16.3 GCM performance
There is an old saying among cryptographers that the real challenge is not to design a secure algorithm, but one that is secure and fast. While this is typically said somewhat jokingly, there is a lot to this saying. Take, for instance, ciphers. It is well known that the composition of functions illustrated in Figure 16.2 can be used to define complicated functions using simpler ones.
Recall that if f : X → Y and g : Y → Z are functions, then the composition of g with f, denoted by g ∘f, is a function mapping elements of X to elements of Z. Moreover, the composition can be extended to any number of functions f1,f2,…,fn (resulting in the composition fn ∘…∘f2 ∘f1) given that the domain of ft equals the co-domain of ft−1.
Figure 16.2: Composition g ∘ f of functions g and f
In cryptography, ciphers combining a sequence of simpler transformations are called product ciphers. So, based on...
