# Write-up

## Note about bsc

If you try to compile stuff using a different build of bsc, it will complain about mismatch of standard library files:

```
The package `Dut' was compiled using a different version of the file
`Prelude.bo' than what was found in the path.
Please recompile the affected packages in dependency order or with -u.
```

So we just use the supplied container. It may be useful to call bsc ourselves with custom command line options.

One can build the container without the entry point by commenting out the `ENTRYPOINT` line in the [Dockerfile](Dockerfile), then:

```
docker build -t ip-protection .
```

## Dump the bytecode

In the [bsc](https://github.com/B-Lang-org/bsc) repository at GitHub, one can read:

> Additional flags of use to developers can be displayed with the following command:
>
> `$ bsc -help-hidden`

Amongst lots of undocumented options:

```
Dump/kill after various passes:
[...]
-dinternal
-dbinary
-dfixup
[...]
```

If you try to use the `-dbinary` option, you realize it dumps the bytecode. You could also find this option by studying bsc's source code at GitHub.

```
docker run --rm ip-protection bsc -dbinary -verilog -cpp -Xcpp -DLICENSE_KEY=123 Tb.bs
```

## Analyze the bytecode

Looking for the string `"invalid license key"` at the dump, one finds the relevant excerpts of code:

```
let p :: Prelude.Integer
p =
0xFC497367DE3520436E844080242730ACAF44F16C31AD45070F6E28455A2DA126F1242008E5D29624A0F47B2D28E9963A7CBFA75D
-- IdProp: p[IdP_keep]
in let q :: Prelude.Integer
q =
0xC68F4A48226124EB1D0FDDDCEACEC20253FDAD180D63BEB0057508A08ACF60EAF63E62FD6727C582A085D4227410364E4E755205
-- IdProp: q[IdP_keep]
in let c1 :: Prelude.Integer
c1 =
0x6138C614261B2F71D9DC990CD6865F8A178994094349A7C4ED286D8D23E2862674C0589763725CDF1A08EF1DFBC89E703066A73C
-- IdProp: c1[IdP_keep]
in let c2 :: Prelude.Integer
c2 =
0x8AD2F15273E7933543E6761E3EA030650890F3233113D1DD04F43A30798A4EFFC8A7A3F9F05CC9290FC990841A9198423642C7EF
-- IdProp: c2[IdP_keep]

[...]

(PrimIf
(_m__ Prelude.PrimUnit)
(PrimBNot
(PrimIntegerEQ (PrimIntegerRem (PrimIntegerAdd q (PrimIntegerMul k c2)) p) 2))
(.Prelude.bind _m__ _tcdict1546
Prelude.PrimUnit
Prelude.PrimUnit
(Prelude.bind_=
_m__
Prelude.Empty
Prelude.PrimUnit
_tcdict1546
(Prelude.setStateName=
_m__
_c__
Prelude.Empty
_tcdict1001
Prelude.primGetName
(Prelude.addRules=
_m__
_c__
_tcdict1001
(PrimAddSchedPragmas
_
(PrimRule
"violation"
_
(PrimOrd
Prelude.Bool
1
(Prelude.True (PrimBuildUndefined Prelude.PrimUnit _ 1)))
(Prelude.toPrimAction=
Prelude.PrimUnit
(Prelude.bind_=
Prelude.ActionValue
Prelude.PrimUnit
Prelude.PrimUnit
Prelude.Prelude.Monad~Prelude.ActionValue=
(Prelude.fromPrimAction=
Prelude.PrimUnit
(Prelude.$display "invalid license key"))
(Prelude.$finish= (PrimIntegerToBit 2 1))))))))
```

So the message is printed whenever `(PrimBNot (PrimIntegerEQ (PrimIntegerRem (PrimIntegerAdd q (PrimIntegerMul k c2)) p) 2))` or, in alternate syntax, whenever `(q + k*c2) % p != 2`.

## Solving the equation

We can solve this equation by inverting `c2`, e.g. using Python with gmpy2:

```python
In [1]: import gmpy2

In [2]: p=0xFC497367DE3520436E844080242730ACAF44F16C31AD45070F6E28455A2DA126F1242008E5D29624A0F47B2D28E9963A7CBFA75D
...:

In [3]: q=0xC68F4A48226124EB1D0FDDDCEACEC20253FDAD180D63BEB0057508A08ACF60EAF63E62FD6727C582A085D4227410364E4E755205
...:

In [4]: c2=0x8AD2F15273E7933543E6761E3EA030650890F3233113D1DD04F43A30798A4EFFC8A7A3F9F05CC9290FC990841A9198423642C7EF
...:

In [5]: ((2-q)*gmpy2.invert(c2,p))%p
Out[5]: mpz(2900588852888817522482663339711888485418294656850552706711080114546549830073)
```

or just throw it at some CAS.

## Getting the flag

Now that you have the license key, just run the container's original entry point to print the flag.

```
$ docker run --rm ip-protection ./entrypoint.sh 2900588852888817522482663339711888485418294656850552706711080114546549830073
bsc -verilog -cpp -Xcpp -DLICENSE_KEY=2900588852888817522482663339711888485418294656850552706711080114546549830073 Tb.bs
Verilog file created: mkTb.v
bsc -verilog -e mkTb -o tb
Verilog binary file created: tb
./tb
CTF-BR{HW_1p_Pr073cT1on_1S_$3Cur1ty_By_oBscUr4n71Sm}
```

Original writeup (https://github.com/pwn2winctf/challenges-2020/blob/master/rev-ip-protection/writeup.md).