed-length messages up to this birthday limit, it fails as a variable-input-length PRF (VIL-PRF) without modifications, as simple relations between tags for messages of different lengths allow distinguishing with constant probability using just two queries.^[13] For instance, querying the all-zero single-block message yields tag t = F_k(0); the two-block message consisting of the all-zero block followed by t then yields the same tag t, a relation unlikely under a random function.^[13] This vulnerability also enables existential forgeries under chosen-message attacks when lengths vary.^[13] To mitigate these limitations, CBC-MAC should be restricted to fixed-length messages in applications requiring FIL-PRF security, or extended with length-prepending or other modifications (such as XCBC or TMAC) to achieve VIL-MAC or VIL-PRF properties while preserving security bounds close to the fixed-length case.^[13]

Handling Variable-Length Messages

Length Prepending Method

The length prepending method addresses the insecurity of basic CBC-MAC for variable-length messages by incorporating an explicit encoding of the message length as the initial block in the input to the algorithm. This ensures that messages of different lengths are processed with distinct starting inputs, thereby preventing forgery attacks that exploit prefix relationships between messages. The approach transforms the input such that no authenticated message can serve as a prefix for another, restoring provable security under standard assumptions for a pseudorandom function family.^[15] In the processing steps, the algorithm begins with an initialization vector C_0 set to the zero block. The first block is then formed by encoding the original message length L (typically in bits) as a fixed-width integer representation within a full block, using big-endian byte order and padding with leading zeros if necessary to fill the block size. For instance, with a 64-bit block size and a message of 100 bits, the length 100 is encoded as the 64-bit binary value $0x0000000000000064 (big-endian). The subsequent blocks consist of the original message, which is padded to a multiple of the block size using ISO 9797-1 padding method 2 (appending a single '1' bit followed by zeros). The chaining then proceeds as in fixed-length CBC-MAC: each block is XORed with the previous ciphertext block and encrypted under the shared key to produce the next ciphertext block, culminating in the final block as the authentication tag.^[15] This method restores PRF-like security for distinct-length messages, with the adversary's advantage bounded by approximately \frac{m^2 q^2}{2^n}, where m is the maximum number of blocks in any query, q is the number of queries, and n is the block size in bits; this bound follows from adapting proofs of CBC-MAC unpredictability to the prepended form, assuming the underlying block cipher is a strong pseudorandom permutation. By including the length upfront, it specifically thwarts length-extension attacks, where an adversary might otherwise append data to a known message-tag pair without altering the tag, as any extension would mismatch the prepended length and invalidate verification. The fixed-width, big-endian encoding avoids ambiguity in length interpretation across systems, ensuring consistent processing regardless of the message's bit length up to the block cipher's capacity.^[15]

Encrypt-Last-Block Method

The encrypt-last-block method provides an extension to CBC-MAC for handling variable-length messages by following the standard CBC processing for all blocks and then encrypting the final chained output using a second key. The message is divided into blocks, with the first block XORed with an initialization vector (typically zero), and each subsequent block XORed with the previous ciphertext before encryption under the key K_1. The final chained value is then encrypted using a second key K_2.^[16] In standards such as ISO/IEC 9797-1 (MAC Algorithm 3), a specific variant employs this approach with triple DES, where the CBC chaining uses single DES with the first subkey for intermediate blocks, but the final block input (XORed with the previous ciphertext) undergoes a full triple DES encryption using both subkeys.^[17] This method offers weaker security compared to length-prepending techniques, as it remains vulnerable to forgery attacks when two messages of different lengths produce the same intermediate CBC state before the last block, allowing length collisions to enable existential forgeries with probability approaching 1 after $2^{n/2} queries, where n is the block size.^[2]^[16] Despite these limitations, the encrypt-last-block approach is more efficient for streaming applications, requiring only one additional block cipher invocation beyond the message length in blocks and enabling online processing without upfront knowledge of the full message length.^[16] It forms the basis for the EMAC (Encrypt-and-MAC) construction, which uses two independent keys to compute the CBC chain under K_1 and then encrypts the resulting tag under K_2, supporting variable-length messages padded to full blocks.^[16]^[18] Contemporary analyses critique the method as less suitable for general-purpose use due to its reliance on careful key derivation and padding to avoid length-extension vulnerabilities, favoring more robust variants like CMAC for broader adoption.^[16]^[18]

