Suppose I intercept the same message m sent to 2 friends. I know what the message is and I know the used modulus n, as well as the ciphertexts but I don't know the respective public exponents. I.e. my system of equations is:
- $c_1 = m^{e_1} \ mod \ n$
- $c_2 = m^{e_2} \ mod \ n$
Is there a way to retrieve the public exponents, without using bruteforce?
A practical example:
- $n = 221$
- $m = 127$
- $c_1 = 155$
- $c_2 = 43$