CBC MACs for arbitrary-length messages : The three-key constructions

• Published in: Journal of cryptology Vol. 18; no. 2; pp. 111 - 131
• Main Authors: BLACK, John, ROGAWAY, Phillip
• Format: Journal Article
• Language: English
• Published: New York, NY Springer 01-04-2005; Springer Nature B.V
• Subjects: Algorithms; Applied sciences; Cryptography; Encryption; Exact sciences and technology; Information, signal and communications theory; Messages; Permutations; Signal and communications theory; Telecommunications and information theory; Access control; CBC MAC; Private key; Block ciphering; Security of data; Message authentication codes; Provable security; Modes of operation; Message authentication; Standards
• ISSN: 0933-2790; 1432-1378
• DOI: 10.1007/s00145-004-0016-3

We suggest some simple variants of the CBC MAC that enable the efficient authentication of arbitrary-length messages. Our constructions use three keys, K1, K2, K3, to avoid unnecessary padding and MAC any message M ∈ {0,1}* using max{1, ⌈ |M|/n⌉} applications of the underlying n-bit block cipher. Our favorite construction, XCBC, works like this: if |M| is a positive multiple of n then XOR the n-bit key K2 with the last block of M and compute the CBC MAC keyed with K1; otherwise, extend M’s length to the next multiple of n by appending minimal 10ℓ padding (ℓ ≥ 0), XOR the n-bit key K3 with the last block of the padded message, and compute the CBC MAC keyed with K1. We prove the security of this and other constructions, giving concrete bounds on an adversary’s inability to forge in terms of his inability to distinguish the block cipher from a random permutation. Our analysis exploits new ideas which simplify proofs compared with prior work.