Attacks on Incorrect Implementations

Shared Key with Encryption

One common misuse of CBC-MAC occurs when the same cryptographic key is shared between CBC mode encryption for confidentiality and CBC-MAC for authentication, particularly in an encrypt-then-MAC construction where the MAC is computed over the ciphertext. This key reuse enables an attacker who observes a valid ciphertext and its accompanying MAC tag to perform forgeries by crafting modified ciphertexts that verify under the MAC but decrypt to attacker-chosen plaintexts. The vulnerability arises because the shared key allows the attacker to exploit the structural similarities in the chaining dependencies of both modes, effectively linking the encryption process to the authentication computation in a predictable manner.^[19] In the specific attack, suppose a message M = M_1 || M_2 || \dots || M_n is encrypted under key K using CBC mode with initialization vector IV^{(0)} to produce ciphertext blocks C_0^{(0)} || C_1^{(0)} || \dots || C_{n-1}^{(0)}, where C_0^{(0)} = IV^{(0)} and C_i^{(0)} = E_K(M_{i+1} \oplus C_{i-1}^{(0)}) for i \geq 1, with E_K denoting the block cipher encryption under K. The corresponding plaintext blocks are P_1^{(0)} || P_2^{(0)} || \dots || P_n^{(0)}, recovered via decryption as P_{i+1}^{(0)} = D_K(C_i^{(0)} \oplus C_{i-1}^{(0)}), where D_K is the decryption function. The valid MAC tag T^{(0)} is then computed as the final chaining value of CBC-MAC over the ciphertext blocks C_0^{(0)} || C_1^{(0)} || \dots || C_{n-1}^{(0)} under the same key K, starting from an all-zero IV: S_0 = 0, S_i = E_K(C_i^{(0)} \oplus S_{i-1}), and T^{(0)} = S_{n-1}. An attacker can now forge a new ciphertext by setting IV' = 0 and constructing blocks C_0' = C_0^{(0)}, C_1' = C_1^{(0)}, ..., up to a manipulation point, such as altering a later block like C_{n-2}' = C_{n-2}^{(0)} \oplus P_n^{(0)} \oplus P_n' and keeping C_{n-1}' = C_{n-1}^{(0)}, where P_n' is the attacker's chosen plaintext block. Due to the shared key, the CBC-MAC computation over this forged ciphertext C' yields the same tag T^{(0)}, as the chaining values align predictably with the original encryption dependencies up to the manipulation. Upon decryption of C', the initial blocks recover the original structure, but the altered block produces the desired P_n', enabling an existential forgery where the attacker controls part of the decrypted message while the MAC verifies successfully. This attack succeeds with probability 1 after observing just one valid (ciphertext, tag) pair.^[19] To illustrate with DES as the underlying block cipher (a 64-bit block cipher historically used in both modes), consider a simplified two-block message M = M_1 || M_2 encrypted under a shared 56-bit DES key K with IV^{(0)} = 0. The ciphertext is C_1 = DES_K(M_1), C_2 = DES_K(M_2 \oplus C_1), and the MAC tag T = DES_K(C_2 \oplus DES_K(C_1)). An attacker observes C_1 || C_2 || T and forges a new two-block ciphertext C_1' = C_1, C_2' = C_2 \oplus \Delta, where \Delta is chosen such that decryption yields a modified M_2' = M_2 \oplus \Delta. The MAC over C_1' || C_2' computes S_1' = DES_K(C_1), T' = DES_K(C_2' \oplus S_1') = DES_K((C_2 \oplus \Delta) \oplus DES_K(C_1)). By selecting \Delta to compensate for the chaining (leveraging the known structure), T' = T, allowing verification while altering the decrypted output. This demonstrates how DES's small block size exacerbates predictability in the attack, though the issue is structural and applies to any secure block cipher under key reuse.^[19] The primary mitigation is to use distinct keys for CBC encryption and CBC-MAC: generate a separate authentication key K_{MAC} independent of the encryption key K_{enc}, or derive K_{MAC} from K_{enc} using an approved key derivation function (e.g., HKDF) to ensure cryptographic separation. NIST guidelines explicitly recommend that a single key be used for only one cryptographic function, such as encryption or integrity protection via MAC, to prevent such cross-mode vulnerabilities and limit the impact of key compromise. Authenticated encryption modes like GCM or CCM, which integrate both functions under a single key in a provably secure manner, may be considered as alternatives to separate CBC-based constructions.^[20]

