AES as Integer Program I read that AES can be broken by solving a Linear Integer Program (IP).


From a given encrypted text, how can one construct this IP?
How big is the system?
First I find the question legitimate and trying to evaluate the complexity is not an easy problem. But regarding how it looks like, I would mention beforehand that AES or any other crypto algorithm could be written in many different ways. 

See for example https://www.iacr.org/archive/asiacrypt2002/25010159/25010159.ps

BTW any crypto function appears like a map $\{0,1\}^n \times \{0,1\}^m \longrightarrow \;\{0,1\}^n$, with appropriate identification of message and key spaces. We then can mathematically modelize with the theory of boolean functions.

For a chosen m-bit key; $y_i=f_{k,i}(x_1,\cdots,x_n)=\sum_{(u_1,\cdots,u_n)}a_u.x_1^{u_1}\cdots x_n^{u_n}=\sum_u.a_ux^u$, with a compact representation where $u=(u_1,\cdots,u_n)$ and $u_i \in \{-1,0,+1\}$, and $u_i^{-1}=1-u_i$ represents the ONE-complement of the bit $u_i$.

This representation by the boolean function is to indicate the complexity of for synthetisation of a crypto algorithm (even in hardware we can easily build a circuit dedicated to DES, AES or even PKC).
The reduction methods employed in logic design analysis (KARNAUGH, QUEEN_McCLUSKEY,...) are generally limited to a restricted number of variables.
However, boolean functions is an active field of research in cryptography and attacks. See for example how Linear and Differantial cryptanalysis manage the question.

I hope this gives a general idea of this interesting question.