In this paper, we describe a technique for optimizing the algebraic method that is applied to higher order differential attack. The higher order differential attack is a well-known attack on block ciphers, in which we derive an attack equation to determine a round key from a property of a higher order differential of a target block cipher. The algebraic method is a linearization of the attack equation and determines the true key by a method such as Gaussian elimination. Our technique is based on linear dependency and can reduce the complexity of that method. We also describe a technique that allows the algebraic method to be used as an attack equation that holds probabilistically. We demonstrate this method by attacking a five-round MISTY1 and show that it needs 221.6 chosen plaintexts and 228.0 encryption times. The computer simulation took about two minutes to complete.

There have been few studies on formal approaches to the specification and realization of asynchronous sequential circuits. For synchronous sequential circuits, an algebraic method is proposed as one of such approaches, but it cannot be applied to asynchronous ones directly. This paper describes an algebraic method of specifying the abstract behavior of asynchronous sequential circuits. We select an daisy chain arbiter as an example of them. In the arbiter, state transitions are caused by input changes, and all the modules do not always make state transitions simultaneously. These are main obstacles to specify it in the same way as sychronous sequential circuits. In order to remove them, we modify the meaning of input in specifications and introduce pseudo state transitions so that we can regard all the modules as if they make state transitions simultaneously. This method can be applied to most of the other asynchronous sequential circuits.

In this paper, we propose a method to simulate the curve surface of the initial height in the movement of the electronic wire bonder using the experimental data. For given measured data (xk, yk, zk (k=1, 2, , m)), we propose an algebraic surface of n-th degree as a methematical model of the initial height surface. The AIC method is a method of evaluating the goodness of a given model. The maximum likelihood model is selected by comparing with the AIC value of each model for n=0, 1, 2, 3, , 11. Useing this model, the initial raise position of the electronic wire bonder can be controlled by computer programing and can make the movement of wire bonder full-automatic. As a resurt, the well-arranged wiring and reliable contacting can be obtained.