Practical Evaluation of Security against Generalized Interpolation Attack

Interpolation attack was presented by Jakobsen and Knudsen at FSE'97. Interpolation attack is effective against ciphers that have a certain algebraic structure like the PURE cipher which is a prototype cipher, but it is difficult to apply the attack to real-world ciphers. This difficulty is due to the difficulty of deriving a low degree polynomial relation between ciphertexts and plaintexts. In other words, it is difficult to evaluate the security against interpolation attack. This paper generalizes the interpolation attack. The generalization makes easier to evaluate the security against interpolation attack. We call the generalized interpolation attack linear sum attack. We present an algorithm that evaluates the security of byte-oriented ciphers against linear sum attack. Moreover, we show the relationship between linear sum attack and higher order differential attack. In addition, we show the security of CRYPTON, E2, and RIJNDAEL against linear sum attack using the algorithm.

Linearization Method and Linear Complexity

We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N ( 2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.

On a Certain Algebraic Property of Block Ciphers

This is a study on a certain group theoretic property of the set of encryption functions of a block cipher. We have shown how to construct a subset which has this property in a given symmetric group by a computer algebra software GAP4.2 (Groups, Algorithms, and Programming, Version 4.2). These observations on group structures of block ciphers suggest us that we may be able to set a trapdoor based on meet-in-the-middle attack on block ciphers.

Correlation analysis of the structures and stability constants of gadolinium(III) complexes

To simplify the abstraction of descriptors, for the correlation analysis of the stability constants of gadolinium(III) complexes and their ligand structures, aiming at gadolinium(III) complexes, we only considered the ligands and ignored the common parts of the structures, i.e., the metal ions. Quantum-chemical descriptors and topological indices were calculated to describe the structures of the ligands. Multiple regression analysis and neural networks were applied to construct the models between the ligands and the stability constants of gadolinium(III) complexes and satisfactory results were obtained.

Effective descriptions of molecular structures and the quantitative structure - Activity relationship studies

In this research. we found CoMFA alone could not obtain sufficiently a strong equation to allow confident prediction for aminobenzenes. When some other parameter. such as heat of molecular formation of the compounds, was introduced into the CoMFA model, the results Were improved greatly. It gives us a hint that a better description for molecular structures will yield a better prediction model, and this hint challenged us to look for another method-the projection areas of molecules in 3D space for 3D-QSAR. It is surprising that much better results than that obtained by using CoMFA Were achieved. Besides the CoMFA analysis. multiregression analysis and neural network methods for building the models were used in this paper.

Developing molecular identification numbers by an all-paths method

A new topological index is devised from an all-paths method. This molecular topological index has highly discriminating power for various kinds of organic compounds such as alkane trees, complex cyclic or polycyclic graphs, and structures containing heteroatoms and thus can be used as a Molecular IDentification number (MID) for chemical documentation. Some published MIDs derived from an all-paths method and their structural selectivity for alkane trees are also reviewed.

On highly discriminating molecular topological index

A highly discriminating molecular topological index, EAID, is proposed based on the extended adjacency matrix. A systematic search for degeneracy was performed for 3 807 434 alkane trees, 202 558 complex cyclic or polycyclic graphs, and 430 472 structures containing heteroatoms. No counterexamples (two or more nonisomorphic structures with the same EAID number) were found. This is a hitherto unheard of power of discrimination. Thus EAID might be possibly used as supplementary reference for CAS Registry Numbers for structure documentation.

NEW TOPOLOGICAL INDEX AND PREDICTION OF PHASE-TRANSFER ENERGY FOR PROTONATED AMINES AND TETRAALKYLAMINES IONS

The applications of new topological indices A(x1)-A(x3) suggested in our laboratory for the prediction of Gibbs energy values of phase transfer (water to nitrobenzene) of amine ions are described with satisfactory results. Multiple regression analysis and neural network were employed simultaneously in this study.

ON HALL AND KIERS TOPOLOGICAL STATE AND TOTAL TOPOLOGICAL INDEX

The topological state and the total topological index, tau, have been tested systematically. Counterexamples are provided proving that the topological state method cannot determine classes of symmetrically equivalent atoms in a molecule fully correct. The

EXTENDED ADJACENCY MATRIX INDEXES AND THEIR APPLICATIONS

In this paper, new topological indices, EA Sigma and EAmax, are introduced. They are based on the extended adjacency matrices of molecules, in which the influences of factors of heteroatoms and multiple bonds were considered. The results show that EA Sigm

A NEW SCHEME FOR ASSIGNMENT OF A CANONICAL CONNECTION TABLE

A new algorithm for deriving canonical numbering of atoms in a molecular graph has been developed. Some graph invariants, such as node properties, degree (connectivity), topological path, the smallest node ring index, etc., are encoded together to partit

STUDY ON STRUCTURE-ACTIVITY-RELATIONSHIPS OF ORGANIC-COMPOUNDS - 3 NEW TOPOLOGICAL INDEXES AND THEIR APPLICATIONS

In this paper, three new topological indices, A(x1), A(x2), and A(x3), have been developed for use in multivariate analysis in structure-property relationship (SPR) and structure-activity relationship (SAR) studies. Good results have been obtained by using them to predict the physical and chemical properties and biological activities of some organic compounds.

AN EXPERT SYSTEM FOR SOLVENT-EXTRACTION OF RARE-EARTHS

An expert system for solvent extraction of rare earths has been developed using LISP. The goal of this project was to mimic the chemists' inferential abilities to assist in the process of solvent extraction of rare earths. The system includes frequently used extractants, separation of specific rare earths, recommendation of procedures for the separation of mixtures of rare earths using (2-ethylhexyl)phosphonic acid 2-ethylhexyl monoester, selection of parameters for counter-current extraction and methods for evaluation of the technique, and the economics of the processing. The expert system runs on an IBM-PC/XT.

CIAC COMPREHENSIVE INFORMATION-SYSTEM OF RARE-EARTHS

The CIAC (Changchun Institute of Applied Chemistry) Comprehensive information System of Rare Earths is composed of three subsystems, namely, extraction data, physicochemical properties, and reference data. This paper describes the databases pertaining to the extraction of rare earths and their physicochemical properties and discusses the relationships between data retrieval and optimization and between the structures of the extractants and the efficiency with which they are extracted. Expert systems for rare earth extraction and calculation of thermodynamic parameters are described, and an application of pattern recognition to the problems of classification of compounds of the rare earths and prediction of their properties is reported.