Many different cryptography solutions are there to protect computers and networks, but since more mobile devices are Internet capable and are being used for day to day computing there is a need for new and more efficient algorithms. The modern cryptography can be divided into two main branches: - Symmetric Cryptography, where the same key is used to encrypt a message and decrypt data. - Asymmetric cryptography, where two different keys are used for encryption and decryption. Asymmetric cryptography is much more complicated and much slower than the symmetric cryptography but it addresses the main concern of symmetric cryptography i.e. key exchange. It allows secure communication over insecure channel like Internet. This work compares the two asymmetric algorithms RSA and ECC and investigates if ECC is more suitable (e.g. faster and power-efficient) for mobile devices than RSA.