Hitoshi Yanami

The Block Cipher SC2000

In this paper, we propose a new symmetric key block cipher SC2000 with 128-bit block length and 128-,192-,256- bit key lengths. The block cipher is constructed by piling two layers: one is a Feistel structure layer and the other is an SPN structure layer. Each operation used in two layers is S-box or logical operation, which has been well studied about security. It is a strong feature of the cipher that the fast software implementations are available by using the techniques of putting together S-boxes in various ways and of the Bitslice implementation.

Development of SyNRAC—Formula Description and New Functions

In this paper we present newly developed functions in Maple-package SyNRAC, for solving real algebraic constraints derived from various engineering problems. The current version of SyNRAC provides quantifier elimination (QE) for the quadratic case and an environment dealing with first-order formulas over the reals (including new simplifiers of formulas) on Maple.

Solving and visualizing nonlinear parametric constraints in control based on quantifier elimination: A MATLAB toolbox for parametric control system design

We present a new method with a software tool for parametric robust control synthesis by symbolic-numeric computation. The method is a parameter space approach and it is especially effective for analysis and design of fixed-structure controllers of rational type, which encompass PI and PID controllers. The real quantifier elimination (QE), which is one of the recent progresses in the symbolic computation, plays a key role in our development. The QE-based approach can uniformly deal with a lot of important design specifications for robust control such as frequency restricted H∞ norm constraints, stability (gain/phase) margin and stability radius specifications, and pole location requirement by reducing such specifications to a particular type of formulae called a “sign definite condition (SDC)”. This is also useful for improving the efficiency of QE computations since we can utilize an efficient QE algorithm specialized to the SDC using the Sturm-Habicht sequence. We have developed a MATLAB toolbox for robust parametric control based on a parameter space approach accomplished by QE. The QE-based parameter space approach and numerical simulation of performances for specific controller parameter values taken from a controller parameter space are integrated conveniently in our toolbox with the assistance of a graphical user interface (GUI). With our toolbox the feasible regions of controller parameters are visualized in a parameter space for the controllers with three or two parameters. This enables control engineers to achieve multi-objective robust controller synthesis smoothly. We also discuss how to merge the numerical computation and the symbolic operation to make our new design methods more efficient in practical control design.

SyNRAC: a maple toolbox for solving real algebraic constraints

We introduce various aspects of design and implementation of a symbolic computation toolbox, called SyNRAC, handling first-order formulas on top of Maple. SyNRAC provides us with a new set of tools for solving real algebraic constraints derived from a broad range of applications in science and engineering.

Differential and Linear Cryptanalysis of a Reduced-Round SC2000

We analyze the security of the SC2000 block cipher against both differential and linear attacks. SC2000 is a six-and-a-half-round block cipher, which has a unique structure that includes both the Feistel and Substitution-Permutation Network (SPN) structures. Taking the structure of SC2000 into account, we investigate one- and two-round iterative differential and linear characteristics. We present two-round iterative differential characteristics with probability 2-58 and two-round iterative linear characteristics with probability 2-56. These characteristics, which we obtained through a search, allowed us to attack four-and-a-half-round SC2000 in the 128-bit user-key case. Our differential attack needs 2103 pairs of chosen plaintexts and 220 memory accesses and our linear attack needs 2115.17 known plaintexts and 242.32 memory accesses, or 2104.32 known plaintexts and 283.32 memory accesses.

SyNRAC: A Toolbox for Solving Real Algebraic Constraints

We introduce various aspects of the design and the implementation of a symbolic/symbolic-numeric computation toolbox, called SyNRAC. SyNRAC is a package of commands written in the Maple language and the C language. This package indeed provides an environment for dealing with first-order formulas over the reals.

Development of a MATLAB toolbox for parametric robust control - new algorithms and functions -

Recently there has been an increasing interest in the application of computer algebra to control system analysis and design. Control system design is to find out feasible parameters to be designed for which a target system satisfies given control design specifications. Many important control system design problems are regarded as parametric and non-convex optimization problems. We have been developing a MATLAB toolbox for robust control via a parameter space approach based on symbolic-numeric computation. First we explain how we can practically solve such control system design problems by using algebraic methods, quantifier elimination. Then we show an effective visualization of the results i.e. the feasible regions of design parameters in a parameter space. All these results are implemented as the MATLAB toolbox for parametric robust control. We also demonstrate our MATLAB toolbox by using actual control design problems

An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for optimization problems

With many applications in engineering and in scientific fields, quantifier elimination (QE) has been attracting more attention these days. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. We propose an effective symbolic-numeric cylindrical algebraic decomposition (SNCAD) algorithm for solving polynomial optimization problems. The main ideas are a bounded CAD construction approach and utilization of sign information. The bounded CAD constructs CAD only in restricted admissible regions to remove redundant projection factors and avoid lifting cells where truth values are constant over the region. By utilization of sign information we can avoid symbolic computation in the lifting phase. Techniques for implementation are also presented. These techniques help reduce the computing time. We have examined our implementation by solving many example problems. Experimental results show that our implementation significantly improves efficiency compared to our previous work.

A Symbolic-Numeric Approach to Multi-Objective Optimization in Manufacturing Design

Some important classes of optimization problems originating from the optimal design of semiconductor memories such as SRAM, aiming at boosting the yield rate, are studied. New optimization methods for the classes based on a symbolic algorithm called quantifier elimination, combined with numerical computation, are proposed. The total efficiency of the design process is improved by reducing the number of numerical yield-rate evaluations. In addition, useful information such as the explicit relations among design variables, objective functions, and the yield rate, is provided.

Policy gradient reinforcement learning method for discrete-time linear quadratic regulation problem using estimated state value function

In this paper, we propose a policy gradient reinforcement learning method which directly estimates the gradient of the state value function (V-function) with respect to a feedback coefficient matrix using measurable data and uses it for policy improvement. The proposed method can be applicable to the case where the state-action value function (Q-function) is difficult to estimate, and can update the policy in an effective direction for reducing the accumulated cost.