Useful Sage documentation link about the syntax for matrices. We are given a somewhat similar to a Diffie-Hellman key-exchange, a secret $s$ is picked out, then $H = G * s$ is calculated. They also generate a random vector $v$ in the matrix space. The product of $H \times v = w$ is calculated. Given the two vectors $v, w$, we have to derive the value of the secret $s$ to obtain the decryption key....
Short and sweet challenge. The script has one fatal flaw when doing Diffie-Hellman: 1 2 3 4 5 def generate_public_int(g, a, p): return g ^ a % p def generate_shared_secret(A, b, p): return A ^ b % p g ^ b % p is equivalent to g ^ (b % p), and ^ is binary xor in Python, not pow. Hence, we can easily retrieve Bob’s secret my doing B ^ g, as B = g ^ (b % p), and b < p, which leads to b % p = b....
This is weirdly RSA, but in a “matrix” context. To decrypt message in RSA, we need to calculate $m = c ^ d \mod p$, where $d = e ^ {-1} \mod \phi(n)$. $\phi(n)$ is the multiplicative order of the group. In this challenge, we are under some group of matrix with size 50x50, or in math notations, $GF(50, GF(2))$ and not under $\mod n$. Thus, $d = e ^ {-1} \mod |G|$, where $|G|$ is the order of the group $GF(50, GF(2))$....