This document describes two cryptographic functions used in GCM authentication and encryption: (1) GHASHH, which is a hash-based message authentication code that hashes multiple inputs X1 through Xm together to produce a single output Ym; and (2) GCTRK, which is a counter-mode encryption function that encrypts an initial counter block ICB and inputs X1 through Xn using a key K to produce outputs Y1 through Yn.

1. Figure 12.10 GCM Authentication and Encryption Functions
(a) GHASHH(X1 || X2 || . . . || Xm) = Ym
(b) GCTRK(ICB, X1 || X2 || . . . || Xn) = Yn
X1
X1
X2
ICB
Xm
Y1
Y1
Y2 Ym
H
E
inc
H H
K
X2
CB2
Y2
EK
Xn–1
CBn–1
Yn–1
E
inc
K
Xn
CBn
Yn
E
MSB
K
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