Bit Security for Lucas-Based One-Way Function

In 1993, Smith and Lennon described a new public key cryptosystem based on a Lucas sequences, called Lucas cryptosystem (LUC). Its construction is similar to RSA, but its computing faster and using smaller key size than RSA with the same security strength. In this paper, we presented a new hardcore predicate of LUC and proved its security by the list decoding method developed by Akavia et al.