In "2.3 Analysis" of Izu, Tetsuya et al. “Extending Bleichenbacher's Forgery Attack.” J. Inf. Process. 16 (2008): 122-129 there is a move, which should be obvious, but I keep struggling with it. Could you help me with an explanation!
They use notion that g should be smaller than $2^{2α+β}$ and then move to consider powers using this higher value for LHS of inequality: $2α+β > 576+α+2β−log_2 3$. I understand that it comes from formula given few lines earlier in the article: $g(α, β) = a^2/3 × 2^{α+2β} − a^3/27 × 2^{3β}$, and by comparing the coefficients (and following logic they describe) I come to the conclusion that the first formula from "2.2 Outline of Bleichenbacher’s Attack" is used to construct the inequality (here's this formula: $a = 2^{288} − (T × 2^{160} + H( \bar{m}))$).
But when we put a into the formula for g(α, β) we clearly are not getting something that could be expressed as a power of 2. So how without this condition, without representing g as a power of 2 can we move to comparison of powers leaving out other members of polynomial?
PS It's my first question in Math section, please hint me if there's anything wrong in it.