Variable Initialization Vector

In CBC-MAC, the standard construction mandates a fixed initialization vector (IV) of all zeros to ensure security for fixed-length messages.^[2] However, a common misuse arises when implementers treat CBC-MAC analogously to CBC-mode encryption, incorporating a variable or message-dependent IV in an attempt to enhance security or reuse components from encryption protocols.^[21] This error, observed in some early implementations that assumed IV practices from encryption could be directly applied, compromises the scheme's core properties.^[22] The vulnerability stems from the CBC-MAC's first processing step, where the IV is XORed with the initial message block before encryption. If the IV is variable and controllable by an attacker—often because it must be transmitted alongside the message and tag for verification—the attacker can exploit this to achieve tag malleability. Specifically, upon obtaining a valid tag T for a message M under IV, the attacker can forge a new tag T' = T \oplus [\delta](/page/Delta) for a modified message M' (with its first block altered by \delta) by simply setting a new IV' = IV \oplus [\delta](/page/Delta). This directly alters the effective first block input to the chaining without invalidating the tag, as the subsequent chaining computations remain consistent.^[21] As a result, unforgeability is completely broken: a single valid (M, T, IV) triple suffices for the attacker to generate arbitrarily many forgeries for related messages, undermining the MAC's ability to detect tampering.^[22] To mitigate this, implementations must strictly enforce the fixed zero IV as per the original design. For scenarios requiring a nonce or variable input to prevent replay attacks, nonce-based MACs such as GMAC—defined in NIST SP 800-38D and used in authenticated encryption modes like GCM—should be adopted instead.

Predictable Initialization Vector

In CBC-MAC, the standard construction requires a fixed all-zero initialization vector to ensure provable security as a pseudorandom function for messages of fixed length.^[13] Deviations from this, such as employing a constant non-zero IV, can introduce vulnerabilities in certain implementations, particularly if the IV is transmitted alongside the message and tag for verification. For example, the nCipher nCore API prior to version 2.18 transmitted the IV when a non-zero value was used, enabling remote attackers to modify messages while bypassing integrity checks by exploiting the exposed IV.^[23] A related issue arises when implementations use a counter or other predictable value, such as a timestamp, as the IV to provide uniqueness across messages. This predictability allows an attacker to anticipate the IV for a target message and perform offline forgery computations. Specifically, upon observing a valid authentication tuple (IV₁, M₁, tag) where M₁ consists of full blocks, the attacker can predict IV₂, compute the adjusted message M₂ such that each block of M₂ is XORed with the corresponding block of (IV₁ XOR IV₂ padded appropriately), and submit the forged tuple (IV₂, M₂, tag); the verification will succeed because the initial chaining value IV₂ XOR first block of M₂ equals IV₁ XOR first block of M₁, yielding identical subsequent chaining and the same tag.^[24] Such attacks facilitate preimage recovery for valid message-tag pairs through simple XOR operations once the IV is known or predicted, effectively reducing the scheme's resistance to offline computation and chosen-IV forgery. The security degrades from the provable bound of roughly $2^{b/2} (where b is the block size) against distinguishing attacks in the standard fixed-zero IV construction to trivial forgery probability 1, severely compromising message authenticity.^[13] To mitigate these risks, CBC-MAC implementations must strictly use the all-zero IV as specified in standards like FIPS 113. For applications needing nonces or counters to handle variable inputs or replay protection, authenticated encryption modes such as GCM are recommended, as they integrate nonce-based confidentiality and authentication without relying on modifiable IVs in the MAC computation.

