Abstract

In 1985 Neal Koblitz and V.S. Miller proposed elliptic curves to be used for public key cryptosystems, whereas RSA, a nowadays widely used public key cryptosystem, was developed by Rivest, Shamir, and Adleman almost ten years earlier in 1977. The elliptic curve cryptosystem benefits from smaller key sizes than RSA, which makes its cryptographic operations, encryption, decryption, signing, and signature verification faster than RSA's operations. A smart card is a single-chip microcomputer with a size of 25 mm² at most. Today smart cards are used mainly for electronic identification and storing user information. Smart cards are also used to store private keys and to execute cryptographic operations which use private keys. This Master's thesis examines whether elliptic curve cryptography is better suited to be used on smart cards than the nowadays widely used RSA. It describes the elliptic curve cryptography and RSA implementations used to compare these two cryptosystems, and presents performance comparisons based on these implementations. In addition, this thesis contains security and space requirement comparisons between these two cryptosystems. According to the test results, signing and decryption operations are faster with the elliptic curve cryptosystem than with RSA, but RSA is faster when encrypting messages or verifying signatures. On the other hand, the elliptic curve cryptosystem needs less space to store the private keys than RSA, and is thus well suited to be used on smart cards. The elliptic curve cryptosystem has the disadvantage that the Menezes-Vanstone encryption increases the size of encrypted messages considerably more than RSA encryption does. In addition, because an elliptic curve cryptosystem implementation is more complicated and requires deeper mathematical understanding than an RSA implementation, it is more susceptible to errors which diminishes its security.

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