Optimizing lifetime of a wireless sensor network has received considerable attention in recent years. In this paper, using the feasibility and simplicity of grid-based clustering and routing schemes, we investigate optimizing lifetime of a two-dimensional wireless sensor network. Thus how to determine the optimal grid sizes in order to prolong network lifetime becomes an important problem. At first, we propose a model for lifetime of a grid in equal-grid model. We also consider that nodes can transfer packets to a grid which is two or more grids away in order to investigate the trade-off between traffic and transmission energy consumption. After developing the model for an adjustable-grid scenario, in order to optimize lifetime of the network, we derive the optimal values for dimensions of the grids. The results show that if radio ranges are adjusted appropriately, the network lifetime in adjustable-grid model is prolonged compared with the best case where an equal-grid model is used.

The security of permutation-based hash functions in the ideal permutation model has been studied when the input-length of compression function is larger than the input-length of the permutation function. In this paper, we consider permutation based compression functions that have input lengths shorter than that of the permutation. Under this assumption, we propose a permutation based compression function and prove its security with respect to collision and (second) preimage attacks in the ideal permutation model. The proposed compression function can be seen as a generalization of the compression function of MD6 hash function.

Information theoretic security is an important security notion in cryptography as it provides a true lower bound for attack complexities. However, in practice attacks often have a higher cost than the information theoretic bound. In this paper we study the relationship between information theoretic attack costs and real costs. We show that in the information theoretic model, many well-known and commonly used hash functions such as MD5 and SHA-256 fail to be preimage resistant.