Standards and Applications

Defining Standards

The Cipher Block Chaining Message Authentication Code (CBC-MAC) has been formally specified in several cryptographic standards, beginning with early definitions for the Data Encryption Standard (DES) and evolving to support modern block ciphers like the Advanced Encryption Standard (AES) while addressing security limitations for variable-length messages.^[25]^[26] One of the earliest standards is FIPS PUB 113, published by the National Institute of Standards and Technology (NIST) in 1985, which defines a Data Authentication Algorithm (DAA) based on DES operating in CBC mode to produce a MAC of 36 to 64 bits (in multiples of 8) for authenticating data blocks. This standard specifies the use of DES as the underlying block cipher with a 64-bit block size and 56-bit effective key length, allowing variable-length messages grouped into 64-bit blocks, with the final partial block padded with zeros if necessary, and mandates iterative encryption starting from an initialization vector of zero. FIPS 113 emphasizes the algorithm's role in detecting unauthorized modifications in computer data, but it was withdrawn on September 1, 2008, following the deprecation of DES.^[25]^[27] The International Organization for Standardization (ISO) and International Electrotechnical Commission (IEC) formalized CBC-MAC more broadly in ISO/IEC 9797-1:2011, which outlines six MAC algorithms using an n-bit block cipher and a secret key to generate an m-bit MAC, with the first mechanism directly corresponding to standard CBC-MAC. This standard supports block ciphers of various sizes (e.g., 64-bit or 128-bit blocks) and specifies three padding methods—basic (zero-padding), CBC (per ISO 10118-1 with '1' bit followed by zeros), and length prepending—along with optional truncation of the MAC output to reduce length while maintaining security, along with rules for key sizes matching the cipher (e.g., 128 bits for AES). ISO/IEC 9797-1 also includes variants like MAC Algorithm 2 (a modified CBC-MAC with additional processing) to enhance security against certain attacks, and it requires the initialization vector to be zero for deterministic operation.^[28] For AES-based implementations, NIST Special Publication 800-38B (updated in 2016) defines the CMAC mode, a refinement of CBC-MAC that securely accommodates variable-length messages through subkey generation for padding the final block, using AES-128, AES-192, or AES-256 with corresponding key sizes of 128, 192, or 256 bits. As of April 2025, NIST has decided to revise SP 800-38B to update guidance on tag lengths and other aspects.^[29] This standard specifies that the MAC tag can be truncated to any length from 32 to 128 bits, with full 128-bit tags recommended for optimal security, and mandates a zero initialization vector while providing test vectors for verification. Complementing this, RFC 4493 (2006) from the Internet Engineering Task Force (IETF) standardizes AES-CMAC for Internet protocols, aligning with NIST SP 800-38B by detailing the same subkey derivation process (using AES in CBC mode with specific constants) and emphasizing its use for authenticating binary data up to 2^61 - 1 blocks. The transition to CMAC in these standards addresses vulnerabilities in plain CBC-MAC for variable lengths by ensuring distinct tags for distinct messages, without relying on length prepending.^[26]^[9]^[30] In the context of resource-constrained devices, ISO/IEC 29192-6:2019 specifies lightweight MAC algorithms based on block ciphers, including CBC-MAC variants tailored for low-power environments, supporting ciphers with 64-bit or 80-bit blocks and key sizes as small as 80 or 128 bits. This standard outlines padding rules similar to ISO/IEC 9797-1 but optimized for minimal computational overhead, allows tag truncation to 32 bits or more, and requires secure key management to achieve at least 80-bit security levels, making it suitable for Internet of Things applications.^[31]^[32]

