GCM security bounds reconsidered

Abstract

A constant of 222 appears in the security bounds of the Galois/Counter Mode of Operation, GCM. In this paper, we first develop an algorithm to generate nonces that have a high counter-collision probability. We show concrete examples of nonces with the counter-collision probability of about 220.75/2128. This shows that the constant in the security bounds, 222, cannot be made smaller than 219.74 if the proof relies on “the sum bound.” We next show that it is possible to avoid using the sum bound, leading to improved security bounds of GCM. One of our improvements shows that the constant of 222 can be reduced to 32.