The cryptographic library provides functions to create and verify digital signatures. Currently the library is available on both Unix and PalmOS platforms. The library provides the Nyberg-Rueppel version of elliptic curve signatures [11] and the SHA1 message digest function.
The implementation of elliptic curve cryptography is based on the algorithms for fast operations in finite fields. [17] that has been tuned to fit the limited processor and memory resources on small personal computers. The current implementation uses a finite field of order GF(136) with fast operations on elements in a subfield of order GF(8). The order of the fixed point on the curve is a 241 bit prime number. This yields Nyberg-Rueppel scheme digital signatures with a total length of 256 bits for both components of the signatures.
The security of the elliptic-curve signature scheme relies on the difficulty of finding discrete logarithms in finite fields. With the current field size and chosen curve parameters the security of the system is estimated to be of similar strength to 1024 bits RSA signatures. Digital signature schemes based on elliptic curves show not only promising results with respect to performance, but also when it comes to strength per bit and memory utilization [8].