Hyperelliptic curves encryption combined with block codes for Gaussian channel

In this paper, a new cryptographic system is constructed using a combination of a hyperelliptic curve of genus g 1⁄4 2 over the Galois field GF(2) and a Reed–Solomon code (N, K) over the Galois field GF(2) and this system uses a smaller key than the elliptic curves cryptosystem and the Rivest, Shamir, and Adleman cryptosystem. The design criterion for the combination can be expressed as the data compression condition and addressing capability of the code. In addition, the system performance is compared with other systems; extraordinary improvements of 8 and 16.5 dB can be obtained for a BER=10 , when compared with binary phase shift keying and differential chaos shift keying, respectively. This system has a polynomial complexity, which depends on data length and the number of operations in GF(2). Copyright # 2005 John Wiley & Sons, Ltd.