Tags: matrix general_linear_group crypto
Rating:
* A common key cryptosystem is defined by the operations on the general linear group of 6th-degree $GL_6(F_p)$ on $F_p$ ($p$: 512bit)
* $p$ is reset to the random primes per connection.
* $U$ as the secret key, $U\cdot X\cdot U^{-1}$ is encryption and $U^{-1}\cdot X\cdot U$ is depcyption.
* We can encrypt/decrypt any value $X$ with all the elements equals to or less than 256.
* The encrypted flag value is given.
### Solution
* General linear group is obviously linear as its name suggests, so I can retrieve the result of encryption of unit vector for all the elements in the matrix and solve it with linear modular equation.
`zer0pts{r1ng_h0m0m0rph1sm_1s_c00l}`
{%gist hakatashi/de69225d17617a0fd8c75c484d3ca6af %}