Common Implementations

CBC-MAC and its secure variants, such as CMAC, are implemented in prominent cryptographic software libraries to facilitate message authentication in various applications. In OpenSSL, a widely used open-source toolkit, CMAC is supported via the EVP_MAC-CMAC interface, which leverages underlying CBC-mode ciphers like AES-128-CBC for computation.^[33] Raw CBC-MAC can also be derived using functions such as EVP_aes_128_cbc with a fixed zero initialization vector, though this requires careful handling to avoid security pitfalls.^[34] Similarly, the Bouncy Castle library for Java provides the CBCBlockCipherMac class, which constructs a standard MAC from any block cipher in CBC mode, defaulting to zero padding when unspecified.^[35] In hardware implementations, CBC-MAC is integrated into FPGA IP cores, particularly for AES-based authenticated encryption modes like CCM, which employs CBC-MAC for message integrity. Vendors such as Helion Technologies offer configurable AES-CCM cores supporting ASIC and FPGA platforms, enabling efficient deployment in high-throughput environments.^[36] For resource-constrained devices like smart cards, CBC-MAC is utilized in EMV payment standards to generate application cryptograms, ensuring secure transaction authentication during card-reader interactions.^[37] Protocol-level deployments of CBC-MAC variants appear in legacy and specialized contexts. In IPsec, the AES-XCBC-MAC-96 algorithm, a modified CBC-MAC, provides authentication for Encapsulating Security Payload (ESP) and Authentication Header (AH) protocols, as standardized in RFC 3566.^[38] AES-CMAC-96 extends this for broader use in IPsec, offering enhanced security for variable-length messages per RFC 4494.^[39] While modern protocols increasingly favor alternatives like Poly1305 for speed—such as in ChaCha20-Poly1305 authenticated encryption—CBC-MAC persists in embedded systems for its simplicity and low overhead in fixed-block scenarios.^[40] A key challenge in CBC-MAC implementations is performance overhead relative to hash-based alternatives like HMAC, stemming from sequential block cipher invocations that limit parallelism and increase latency in software. Benchmarks indicate HMAC-SHA256 achieves superior efficiency over AES-CBC-MAC, as shown in evaluations for IPsec where HMAC-SHA256 outperforms AES-CBC-MAC.^[41] To mitigate vulnerabilities in variable-length messages, best practices recommend adopting CMAC, a NIST-approved refinement of CBC-MAC that incorporates subkey tweaks for provable security.^[9]

