SPAnosaurus

Description

The MegaSecure company has just released a security update for their servers. After analyzing the update, you notice that the editor now uses this code for exponentiation:

unsigned long exp_by_squaring(unsigned long x, unsigned long n) {
  // n is the secret exponent
  if (n == 0) {
    return 1;
  } else if (n % 2 == 0) {
    return exp_by_squaring(x * x, n / 2);
  } else {
    return x * exp_by_squaring(x * x, (n - 1) / 2);
  }
}

You have access to a server on which you can run as a user exp_by_squaring(2, 2727955623) while measuring its power consumption. The exponent here is therefore n = 2727955623, or 10100010100110010100110010100111 in binary. This consumption trace is saved in user_trace.csv.

You have also managed to measure the energy consumption during exponentiation of an administrator data. This consumption trace is saved in trace_admin.csv. Can you find its secret exponent n?

The flag is in FCSC{1234567890} format with 1234567890 to be replaced by the secret exponent of the administrator written in decimal.