Discovering private exponent from public key
When using a Discrete Logarithm based scheme, such as SRP, the rule of thumb is to always use private exponents with a bit length twice the desired security strength. Hence, a 128 bit exponent $a$ will at most give you 64 bits of security. If you want 128 bit security, you need (at least) a 256 bit exponent. This is because the algebraic structure of the groups used for such schemes, make it possible to calculate discrete algorithms using a meet-in-the-middle approach that effectively halves the necessary effort, compared to a naive brute force approach.

In this case, for instance, let $q$ be the order of $g$ in $\mathbb Z_N$. Calculate $y = A(g^{q-x2^n}) \bmod N$ for all $0 \le x \lt 2^{128-n}$ and put the pairs $y,x$ in a table for fast access, indexed by the $y$ component. Next calculate $y' = g^z \bmod N$ for all $0 \le z \lt 2^n$. If you find a $y$ in the table such that $y = y'$, then you know that $z = a - x2^n \bmod q$, and hence that $a = z + x2^n$. 

The latter calculations might be carried out in parallel and might be more effectively optimized than the former, so the optimal trade-off might e.g. be to set $n = 80$, meaning you put $2^{48}$ pairs $y,x$ in your table and perform a total of $2^{80}$ parallel calculations $y' = g^z \mod N$. This is feasible using modern hardware.