References

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Fast and Secure CBC-Type MAC Algorithms | CSRC
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https://www.iso.org/standard/51304.html
[12]
[PDF] The Security of the Cipher Block Chaining Message Authentication ...
Sep 12, 2001 · Desmedt ed., Springer-Verlag, 1994. The Security of the Cipher Block Chaining. Message Authentication Code. Mihir Bellare*. Joe Kilian†.
[13]
[PDF] Improved Security Analyses for CBC MACs - UCSD CSE
The new bounds translate into improved guarantees on the probability of forging these MACs. Keywords: CBC MAC, message authentication, provable security. ∗Dept.
[14]
[PDF] On the Security of Cipher Block Chaining Message Authentication ...
In this paper we show that Bernstein's proof can be used to prove security of CBC MAC against adversaries querying non-empty messages that are not prefixes of ...
[15]
[PDF] Defeating ISO9797-1 MAC Algo 3 by Combining Side-Channel and ...
This article introduces a new attack on MAC algorithm implementing. ISO/IEC-9797-1 specification. Whereas it concerns only products imple- menting the MAC ...Missing: distinguishing | Show results with:distinguishing<|control11|><|separator|>
[16]
[PDF] CBC MACs for Arbitrary-Length Messages: The Three-Key ...
Dec 3, 2003 · The three-key CBC MAC variants (ECBC, FCBC, XCBC) use three keys to handle arbitrary-length messages, unlike the basic CBC MAC, and avoid ...
[17]
[PDF] Revisiting Structure Graphs: Applications to CBC-MAC and EMAC
Abstract. In Crypto'05, Bellare et al. proved an O(`q2/2n) bound for the PRF (pseudorandom function) security of the CBC-MAC based on.
[18]
Is reusing keys for CBC and CBC-MAC secure when using encrypt ...
Feb 9, 2016 · If you can't and no one else has, then don't assume it's OK (even if you can't think of an attack). ... CBC encryption + CBC MAC reusing key in ...CBC encryption + CBC MAC reusing key in MAC-then-EncryptDoes length prepending fix the key reuse problems with CBC and ...More results from crypto.stackexchange.com
[19]
[PDF] Recommendation for Key Management: Part 1 - General
May 5, 2020 · Key-transport keys are usually used to establish symmetric keys (e.g., key-wrapping keys, data-encryption keys, or MAC keys) and, optionally ...
[20]
[PDF] CBC-MAC 1 Overview 2 Construction of Basic CBC-MAC
Mar 19, 2015 · We now output t1 as a valid tag for message m0 = CCC4E6. Clearly, while calculating. CBC-MAC value of m0, we get intermediate tag value, t3 for ...
[21]
Why I hate CBC-MAC - A Few Thoughts on Cryptographic Engineering
this ...
[22]
https://blog.cryptographyengineering.com/2013/02/15/why-i-hate-cbc-mac/
[23]
None
Below is a merged summary of all the provided segments regarding CBC-MAC, Initialization Vector (IV), and the Security of Random/Variable IV in CBC-MAC. To retain all information in a dense and organized manner, I will use a table in CSV format for key details, followed by a narrative summary that consolidates additional context and notes. This approach ensures comprehensive coverage while maintaining clarity and conciseness.
[24]
FIPS 113, Computer Data Authentication | CSRC
**Summary of CBC-MAC Algorithm in FIPS 113**
[25]
SP 800-38B, Recommendation for Block Cipher Modes of Operation
Oct 6, 2016 · This block cipher-based MAC algorithm, called CMAC, may be used to provide assurance of the authenticity and, hence, the integrity of binary data.
[26]
[PDF] FIPS PUB 113 - NIST Technical Series Publications
May 30, 1985 · The standard specifies a cryptographic authentication algorithm for use in ADP systems and networks. The authentication algorithm makes use of ...
[27]
[PDF] INTERNATIONAL STANDARD ISO/IEC 9797-1
Mar 1, 2011 · The first mechanism specified in this part of ISO/IEC 9797 is commonly known as CBC-MAC (CBC is an abbreviation of Cipher Block Chaining). The ...
[28]
RFC 4493 - The AES-CMAC Algorithm - IETF Datatracker
This memo specifies an authentication algorithm based on CMAC with the 128-bit Advanced Encryption Standard (AES). This new authentication algorithm is named ...
[29]
ISO/IEC 29192-6:2019 - Message authentication codes (MACs)
2–5 day deliveryThis document specifies MAC algorithms suitable for applications requiring lightweight cryptographic mechanisms.
[30]
[PDF] INTERNATIONAL STANDARD ISO/IEC 29192-6
This clause specifies a lightweight MAC algorithm that uses a lightweight hash-function to compute a MAC. ... lightweight hash-functions specified in ISO/IEC ...
[31]
EVP_MAC-CMAC - OpenSSL Documentation
DESCRIPTION. Support for computing CMAC MACs through the EVP_MAC API. This implementation uses EVP_CIPHER functions to get access to the underlying cipher.
[32]
Compute the CBC-MAC with AES-256 and openssl in C
Jul 6, 2017 · The extra block is because OpenSSL adds padding to the plain text, so that it is a multiple of the block size (16 bytes for AES). In this case ...How to choose an AES encryption mode (CBC ECB CTR OCB CFB)?CBC-MAC decryption, how MAC works in encryption - Stack OverflowMore results from stackoverflow.com
[33]
CBCBlockCipherMac (Bouncy Castle Library 1.81 API Specification)
create a standard MAC based on a block cipher with the size of the MAC been given in bits. This class uses CBC mode as the basis for the MAC generation. Note: ...
[34]
AES-CCM core - Xilinx, Altera, Microsemi, Lattice and ASIC
AES-CCM is an authenticated encryption algorithm providing both authentication and privacy, using Counter Mode and CBC-MAC. Helion offers solutions for ASIC, ...
[35]
[PDF] Inducing Authentication Failures to Bypass Credit Card PINs - USENIX
AC = MACS(X||AIP||ATC||IAD), where MAC is a block-cipher-based CBC-MAC using the key S. Note that the signed message in the ...
[36]
RFC 4494: The AES-CMAC-96 Algorithm and Its Use with IPsec
This memo specifies the use of CMAC mode on the authentication mechanism of the IPsec Encapsulating Security Payload (ESP) and the Authentication Header (AH) ...
[37]
[PDF] Message Authentication Codes On Ultra-Low SWaP Devices
May 11, 2022 · An alternative way to construct MACs is to use AES cipher block chaining(CBC), which we mentioned in chapter 2.3. Figure 2.20 describes the ...<|control11|><|separator|>
[38]
Comparison of the performance of Digital Signature and MAC ...
Jun 26, 2023 · HMAC-SHA256 was the most efficient, followed by HMAC-SHA512, ECDSA, CBC-MAC-AES128, and CBC-MAC-AES256. HMAC-SHA256 was most efficient with ...