Recently, Smith and Lennon proposed a new public key cryptosystem, called LUC, which uses the Lucas function as the one-way function in their cryptographic mechanisms instead of using the exponentiation function. They conjectured that LUC is cryptographically stronger than RSA in 1993. Since then, many weaknesses of LUC have been discoverd, e. g., similar to RSA, LUC also suffers from the chosen-message attacks and the evaluation in LUC is slightly less efficient than that in RSA. In this paper, we analyze another possible weakness of LUC that was not pointed out before. We show that the number of messages which cannot be concealed in LUC is at least as the same as that in RSA regardless of the choice of public keys. In particular, in many cases, the number of messages which cannot be concealed in LUC is greater than that in RSA. This implies that the choice of public keys in LUC needs more limitations than that used in RSA. Our results are useful to designers who consider to use LUC type systems.

In, Okeya and Sakurai proposed the recovery of the y-coordinate on a Montgomery-form elliptic curve. With their method, it can calculate efficiently coordinates of scalar multiplication of point, in which we need only x-coordinate and finally, (x,y) of the terminal point can be recovered. The method is very suitable for some applications such as ECDSA-V and MQV, etc. Unfortunately, there is a significant fault in that paper. Thus, many results about computation amount are wrong due to the significant fault. First, we will show this fault, and then raise the correction of the significant fault. Finally, Table A1 about comparison of computation amount in is also corrected.

In this paper, two new signature schemes whose security is based on both discrete logarithms and factorization are proposed to enhance the security of the OSS signature scheme. The major benefit of these new signature schemes is that the signer dose not need to know how to factor p-1, thus it is possible for every user to employ the same modulus p, where p is the modulus commonly used in the system. Furthermore, two identification schemes based on this advantage are also developed in this paper.

Many EMD-type data hiding schemes have been proposed. However, the data hiding capacity is less than 2bpp when the embedding procedure uses formula operations. In order to improve the data hiding capacity from 1bpp to 4.5bpp, a new data hiding scheme is proposed in this paper based on a formula using the fully exploiting modification directions method (FEMD). By using our proposed theorem, the secret data can be embedded by formula operations directly without using a lookup matrix. The simulation results and performance analysis show the proposed scheme not only maintains good embedding capacity and stegoimage quality but also solves the overflow problem. It does so without using extra memory resources and performs within a reasonable computing time. The resource usage and capabilities of this scheme are well matched to the constraints and requirements of resource-scarce mobile devices.