Abstract: A system comprises at least, two parts, connected to each other by the means of a common communication interface wherein a first communicating apparatus A, having data processing means, communication means, memory means and random or pseudo-random generation means relies of the computational power of a second communicating apparatus B having data processing means, communication means and memory means in order to compute the inverse of a first number x modulo a second number n and use the resulting modular inverse in an encryption, decryption, key exchange, identification or digital signature cryptographic protocol.