## TL;DRWe're given a binary with all protections enabled (notably PIE and full RELRO) that allows us to do basic arithmetic in integer mode using mmx registers and floating point mode using x87 registers. The main trick is that on modern x64 processors, mmx registers maps the 64 lsb of the x87 80bit registers. In particular, this program uses mm7 as a pointer to load and save mmx values. We have full control on mm7 by storing carefully crafted floating point numbers and we leverage that for arbitrary read/write.
## interface & mechanisms### menu```Welcome to the frog math calculation facilityHere we provide state of the art processors for fp and integer math0) exit1) floating point2) integer>```### floating point mode```fp processing0) finish1) push2) pop3) add4) sub5) mul6) div7) inspect> ```x87 registers work as a stack, you can push values and the two top values are used for operations. You can also print the top value as a float and as an int using `inspect`.When you push a value on the fp stack, `st0` always holds the top of the stack. This means that each time you push or pop, you move around the values of the x87 registers that are on this stack.
### integer mode```integer processor0) finish1) set2) get3) add4) sub5) mul6) div7) load8) save9) clear> ```- `load` loads `mm0-mm6` from the buffer on the heap pointed to by `mm7`, then frees and sets `mm7` to `null`.- `save` saves `mm0-mm6` to the buffer on the heap pointed to by `mm7` or if `null`, allocates a new buffer
Note that the program logic prevents us from directly setting/getting or doing any operation on mm7 in integer mode
### Confusing quirkOperations on the mmx registers after pushing floating point values moves back the floating point stack in a circular fashion so that if you set say register `mm0` in integer mode then push a floating point, then switching back to int mode and `get(0)` wont get you the floating point you just pushed but the actual value you set for `mm0` beforehand. However, switching back to floating point won't switch the stack back ! To get a better grasp of this, it's better to see for yourself in gdb (use the `i r f` command to print x87 registers). It is the reason why we cannot store an integer in `mm7`, from setting `mm6` and then pushing a dummy float on the stack. We have to instead rely on setting `st` registers in floating point mode.
## Heap leakSince PIE is enabled, we have to start from a leak to somewhere. Luckily it is quite straight forward to leak `mm7`.- Push 7 values (`mm7` needs to be null to avoid crash when saving so pushing only 0s gaurantees that)- Save mmx registers (`mm7` now holds a heap pointer)- Pop 7 times (the stack is now empty so `st0` holds the pointer first stored in `mm7`)- Inspect, which will print the pointer
## Setting mm7Assuming the fp stack is empty, you push the desired value on the fp stack then switch back to int mode and do any integer operation. Because of the stack rolling back in a circular fashion, `mm7` will now hold the value you pushed. 
Easy right ? *NO !!!*
Info on floating point representation : - [x87 floats](https://en.wikipedia.org/wiki/Extended_precision#x86_extended_precision_format)- [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754)
`mm7` corresponds to the mantissa of `st7` and the mantissa must almost always start with a msb of 1 which is problematic to store addresses since they have 2 most significant null bytes (the exponent will be decreased, and the mantissa will be shifted to the left and not correspond anymore to our address). It took me a while to find a trick to accomodate for that. In fact, [subnormal numbers](https://en.wikipedia.org/wiki/Subnormal_number), which have an exponent of 1 (but stored as 0), can have leading null most significant bits without being equal to 0. So to store value v in mm7 we need to craft a subnormal number whose mantissa is v.
The cherry on top is that classic floats from python are not precise enough to compute subnormal numbers in extended precision floating points. I thus used the library [mp-math](https://mpmath.org/) to do the computations
## The *easy* partWith a heap leak and full control of `mm7`,  there's arbitrary write and read thanks to the `load` and `store` operations from integer mode.From there I got a libc leak from crafting and freeing a fake chunk in unsorted bin range (`size > 0x410`), then loading from this chunk (which contains a head pointer into libc)From the libc leak I leaked environ which is a stack pointer at constant offset from stack frames, and from there it's just classic return to system to pop a shell.
Note that since `load` calls `free` after loading `mm0-mm6`, a valid chunk containing the values we want to leak is required to avoid a crash. Thus, I crafted a 0x40 sized chunk near environ (just set the chunk size to something in tcache range 8 bytes above environ, and make sure the chunk is aligned since they are no additional checks when freeing to tcache).
## Flag```$ python3 exp3.py [*] '/home/skuuk/ama23/chal3'    Arch:     amd64-64-little    RELRO:    Full RELRO    Stack:    Canary found    NX:       NX enabled    PIE:      PIE enabled[*] '/usr/lib/x86_64-linux-gnu/libc.so.6'    Arch:     amd64-64-little    RELRO:    Partial RELRO    Stack:    Canary found    NX:       NX enabled    PIE:      PIE enabledMpmath settings:  mp.prec = 200               [default: 53]  mp.dps = 59                 [default: 15]  mp.trap_complex = False     [default: False][+] Opening connection to amt.rs on port 31171: Done[*] heap : 0x55a6e6ae6000[*] libc : 0x7f6f1ab56000[*] env : 0x7ffd045b8e88[*] Loaded 218 cached gadgets for '/usr/lib/x86_64-linux-gnu/libc.so.6'[*] Switching to interactive mode$ cat flag.txtamateurctf{n3v3r_m1x_x87_and_mmx_t0g3th3r}```