This paper proposes a novel tree representation which is suitable for the analysis of RLC (i.e., resistor, inductor, and capacitor) circuits. Genetic programming (GP) based on the tree representation is applied to passive filter synthesis problems. The GP is optimized and then incorporated into an algorithm which can automatically find parsimonious solutions without predetermining the number of the required circuit components. The experimental results show the proposed method is efficient in three aspects. First, the GP-evolved circuits are more parsimonious than those resulting from traditional design methods in many cases. Second, the proposed method is faster than previous work and can effectively generate parsimonious filters of very high order where conventional methods fail. Third, when the component values are restricted to a set of preferred values, the GP method can generate compliant solutions by means of novel circuit topology.

Two algorithms are proposed to improve the Merkle-Hellman knapsack public-key cryptosystem. an approach to transform a superincreasing sequence to a high-density knapsack sequence is proposed. The algorithm is easy to implement and eliminates the redundancy of many knapsack cryptosystems. A linear shift method is used to improve the security of the knapsack public-key cryptosystem. It is shown that several knapsacks (e.g., the so-called useless knapsack), which cannot be generated by using the Merkle-Hellman scheme, can be generated by the linear shift method. Thus A. Shamir's (1982, 1984) attack to the original knapsack, as well as the low-density attack to the iterated knapsack, cannot be applied to this system successfully. It is interesting to note that the concept of the requirement of being one-to-one in practical enciphering keys is not necessary for this system.>