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Message Authentication Code (MAC) algorithm

Definitions:

A family of cryptographic functions that is parameterized by a symmetric key. Each of the functions can act on input data (called a “message”) of variable length to produce an output value of a specified length. The output value is called the MAC of the input message. An approved MAC algorithm is expected to satisfy the following property (for each of its supported security levels): It must be computationally infeasible to determine the (as yet unseen) MAC of a message without knowledge of the key, even if one has already seen the results of using that key to compute the MAC's of other (different) messages. A MAC algorithm can be used to provide data-origon authenication and data-integrity protection. In this Recommendaton, a MAC algorithm is used for key confirmation; the use of MAC algorithms for key derivation is addressed in SP 800-56C.
Sources:

A family of cryptographic functions that is parameterized by a symmetric key. Each of the functions can act on input data (called a “message”) of variable length to produce an output value of a specified length. The output value is called the MAC of the input message. MAC(k, x, …) is used to denote the MAC of message x computed using the key k (and any additional algorithm-specific parameters). An approved MAC algorithm is expected to satisfy the following property (for each supported security strength):

Without knowledge of the key k, it must be computationally infeasible to predict the (as-yet-unseen) value of MAC(k, x, …) with a probability of success that is a significant improvement over simply guessing either the MAC value or k, even if one has already seen the results of using that same key to compute MAC(k, xj, …) for (a bounded number of) other messages \(x_{j}\neq x\).

A MAC algorithm can be employed to provide authentication of the origin of data and/or to provide data-integrity protection. In this Recommendation, approved MAC algorithms are used to determine families of pseudorandom functions (indexed by the choice of key) that may be employed during key derivation.

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